Vehicle system vibration suppression control device and vibration suppression control method

Abstract

A vehicle system vibration suppression control device is provided for a vehicle system in which a vehicle is driven via an elastic shaft by a motor drive device having a torque control function. The vehicle system vibration suppression control device includes: a section containing an approximate model to which an output torque command is inputted; and a feedback control section. The feedback control section is configured to: employ the approximate model; calculate a motor-accelerating torque component by differentiating a measured speed component of a motor rotational speed; produce a compensation torque component by causing the motor-accelerating torque component to pass through a vibration suppression control filter; and calculate the output torque command by subtracting the compensation torque component from an input torque command. The vibration suppression control filter is expressed by a second order mathematical expression.

Claims

1. A vehicle system vibration suppression control device for a vehicle system in which a vehicle is driven via an elastic shaft by a motor drive device having a torque control function, the vehicle system vibration suppression control device comprising: at least one controller configured to: contain an approximate model to which an output torque command (T.sub.m) is inputted; calculate a motor-accelerating torque component (T.sub.mA*) by differentiating a measured speed component (?.sub.m) of a motor rotational speed; produce a compensation torque component (T.sub.Fcomp) by causing the motor-accelerating torque component (T.sub.mA*) to pass through a vibration suppression control filter (F.sub.comp(s)); calculate the output torque command (T.sub.m) by subtracting the compensation torque component (T.sub.Fcomp) from an input torque command (T.sub.ref); and instruct the motor drive device to generate a motor torque corresponding to the calculated output torque command (T.sub.m); wherein the vibration suppression control filter (F.sub.comp(s)) is expressed by a mathematical expression (13), $\begin{array}{cc}{F}_{\mathrm{comp}}\left(s\right)=\frac{2.Math.\left({?}_A-{?}_r\right).Math.{?}_r.Math.s}{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}& \left(13\right)\end{array}$ where s: a Laplace operator, ?.sub.r=?(K.sub.d.Math.(1/TJ.sub.m+1/TJ.sub.wM), ?.sub.a=?(K.sub.d.Math.(1/TJ.sub.wM)), ?.sub.r=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.r), ?.sub.a=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.a), ?.sub.A: an adjustable parameter, D.sub.s=TJ.sub.M/(TJ.sub.w+TJ.sub.M).Math.K.sub.t, TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of multiple driving wheels), TJ.sub.M: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline, K.sub.t: a coefficient relating to friction between tire and road surface, and TJ.sub.wM=TJ.sub.w+TJ.sub.M.

2. The vehicle system vibration suppression control device as claimed in claim 1, comprising a disturbance torque observer, wherein: the approximate model includes: a subtractor configured to subtract an estimated disturbance torque ({circumflex over ()}T.sub.obs), which is calculated by the disturbance torque observer, and a shaft torsional torque ({circumflex over ()}T.sub.d) from the output torque command (T.sub.m) to output an estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA); a block configured to calculate a motor side acceleration by dividing the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a time constant equivalent to motor rotational inertia; a block configured to calculate a vehicle body side acceleration by dividing the shaft torsional torque ({circumflex over ()}T.sub.d) by a combined rotational inertia of a vehicle body and tires; a block configured to calculate a relative speed between the motor and the vehicle body by time-integrating a difference between the motor side acceleration and the vehicle body side acceleration; a block configured to calculate a tire slip speed by multiplying the shaft torsional torque ({circumflex over ()}T.sub.d) by a slip coefficient ({circumflex over ()}D.sub.s); and a block configured to calculate the shaft torsional torque ({circumflex over ()}T.sub.d) by transforming a difference between the tire slip speed and the relative speed between the motor and the vehicle body into a torsional phase of the elastic shaft by time integration, and multiplying the torsional phase of the elastic shaft by a torsional stiffness coefficient ({circumflex over ()}K.sub.d) of driveline; wherein the disturbance torque observer is configured to: integrate with the time constant equivalent to motor rotational inertia a deviation between the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) and the motor-accelerating torque component (T.sub.mA*) calculated by differentiating the measured speed component (?.sub.m) of the motor rotational speed to produce an integrated quantity; calculate the estimated disturbance torque ({circumflex over ()}T.sub.obs) by multiplying the integrated quantity by an observer gain (K.sub.g); and input the estimated disturbance torque ({circumflex over ()}T.sub.obs) to the subtractor.

3. The vehicle system vibration suppression control device as claimed in claim 2, wherein the motor-accelerating torque component (T.sub.mA*) is replaced with the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) for input to the vibration suppression control filter (F.sub.comp(s)).

4. The vehicle system vibration suppression control device as claimed in claim 3, comprising a delay compensator configured to delay the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) for time matching between the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) and the measured speed component of the motor rotational speed.

5. The vehicle system vibration suppression control device as claimed in claim 4, comprising a low-pass filter configured to delay the deviation between the motor-accelerating torque component (T.sub.mA*) and the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA).

6. The vehicle system vibration suppression control device as claimed in claim 3, comprising: a first multiplier configured to multiply the motor-accelerating torque component (T.sub.mA*) by a variable weighting factor; a second multiplier configured to multiply the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a variable weighting factor; and an adder configured to sum outputs of the first and second multipliers; wherein an output of the adder is inputted to the vibration suppression control filter (F.sub.comp(S)).

7. The vehicle system vibration suppression control device as claimed in claim 4, comprising: a first multiplier configured to multiply the motor-accelerating torque component (T.sub.mA*) by a variable weighting factor; a second multiplier configured to multiply the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a variable weighting factor; and an adder configured to sum outputs of the first and second multipliers; wherein an output of the adder is inputted to the vibration suppression control filter (F.sub.comp(S)).

8. The vehicle system vibration suppression control device as claimed in claim 5, comprising: a first multiplier configured to multiply the motor-accelerating torque component (T.sub.mA*) by a variable weighting factor; a second multiplier configured to multiply the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a variable weighting factor; and an adder configured to sum outputs of the first and second multipliers; wherein an output of the adder is inputted to the vibration suppression control filter (F.sub.comp(S)).

9. A vehicle system vibration suppression control device for a vehicle system in which a vehicle is driven via an elastic shaft by a motor drive device having a torque control function, the vehicle system vibration suppression control device comprising: a disturbance torque observer configured to: calculate a measured motor rotational speed (?.sub.m_det) based on a measured value of a motor rotational phase and a measured value of time; determine an estimated motor rotational speed ({circumflex over ()}?.sub.m) by a vehicle model to which an output torque command (T.sub.m) is inputted; determine a first quantity ({circumflex over ()}?.sub.m_dly) by delaying the estimated motor rotational speed ({circumflex over ()}?.sub.m) by a time equal to an overall delay time including a speed measurement side delay time; and determine an estimated disturbance torque ({circumflex over ()}T.sub.obs) based on a deviation between the measured motor rotational speed (?.sub.m_det) and the first quantity ({circumflex over ()}?.sub.m_dly); and a feedback control section configured to: produce a torque command (T.sub.ref_LPF) by causing an input torque command (T.sub.ref) to pass through a prefilter; produce a compensation torque component (?T.sub.comp) by causing an estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) to pass through a vibration suppression control filter, wherein the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) is calculated by the vehicle model; calculate the output torque command (T.sub.m) by subtracting the compensation torque component (?T.sub.comp) from the torque command (T.sub.ref_LPF); and instruct the motor drive device to generate a motor torque corresponding to the calculated output torque command (T.sub.m); wherein the disturbance torque observer is a first block based on a sampled-data system model and configured to: receive input of a second quantity ({circumflex over ()}T.sub.m) calculated by subtracting the estimated disturbance torque ({circumflex over ()}T.sub.obs) from the output torque command (T.sub.m); and calculate the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) based on the second quantity ({circumflex over ()}T.sub.m); wherein the disturbance torque observer includes: a second block or a {circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block; wherein the second block includes a subtractor configured to subtract a shaft torsional torque ({circumflex over ()}T.sub.d) from the second quantity ({circumflex over ()}T.sub.m) to output the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA); wherein the second block is configured to: calculate the estimated motor rotational speed ({circumflex over ()}?.sub.m) by approximately integrating the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA); calculate a vehicle speed ({circumflex over ()}?.sub.Wm) by approximately integrating the shaft torsional torque ({circumflex over ()}T.sub.d); calculate a tire slip speed by multiplying the shaft torsional torque ({circumflex over ()}T.sub.d) by a slip coefficient ({circumflex over ()}D.sub.s); calculate a shaft torsional speed ({circumflex over ()}?.sub.d) by subtracting the vehicle speed ({circumflex over ()}?.sub.Wm) and the tire slip speed from the estimated motor rotational speed ({circumflex over ()}?.sub.m); produce a third quantity by approximately integrating a product of the shaft torsional speed ({circumflex over ()}?.sub.d) and an integral coefficient ({circumflex over ()}K.sub.d.Math.T.sub.c); produce the shaft torsional torque ({circumflex over ()}T.sub.d) by causing the third quantity to pass through a delayer; wherein the {circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block is composed of a second order filter having a coefficient designed based on a second order transfer function expressed by a mathematical expression (12), $\begin{array}{cc}{G}_{\mathrm{pTmA}2}\left(s\right)=\frac{s^2+\left(K_d.Math.D_s\right).Math.s+K_d.Math.\frac{1}{{\mathrm{TJ}}_{\mathrm{wM}}}}{s^2+\left(K_d.Math.D_s.Math.s\right)+K_d.Math.\left(\frac{1}{{\mathrm{TJ}}_m}+\frac{1}{{\mathrm{TJ}}_{\mathrm{wM}}}\right)}=\frac{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}{s^2+2.Math.{?}_r.Math.{?}_r.Math.s+{?}_r^2}& \left(12\right)\end{array}$ where s: a Laplace operator, ?.sub.r=?(K.sub.d.Math.(1/TJ.sub.m+1/TJ.sub.wM), ?.sub.a=?(K.sub.d.Math.(1/TJ.sub.wM)), ?.sub.r=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.r), ?.sub.a=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.a), D.sub.s=TJ.sub.M/(TJ.sub.w+TJ.sub.M).Math.K.sub.t, TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of multiple driving wheels), TJ.sub.M: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline, K.sub.t: a coefficient related to friction between tire and road surface, and TJ.sub.wM=TJ.sub.w+TJ.sub.M; wherein the disturbance torque observer further includes: a gain multiplier configured to multiply the deviation between the first quantity ({circumflex over ()}?.sub.m_dly) and the measured motor rotational speed (?.sub.m_det) by an observer gain (K.sub.g); and a delayer configured to delay an output of the gain multiplier to produce the estimated disturbance torque ({circumflex over ()}T.sub.obs); wherein the deviation between the measured motor rotational speed (?.sub.m_det) and the estimated motor rotational speed ({circumflex over ()}?.sub.m) is determined by first, second, or third sampled data system model calculation; wherein the first sampled data system model calculation is configured to: calculate the measured motor rotational speed (?.sub.m_det) by dividing a phase difference from a past sampled value of the motor rotational phase by a time difference; produce the first quantity ({circumflex over ()}?.sub.m_dly) by delaying the estimated motor rotational speed ({circumflex over ()}?.sub.m) by a delay block; and calculate the deviation between the measured motor rotational speed (?.sub.m_det) and the first quantity ({circumflex over ()}?.sub.m_dly); wherein the second sampled data system model calculation is configured to: calculate the measured motor rotational speed (?.sub.m_det) by dividing a phase difference from a past sampled value of the motor rotational phase by a constant sampling period; produce the first quantity ({circumflex over ()}?.sub.m_dly) by delaying the estimated motor rotational speed ({circumflex over ()}?.sub.m) by a delay block; and calculate the deviation between the measured motor rotational speed (?.sub.m_det) and the first quantity ({circumflex over ()}?.sub.m_dly); wherein the third sampled data system model calculation is configured to: calculate the measured motor rotational speed (?.sub.m_det) by dividing an input signal from an integrating part of a sampled data system first-order delay filter by a sampling period (Tc), wherein the sampled data system first-order delay filter is configured to process a measured value of the motor rotational phase; produce the first quantity ({circumflex over ()}?.sub.m_dly) by delaying the estimated motor rotational speed ({circumflex over ()}?.sub.m) by a delay block having a first-order delay filter identical in coefficient to the sampled data system first-order delay filter; and calculate the deviation between the measured motor rotational speed (?.sub.m_det) and the first quantity ({circumflex over ()}?.sub.m_dly); and wherein the vibration suppression control filter (F.sub.comp(s)) is expressed by a mathematical expression (13), $\begin{array}{cc}{F}_{comp}\left(s\right)=\frac{2.Math.\left({?}_A-{?}_r\right).Math.{?}_r.Math.s}{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}& \left(13\right)\end{array}$ where s: a Laplace operator, ?.sub.r=?(K.sub.d.Math.(1/TJ.sub.m+1/TJ.sub.wM), ?.sub.a=?(K.sub.d.Math.(1/TJ.sub.wM)), ?.sub.r=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.r), ?.sub.a=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.a), ?.sub.A: an adjustable parameter, D.sub.s=TJ.sub.M/(TJ.sub.w+TJ.sub.M).Math.K.sub.t, TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of multiple driving wheels), TJ.sub.M: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline, K.sub.t: a coefficient relating to friction between tire and road surface, and TJ.sub.wM=TJ.sub.w+TJ.sub.M.

10. A vehicle system vibration suppression control device for a vehicle system in which a vehicle is driven via an elastic shaft by a motor drive device having a torque control function, the vehicle system vibration suppression control device comprising: a disturbance torque observer configured to: calculate a measured motor rotational speed (?.sub.m_det) based on a measured value of a motor rotational phase and a measured value of time; and determine an estimated disturbance torque ({circumflex over ()}T.sub.obs) based on a time differential component (T.sub.mA_det) of the measured motor rotational speed (?.sub.m_det) and an output torque command (T.sub.m); and a feedback control section configured to: produce a torque command (T.sub.ref_LPF) by causing an input torque command (T.sub.ref) to pass through a prefilter; produce a compensation torque component (?T.sub.comp) by causing an estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) to pass through a vibration suppression control filter, wherein the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) is calculated by a model of the vehicle; calculate the output torque command (T.sub.m) by subtracting the compensation torque component (?T.sub.comp) from the torque command (T.sub.ref_LPF); and instruct the motor drive device to generate a motor torque corresponding to the calculated output torque command (T.sub.m); wherein the disturbance torque observer is a first block based on a sampled-data system model and configured to: receive input of a second quantity ({circumflex over ()}T.sub.m) calculated by subtracting the estimated disturbance torque ({circumflex over ()}T.sub.obs) from the output torque command (T.sub.m); and calculate the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) based on the second quantity ({circumflex over ()}T.sub.m); wherein the disturbance torque observer includes: a second block or a {circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block; wherein the second block includes a subtractor configured to subtract a shaft torsional torque ({circumflex over ()}T.sub.d) from the second quantity ({circumflex over ()}T.sub.m) to output the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA); wherein the second block is configured to: calculate a first quantity by subtracting a product of the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) and an integral coefficient (T.sub.c/{circumflex over ()}TJ.sub.m) from a product of the shaft torsional torque ({circumflex over ()}T.sub.d) and an integral coefficient (T.sub.c/{circumflex over ()}TJ.sub.wM); calculate a third quantity by first approximate integration of the first quantity; calculate a tire slip speed by multiplying the shaft torsional torque ({circumflex over ()}T.sub.d) by a slip coefficient ({circumflex over ()}D.sub.s); calculate a shaft torsional speed ({circumflex over ()}?.sub.d) by subtracting the tire slip speed from the third quantity; produce a fourth quantity by second approximate integration of a product of the shaft torsional speed ({circumflex over ()}?.sub.d) and an integral coefficient ({circumflex over ()}K.sub.d.Math.T.sub.c); produce the shaft torsional torque ({circumflex over ()}T.sub.d) by causing the fourth quantity to pass through a delayer; wherein the {circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block is composed of a second order filter having a coefficient designed based on a second order transfer function expressed by a mathematical expression (12), $\begin{array}{cc}{G}_{\mathrm{pTmA}2}\left(s\right)=\frac{s^2+\left(K_d.Math.D_s\right).Math.s+K_d.Math.\begin{array}{c}1\\ {\mathrm{TJ}}_{\mathrm{wM}}\end{array}}{s^2+\left(K_d.Math.D_s.Math.s\right)+K_d.Math.\left(\frac{1}{{\mathrm{TJ}}_m}+\frac{1}{{\mathrm{TJ}}_{\mathrm{wM}}}\right)}=\frac{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}{s^2+2.Math.{?}_r.Math.{?}_r.Math.s+{?}_r^2}& \left(12\right)\end{array}$ wherein the disturbance torque observer further includes: an integrator configured to integrate a deviation component ({circumflex over ()}T.sub.mA_dly) between a fifth quantity ({circumflex over ()}T.sub.mA_dly) and the time differential component (T.sub.mA_det), wherein the fifth quantity ({circumflex over ()}T.sub.mA_dly) is produced by delaying the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA); a gain multiplier configured to multiply an output of the integrator by an observer gain (K.sub.g); and a delayer configured to delay an output of the gain multiplier to produce the estimated disturbance torque ({circumflex over ()}T.sub.obs); wherein the deviation (?T.sub.mA_det) is determined by first, second, or third sampled data system model calculation; wherein the first sampled data system model calculation is configured to: calculate the measured motor rotational speed (?.sub.m_det) by dividing a phase difference from a past sampled value of the motor rotational phase by a time difference; produce a sixth quantity by delaying the measured motor rotational speed (?.sub.m_det); calculate the time differential component ({circumflex over ()}T.sub.mA_det) by differentiating the sixth quantity with a coefficient (TJ.sub.m/Tc); produce the fifth quantity ({circumflex over ()}T.sub.mA_dly) by delaying the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a delay block; and calculate the deviation between the time differential component ({circumflex over ()}T.sub.mA_det) and the fifth quantity ({circumflex over ()}T.sub.mA_dly); wherein the second sampled data system model calculation is configured to: calculate the measured motor rotational speed (?.sub.m_det) by dividing a phase difference from a past sampled value of the motor rotational phase by a constant sampling period; produce a sixth quantity by delaying the measured motor rotational speed (?.sub.m_det); calculate the time differential component ({circumflex over ()}T.sub.mA_det) by differentiating the sixth quantity with a coefficient (TJ.sub.m/Tc); produce the fifth quantity ({circumflex over ()}T.sub.mA_dly) by delaying the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a delay block; and calculate the deviation between the time differential component ({circumflex over ()}T.sub.mA_det) and the fifth quantity ({circumflex over ()}T.sub.mA_dly); wherein the third sampled data system model calculation is configured to: determine the time differential component ({circumflex over ()}T.sub.mA_det) as an input signal from an integrating part of a sampled data system first-order delay filter, wherein the sampled data system first-order delay filter is configured to process the measured motor rotational speed (?.sub.m_det) produced by differentiating a measured value of the motor rotational phase; produce the fifth quantity ({circumflex over ()}T.sub.mA_dly) by delaying the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA) by a delay block having a first-order delay filter identical in coefficient to the sampled data system first-order delay filter; and calculate the deviation between the time differential component ({circumflex over ()}T.sub.mA_det) and the fifth quantity ({circumflex over ()}T.sub.mA_dly); and wherein the vibration suppression control filter (F.sub.comp(S)) is expressed by a mathematical expression (13), $\begin{array}{cc}{F}_{comp}\left(s\right)=\frac{2.Math.\left({?}_A-{?}_r\right).Math.{?}_r.Math.s}{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}& \left(13\right)\end{array}$ where s: a Laplace operator, ?.sub.r=?(K.sub.d.Math.(1/TJ.sub.m+1/TJ.sub.wM), ?.sub.a=?(K.sub.d.Math.(1/TJ.sub.wM)), ?.sub.r=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.r), ?.sub.a=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.a), ?.sub.A: an adjustable parameter, D.sub.s=TJ.sub.M/(TJ.sub.w+TJ.sub.M).Math.K.sub.t, TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of multiple driving wheels), TJ.sub.M: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline, K.sub.t: a coefficient relating to friction between tire and road surface, and TJ.sub.wM=TJ.sub.w+TJ.sub.M.

11. The vehicle system vibration suppression control device as claimed in claim 9, comprising: a backlash period detection section configured to detect a backlash period; a compensation torque subtractor configured to subtract the compensation torque component (?T.sub.comp) from the torque command (T.sub.ref_LPF) to output the output torque command (T.sub.m), wherein the torque command (T.sub.ref_LPF) is produced by causing the input torque command (T.sub.ref) to pass through the prefilter to suppress a high frequency band; first and second torque limiters configured to limit the output torque command (T.sub.m) outputted from the compensation torque subtractor, wherein the first torque limiter has a first torque limit value, and wherein the second torque limiter has a second torque limit value smaller than the first torque limit value; a switch configured to select one of an output of the first torque limiter and an output of the second torque limiter, and when the backlash period detection section detects the backlash period, select the output of the second torque limiter; and an adder configured to calculate a first sum of the output of one of the torque limiters selected by the switch and the compensation torque component (?T.sub.comp), and feed the first sum back to the prefilter; wherein the backlash period detection section includes: a torque-to-phase transformation section configured to receive input of the shaft torsional torque ({circumflex over ()}T.sub.d) estimated, which is a difference between the second quantity ({circumflex over ()}T.sub.m) and the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA), and transform the estimated shaft torsional torque ({circumflex over ()}T.sub.d) into an estimated shaft torsional phase ({circumflex over ()}?.sub.d); a backlash start timing detection section configured to detect a zero cross point of the estimated shaft torsional phase ({circumflex over ()}?.sub.d) as a start timing of the backlash period; a torsional speed estimation section configured to estimate the shaft torsional speed by time-differentiating the estimated shaft torsional phase ({circumflex over ()}?.sub.d); a speed change estimation section configured to estimate a speed change component during the backlash period by time-integrating the output torque command (T.sub.m); a torsional displacement estimation section configured to calculate an estimated phase change amount ({circumflex over ()}??.sub.BL) corresponding to backlash by: calculating a second sum of the shaft torsional speed, which is estimated by the torsional speed estimation section, an initial torsional speed, which is stored at the start timing of the backlash period detected by the backlash start timing detection section, and the speed change component during the backlash period, which is estimated by the speed change estimation section; and time-integrating the second sum; and a backlash end detection section configured to detect an end of the backlash period by comparing the phase change amount ({circumflex over ()}??.sub.BL), which is estimated by the torsional displacement estimation section, with an absolute value of backlash phase width ({circumflex over ()}?.sub.d) and a margin width (??) as set values; and wherein the backlash period is detected based on the backlash start timing detected by the backlash start timing detection section and the backlash end signal detected by the backlash end detection section.

12. The vehicle system vibration suppression control device as claimed in claim 10, comprising: a backlash period detection section configured to detect a backlash period; a compensation torque subtractor configured to subtract the compensation torque component (?Tcomp) from the torque command (T.sub.ref_LPF) to output the output torque command (T.sub.m), wherein the torque command (T.sub.ref_LPF) is produced by causing the input torque command (T.sub.ref) to pass through the prefilter to suppress a high frequency band; first and second torque limiters configured to limit the output torque command (T.sub.m) outputted from the compensation torque subtractor, wherein the first torque limiter has a first torque limit value, and wherein the second torque limiter has a second torque limit value smaller than the first torque limit value; a switch configured to select one of an output of the first torque limiter and an output of the second torque limiter, and when the backlash period detection section detects the backlash period, select the output of the second torque limiter; and an adder configured to calculate a first sum of the output of one of the torque limiters selected by the switch and the compensation torque component (?T.sub.comp), and feed the first sum back to the prefilter; wherein the backlash period detection section includes: a torque-to-phase transformation section configured to receive input of the shaft torsional torque ({circumflex over ()}T.sub.d) estimated, which is a difference between the second quantity ({circumflex over ()}T.sub.m) and the estimated motor-accelerating torque component ({circumflex over ()}T.sub.mA), and transform the estimated shaft torsional torque ({circumflex over ()}T.sub.d) into an estimated shaft torsional phase ({circumflex over ()}?.sub.d); a backlash start timing detection section configured to detect a zero cross point of the estimated shaft torsional phase ({circumflex over ()}?.sub.d) as a start timing of the backlash period; a torsional speed estimation section configured to estimate the shaft torsional speed by time-differentiating the estimated shaft torsional phase ({circumflex over ()}?.sub.d); a speed change estimation section configured to estimate a speed change component during the backlash period by time-integrating the output torque command (T.sub.m); a torsional displacement estimation section configured to calculate an estimated phase change amount ({circumflex over ()}??.sub.BL) corresponding to backlash by: calculating a second sum of the shaft torsional speed, which is estimated by the torsional speed estimation section, an initial torsional speed, which is stored at the start timing of the backlash period detected by the backlash start timing detection section, and the speed change component during the backlash period, which is estimated by the speed change estimation section; and time-integrating the second sum; and a backlash end detection section configured to detect an end of the backlash period by comparing the phase change amount ({circumflex over ()}??.sub.BL), which is estimated by the torsional displacement estimation section, with an absolute value of backlash phase width ({circumflex over ()}?.sub.d) and a margin width (??) as set values; and wherein the backlash period is detected based on the backlash start timing detected by the backlash start timing detection section and the backlash end signal detected by the backlash end detection section.

13. The vehicle system vibration suppression control device as claimed in claim 11, wherein the estimated shaft torsional torque ({circumflex over ()}T.sub.d) is replaced with the output torque command (T.sub.m) for input to the torque-to-phase transformation section.

14. The vehicle system vibration suppression control device as claimed in claim 12, wherein the estimated shaft torsional torque ({circumflex over ()}T.sub.d) is replaced with the output torque command (T.sub.m) for input to the torque-to-phase transformation section.

15. A vehicle system vibration suppression control method comprising operating the vehicle system vibration suppression control device as claimed in claim 1.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a block diagram showing a normalized control model of a vehicle system to which the present invention is applied.

(2) FIG. 2 is a block diagram showing a simplified control model according to an embodiment of the present invention.

(3) FIG. 3 is a block diagram showing an approximate model according to an embodiment of the present invention.

(4) FIG. 4 is a block diagram showing a feedback section and an approximate transfer function of a vibration suppression control device according to a first embodiment of the present invention.

(5) FIG. 5 is a block diagram showing a general system of disturbance torque observer.

(6) FIG. 6 is a block diagram showing a disturbance torque observer according to a second embodiment of the present invention.

(7) FIG. 7 is a block diagram showing a vibration suppression control device according to the second embodiment of the present invention.

(8) FIG. 8 is a block diagram showing a vibration suppression control device according to a third embodiment of the present invention.

(9) FIG. 9 is a block diagram showing a vibration suppression control device according to an example of a fourth embodiment of the present invention.

(10) FIG. 10 is a block diagram showing a vibration suppression control device according to another example of the fourth embodiment of the present invention.

(11) FIG. 11 is a block diagram showing a vibration suppression control device according to a fifth embodiment of the present invention.

(12) FIG. 12 is a block diagram showing a simulated plant model for verification.

(13) FIG. 13 is a block diagram showing a simulation model for verification of effects of a vibration suppression control employing a disturbance torque observer.

(14) FIG. 14 is an explanatory diagram showing a pattern of an input torque command and a load disturbance used for simulation.

(15) FIG. 15 is a Bode diagram of a conventional high order (third order) model and a second order approximate model used in the first embodiment.

(16) FIG. 16 is an explanatory diagram showing a result of simulation where no vibration suppression control is performed.

(17) FIG. 17 is an explanatory diagram showing a result of simulation where the first embodiment of the present invention is employed.

(18) FIG. 18 is an explanatory diagram showing a result of simulation where the first embodiment of the present invention is employed and the influence of gear backlash components is taken into account.

(19) FIG. 19 is an explanatory diagram showing a result of simulation where tire slip is taken into account in addition to the condition of FIG. 18.

(20) FIG. 20 is an explanatory diagram showing a result of simulation where the third embodiment of the present invention is employed.

(21) FIG. 21 is an explanatory diagram showing a result of simulation where the third embodiment of the present invention is employed and the influence of gear backlash components is taken into consideration.

(22) FIG. 22 is an explanatory diagram showing a result of simulation where tire slip is taken into account in addition to the condition of FIG. 21.

(23) FIG. 23 is an explanatory diagram of a result of simulation where the third embodiment of the present invention is employed, the influence of gear backlash components is taken into consideration, and a delay time in electric current control and speed measurement is simulated and added as LPF1.

(24) FIG. 24 is an explanatory diagram showing a result of simulation where the fourth embodiment of the present invention is employed, and a delay time on the approximate model side and a delay time on the speed measurement side are matched with each other.

(25) FIG. 25 is a block diagram showing a vehicle model where a disturbance torque component is taken into account.

(26) FIG. 26 is a block diagram showing a vehicle model produced by reducing the order of the vehicle model of FIG.

(27) FIG. 27 is a block diagram showing a vibration suppression control device according to a sixth embodiment of the present invention.

(28) FIG. 28 is a block diagram showing a sampled data system to which the vibration suppression control device of FIG. 27 is transformed.

(29) FIG. 29 is a block diagram showing a continuous data system model of a vehicle model section in a disturbance torque observer according to the sixth embodiment of the present invention.

(30) FIG. 30 is a block diagram showing an example of the sampled data system model of the vehicle model section in the disturbance torque observer according to the sixth embodiment of the present invention.

(31) FIG. 31 is a block diagram showing another example of the sampled data system model of the vehicle model section in the disturbance torque observer according to the sixth embodiment of the present invention.

(32) FIG. 32 is a block diagram showing a method of calculation of a difference between a measured speed and an estimated speed of the disturbance torque observer according to the sixth embodiment of the present invention.

(33) FIG. 33 is a diagram showing an example of moving average calculation according to the sixth embodiment of the present invention, where (a) is a block diagram, and (b) is a time chart illustrating time matching by moving averaging.

(34) FIG. 34 is a block diagram showing a vibration suppression control device according to a seventh embodiment of the present invention.

(35) FIG. 35 is a block diagram showing an example of a sampled data system model of a vehicle model section in a disturbance torque observer according to the seventh embodiment of the present invention, where (a) shows an example of configuration, and (b) shows another example of configuration.

(36) FIG. 36 is a block diagram showing a method of calculation of a difference between a measured speed and an estimated speed of the disturbance torque observer according to the seventh embodiment of the present invention.

(37) FIG. 37 is a block diagram showing a vibration suppression control device according to eighth and ninth embodiments of the present invention.

(38) FIG. 38 is a block diagram showing a backlash period detection section shown in FIG. 37.

(39) FIG. 39 is a diagram showing characteristics of acceleration/deceleration when no vibration suppression control is employed.

(40) FIG. 40 is a diagram showing characteristics of acceleration/deceleration when the sixth embodiment of the present invention is employed and no backlash is assumed in an actual vehicle.

(41) FIG. 41 is a diagram showing characteristics of acceleration/deceleration when the seventh embodiment of the present invention is employed and no backlash is assumed in the actual vehicle.

(42) FIG. 42 is a diagram showing characteristics of acceleration/deceleration when the seventh embodiment of the present invention is employed and backlash is assumed in the actual vehicle.

(43) FIG. 43 is a diagram showing characteristics of acceleration/deceleration when the eighth embodiment of the present invention is employed and backlash is assumed in the actual vehicle.

(44) FIG. 44 is a diagram showing characteristics of acceleration/deceleration, showing behavior of a function of estimating a backlash period, when the eighth embodiment of the present invention is employed.

(45) FIG. 45 is a diagram showing characteristics of acceleration/deceleration when the ninth embodiment of the present invention is employed and backlash is assumed in the actual vehicle.

(46) FIG. 46 is a diagram showing characteristics of acceleration/deceleration, showing behavior of a function of estimating a backlash period, when the ninth embodiment of the present invention is employed.

MODE(S) FOR CARRYING OUT INVENTION

(47) The following describes embodiments of the present invention with reference to the drawings. The present invention is not limited to the following embodiments, but may be implemented in various manners. In patent document 1, a model of a vehicle is defined by a mathematical expression. When expressed as a block diagram and a transfer function using a Laplace operator, the model is expressed by G.sub.p(S) in FIG. 1.

(48) Basically, the vehicle model is the same as in FIG. 4 of patent document 1. However, a model becomes complicated due to factors such as gear ratios, a tire radius, etc. Therefore, a general concept of a per-unit system is used to transform the vehicle model to a normalized model based on a rated torque and a rated rotational speed. As a result, the unit system is unified, so that gear ratios, a tire radius, etc., do not appear explicitly, and the control block diagram is simplified. Although description of terms, per-unit system and normalization, is omitted, the rotational inertia of a motor and the inertia of a vehicle body are each replaced by a time constant until the rated speed is reached after the rated torque is inputted. By introducing the time constants, it becomes possible to quantitatively compare a plurality of inertial components with each other, and use the time constants for judgment about approximation.

(49) Variables and constants in FIG. 1 are defined as follows. TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of driving wheels), TJ.sub.m: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline, K.sub.t: a coefficient relating to friction between tire and road surface, ?.sub.m: a motor angular speed, ?.sub.w: a driving wheel angular speed, ?.sub.m: a vehicle speed, T.sub.m: a motor torque, T.sub.d: a driving wheel torque, T.sub.t: a torque between tire and road surface, and T.sub.F: an external force applied to vehicle (disturbance torque component).

(50) In the above description, T is used for variables relating to torque, and TJ is used for time constants produced by conversion from rotational inertias, in order to avoid confusion between torques and time constants.

(51) For description of a control system, an actual plant and a model used in a control section are described. This may be likely to cause confusion between them. Therefore, for distinguishing a coefficient or variable relating to the control model, a symbol {circumflex over ()} is added to the beginning of the coefficient or variable, in second and following embodiments.

(52) Integral blocks are represented by transfer functions in mathematical expression (1), where s is the Laplace operator.

(53) $\begin{array}{cc}{G}_d\left(s\right)=\frac{K_d}{s},G_m\left(s\right)=\frac{1}{T{J}_m.Math.s},G_w\left(s\right)=\frac{1}{{\mathrm{TJ}}_w.Math.s},G_M\left(s\right)=\frac{1}{{\mathrm{TJ}}_M.Math.s}& \left(1\right)\end{array}$

(54) A subtractor 11 subtracts the driving wheel torque T.sub.d from the motor torque (output torque command) T.sub.m to output the motor torque (motor-accelerating torque) T.sub.mA.

(55) A G.sub.m(s) block 12 multiplies the output of the subtractor 11 by a transfer function G.sub.m(s) to output the motor angular speed ?.sub.m. A subtractor 13 subtracts the driving wheel angular speed ?.sub.w from the motor angular speed ?.sub.m. A G.sub.d(s) block 14 multiplies the output of the subtractor 13 by a transfer function G.sub.d(s) to output the driving wheel torque T.sub.d.

(56) A subtractor 15 subtracts the torque Tt between tires and a road surface from the driving wheel torque T.sub.d. A G.sub.w(s) block 16 multiplies the output of the subtractor 15 by a transfer function G.sub.w(s) to output the driving wheel angular speed ?.sub.w. A subtractor 17 subtracts the vehicle speed ?.sub.M from the driving wheel angular speed ?.sub.w. A K.sub.t block 18 multiplies the output of the subtractor 17 by a coefficient K.sub.t relating to friction between the tires and the road surface, and outputs the torque T.sub.t between the tires and the road surface. A subtractor 19 subtracts the external force (disturbance torque component) T.sub.F applied to the vehicle from the torque T.sub.t between the tire and the road surface. A G.sub.M(s) block 20 multiplies the output of the subtractor 19 by a transfer function G.sub.M(s) to output the vehicle speed ?.sub.M.

(57) The subtractors 15, 17, 19 and blocks 16, 18, 20 are defined as a transfer function G.sub.TdWw(s).

(58) The configuration of FIG. 1 is a multi-stage feedback configuration. Accordingly, as the disturbance component T.sub.F is ignored and the blocks are developed in order from the bottom, this model system is expressed by transfer functions of mathematical expressions (2) and (3).

(59) Namely, as the section from the torsional torque of the elastic shaft (driving wheel torque) T.sub.d to the tire speed (driving wheel angular speed) ?.sub.w is defined as a transfer function G.sub.TdWw(s), G.sub.TdWw(s) is expressed by mathematical expression (2).

(60) $\begin{array}{cc}{G}_{\mathrm{TdWw}}\left(s\right)=\frac{{?}_w}{T_d}=\frac{\begin{array}{c}1\\ {\mathrm{TJ}}_w.Math.s\end{array}}{1+\frac{1}{T{J}_w.Math.s}.Math.G_{\mathrm{WwTt}}\left(s\right)}=\frac{\begin{array}{c}1\\ {\mathrm{TJ}}_w.Math.s\end{array}}{1+\frac{1}{T{J}_w.Math.s}.Math.\frac{T{J}_M.Math.s}{\frac{T{J}_M}{\mathrm{Kt}}.Math.s+1}}=\frac{1}{\left(T{J}_w+{\mathrm{TJ}}_M\right).Math.s}.Math.\frac{\frac{T{J}_M}{\mathrm{Kt}}.Math.s+1}{\frac{1}{Kt}.Math.\frac{T{J}_w.Math.{\mathrm{TJ}}_M}{T{J}_w+T{J}_M}.Math.s+1}& \left(2\right)\end{array}$

(61) The transfer function G.sub.p(s), which is a transfer function of the entire model from the electromagnetically generated motor torque (output torque command) T.sub.m to the motor rotational speed (angular speed) ?.sub.m, is a product of an integral term and a third order term as expressed by mathematical expression (3). Here, the sum of rotational inertias is represented by TJ.sub.?=TJ.sub.m+TJ.sub.w+TJ.sub.M.

(62) $\begin{array}{cc}{G}_p\left(s\right)=\frac{{?}_m}{T_m}=\frac{1}{{\mathrm{TJ}}_{.Math.}.Math.s}.Math.\frac{\frac{T{J}_w{\mathrm{TJ}}_M}{\mathrm{Kt}.Math.K_d}.Math.s^3+\frac{T{J}_w+T{J}_M}{K_d}.Math.s^2+\frac{T{J}_M}{Kt}.Math.s+1}{\begin{array}{c}T{J}_m.Math.{\mathrm{TJ}}_w.Math.{\mathrm{TJ}}_M\\ {\mathrm{TJ}}_{.Math.}.Math.\mathrm{Kt}.Math.K_d\end{array}.Math.s^3+\begin{array}{c}{\mathrm{TJ}}_m.Math.\left({\mathrm{TJ}}_w+{\mathrm{TJ}}_M\right)\\ {\mathrm{TJ}}_{.Math.}.Math.K_d\end{array}.Math.s^2+\begin{array}{c}\left({\mathrm{TJ}}_M.Math.{\mathrm{TJ}}_w\right)\\ {\mathrm{TJ}}_{.Math.}.Math.Kt\end{array}.Math.s+1}\left({\mathrm{TJ}}_{.Math.}={\mathrm{TJ}}_m+{\mathrm{TJ}}_w+{\mathrm{TJ}}_M\right)& \left(3\right)\end{array}$

(63) The integral term in mathematical expression (3) contains a time constant equivalent to a combined component of all of the rotational inertias. Correcting coefficients so as to separate the integral term into a combination of an integral term of the motor rational inertia, G.sub.m(s)=1/(TJ.sub.m.Math.s), and F.sub.p(s), as in mathematical expression (4), gives a filter section (F.sub.p(s)) expressed by mathematical expression (5).

(64) $\begin{array}{cc}{G}_p\left(s\right)=G_m\left(s\right).Math.F_p\left(s\right)& \left(4\right)\end{array}$$\begin{array}{cc}{F}_p\left(s\right)=\frac{T{J}_m}{T{J}_{?}}.Math.\frac{\frac{{\mathrm{TJ}}_w.Math.{\mathrm{TJ}}_M}{\mathrm{Kt}.Math.K_d}.Math.s^3+\frac{T{J}_w+T{J}_M}{K_d}.Math.s^2+\frac{T{J}_M}{Kt}.Math.s+1}{\frac{T{J}_m.Math.{\mathrm{TJ}}_w.Math.{\mathrm{TJ}}_M}{T{J}_{?}.Math.\mathrm{Kt}.Math.K_d}.Math.s^3+\frac{T{J}_m.Math.\left({\mathrm{TJ}}_w+T{J}_M\right)}{{\mathrm{TJ}}_{?}.Math.K_d}.Math.s^2+\frac{{\mathrm{TJ}}_M.Math.\left({\mathrm{TJ}}_m+T{J}_w\right)}{T{J}_{?}.Math.\mathrm{Kt}}.Math.s+1}& \left(5\right)\end{array}$

(65) In a first embodiment, mathematical expression (5) is simplified and then used for vibration suppression control.

(66) Mathematical expressions (4) and (5) represent the configuration of FIG. 1. This configuration is approximated to reduce the number of components as shown in FIG. 2. This approximation is described in terms of transfer functions.

(67) The approximation is applied to mathematical expression (2), which corresponds to replacing G.sub.TdWw(s) in FIG. 1 with G.sub.TdWw2(s) in FIG. 2.

(68) The transfer function G.sub.TdWw2(s) in FIG. 2 includes: a D.sub.s block 21 that multiplies the driving wheel torque T.sub.d by a slip coefficient D.sub.s to output a tire slip speed ?.sub.slip; a 1/TJ.sub.wM(s) block 22 that integrates the driving wheel torque T.sub.d by the combined rotational inertia TJ.sub.wM of the tires and the vehicle body to output the tire and vehicle body speed ?.sub.wM; and an adder 23 that sums the speeds ?.sub.slip and ?.sub.wM to output the driving wheel angular speed ?.sub.w.

(69) Mathematical expression (2) is composed of a product of an integral term and a first order filter. The coefficients in the denominator of the first order filter are approximated as mathematical expression (6).

(70) 0$\begin{array}{cc}\frac{1}{Kt}.Math.\frac{T{J}_w.Math.{\mathrm{TJ}}_M}{{\mathrm{TJ}}_w+{\mathrm{TJ}}_M}\frac{1}{Kt}.Math.\frac{T{J}_w.Math.{\mathrm{TJ}}_M}{T{J}_M}\frac{T{J}_w}{Kt}?1& \left(6\right)\end{array}$

(71) In general, when the inertia of the vehicle body and the rotational inertia of the tires are compared in terms of time constants, the time constant of the tires is much smaller (TJ.sub.M>>TJ.sub.w). Furthermore, the tire coefficient K.sub.t has a large value (K.sub.t>>1). From these two characteristics, it can be seen that the coefficient of the denominator of the first order filter part in mathematical expression (2) is much smaller than 1 with reference to a relationship in mathematical expression (6).

(72) The denominator of this first order filter part represents characteristics of a low-pass filter (LPF), where the reciprocal of mathematical expression (6) corresponds to a corner frequency. The fact that mathematical expression (6) has a small value means that this LPF attenuates only fairly high frequency components. Accordingly, if the corner frequency is sufficiently high with respect to a resonant frequency or a band of compensation of the vibration suppression control, it can be considered irrelevant from the vibration suppression control. By regarding the value of mathematical expression (6) as zero and approximating the denominator side of the first order filter part to a unity gain (=1), the mathematical expression (2) is approximated to mathematical expression (7), which is equivalent to a sum of a proportional term D.sub.s in mathematical expression (8) and an integral with the time constant TJ.sub.wM in mathematical expression (9).

(73) $\begin{array}{cc}{G}_{\mathrm{TdWw2}}\left(s\right)\stackrel{.Math.}{\underset{.Math.}{=}}\frac{\left(T{J}_M/Kt\right).Math.s+1}{\left(T{J}_w+T{J}_M\right).Math.s}=\frac{T{J}_M}{\left(T{J}_w+T{J}_M\right).Math.\mathrm{Kt}}+\frac{1}{\left(T{J}_w+T{J}_M\right).Math.s}=D_s+\frac{1}{T{J}_{\mathrm{wM}}.Math.s}& \left(7\right)\end{array}$$\begin{array}{cc}{D}_s=\frac{T{J}_M}{\left(T{J}_w+T{J}_M\right).Math.\mathrm{Kt}}& \left(8\right)\end{array}$$\begin{array}{cc}{\mathrm{TJ}}_{\mathrm{wM}}=T{J}_w+{\mathrm{TJ}}_M& \left(9\right)\end{array}$

(74) As in mathematical expression (9), TJ.sub.wM represents the combined rotational inertia of the tires and the vehicle body. In mathematical expression (8), D s is a coefficient representing a tire slip characteristic, and corresponds to a slip coefficient for calculating the slip speed ?.sub.slip that is caused by the driving force (driving wheel torque) T.sub.d applied to the tire axle.

(75) By applying the above approximation, mathematical expressions (4) and (5) are simplified to mathematical expressions (10) and (11).

(76) $\begin{array}{cc}{G}_p\left(s\right)\stackrel{.Math.}{\underset{.Math.}{=}}{G}_{p2}\left(s\right)=G_m\left(s\right).Math.F_{p2}\left(s\right)& \left(10\right)\end{array}$$\begin{array}{cc}{F}_{p2}\left(s\right)=\frac{s^2+K_d.Math.D_s.Math.s+\frac{K_d}{T{J}_{\mathrm{wM}}}}{s^2+K_d.Math.D_s.Math.s+K_d.Math.\left(\frac{1}{T{J}_{wM}}+\frac{1}{T{J}_m}\right)}& \left(11\right)\end{array}$

(77) By simplifying the third order filter F.sub.p(s) expressed by mathematical expression (5) to the second order filter F.sub.p2(S) expressed by mathematical expression (11), characteristics can be represented in a general system with a natural frequency of a second order equation and a viscosity ratio, and control design can be carried out using a model approximated into a two-inertia system.

(78) Ends of the elastic shaft are connected to the motor shaft and the tire axle. The vibration suppression control uses a difference in speed between both ends and a torsional phase, wherein the torsional phase is produced by time-integrating the speed difference. If there is no need to refer to individual speeds of the motor and tires, the integral terms in the block diagram shown in FIG. 2 can be commonized and reduced as shown in FIG. 3 (approximate model of this embodiment).

(79) First, the integral time constants TJ.sub.m and TJ.sub.wM are isolated and used to calculate individual acceleration components (A.sub.m and A.sub.wM). Then, the difference between these accelerations is integrated to calculate the speed difference (torsional speed). Furthermore, since the component obtained by differentiating the motor speed is used for the vibration suppression control as described below, it is modified so that the input component T.sub.mA to the integral term of the motor is outputted. With the configuration shown in FIG. 3, the number of integrators can be reduced to two.

(80) This output component T.sub.mA is produced by subtracting a reaction force (driving wheel torque) T.sub.d, which corresponds to a torque transmitted to the elastic shaft and is applied to the output shaft of the motor, from the electromagnetic torque (T.sub.m) generated between the stator and rotor of the motor. Since the output component T.sub.mA is proportional to the acceleration Am of the motor, the output component T.sub.mA is henceforth referred to as motor-accelerating torque.

(81) In FIG. 3, the same parts as those in FIGS. 1 and 2 are denoted by the same reference numerals. A divider 25 divides the motor-accelerating torque T.sub.mA, which is obtained by subtracting the driving wheel torque T.sub.d from the output torque command T.sub.m by the subtractor 11, by the time constant equivalent to the rotational inertia of the motor (TJ.sub.m), and outputs the motor side acceleration A.sub.m.

(82) A divider 26 divides the driving wheel torque T.sub.d by the combined rotational inertia TJ.sub.wM of the tires and the vehicle body to output the vehicle body side acceleration A.sub.wM.

(83) A subtractor 27 obtains a deviation between the motor-side acceleration Am and the vehicle-side acceleration A.sub.wM. An integrator 28 time-integrates the outputted deviation to produce a relative speed (?.sub.m-?.sub.wM) between the motor and the vehicle body.

(84) A subtractor 29 subtracts the tire slip speed ?.sub.slip, which is produced by multiplying the driving wheel torque T.sub.d by the slip coefficient D.sub.s, from the motor/vehicle relative speed (?.sub.m-?.sub.wM) to produce a motor/tire relative speed (relative torsional speed of the elastic shaft) ?.sub.d.

(85) A G.sub.d(s) block 14 multiplies the motor/tire relative speed ?.sub.d, which is outputted from the subtractor 29, by a transfer function G.sub.d(s) to output the driving wheel torque T.sub.d.

(86) When represented by a transfer function, the configuration of FIG. 3 is expressed by G.sub.PTmA2(s) in mathematical expression (12), which is equal to the second order filter F.sub.P2(s) in mathematical expression (11). It is known that in a two-inertia system, the denominator represents resonant characteristics and the numerator represents anti-resonant characteristics. A second order mathematical expression like mathematical expression (12) can be treated in terms of a natural frequency and a damping ratio. In this embodiment, this mathematical expression (12) is used for designing a vibration suppression control.

(87) $\begin{array}{cc}{G}_{\mathrm{pTmA}2}=\frac{s^2+\left(K_d.Math.D_s\right).Math.s+K_d.Math.\begin{array}{c}1\\ {\mathrm{TJ}}_{\mathrm{wM}}\end{array}}{s^2+\left(K_d.Math.D_s.Math.s\right)+K_d.Math.\left(\frac{1}{{\mathrm{TJ}}_m}+\frac{1}{{\mathrm{TJ}}_{\mathrm{wM}}}\right)}=\frac{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}{s^2+2.Math.{?}_r.Math.{?}_r.Math.s+{?}_r^2}& \left(12\right)\end{array}$ where s: a Laplace operator, ?.sub.r=?/(K.sub.d.Math.(1/TJ.sub.m+1/TJ.sub.wM), ?.sub.a=?/(K.sub.d.Math.(1/TJ.sub.wM)), ?.sub.r=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.r), ?.sub.a=(K.sub.d.Math.D.sub.s)/(2.Math.?.sub.a), D.sub.s=TJ.sub.M/(TJ.sub.w+TJ.sub.M).Math.K.sub.t, TJ.sub.m: a time constant equivalent to motor inertia, TJ.sub.w: a time constant equivalent to driving wheel inertia (a combined value of multiple driving wheels), TJ.sub.M: a time constant equivalent to vehicle mass, K.sub.d: a torsional stiffness coefficient of driveline (gears, an elastic shaft, etc.), K.sub.t: a coefficient relating to friction between tire and road surface, and TJ.sub.wM=TJ.sub.w+TJ.sub.M.

First Embodiment

(88) FIG. 4 (a) shows an example of configuration of a vibration suppression control system according to the first embodiment, in which feedback compensation of G.sub.comp(s) is applied to a controlled plant G.sub.P(s). In G.sub.comp(s), a measured speed ?.sub.m is differentiated by 1/{circumflex over ()}G.sub.m(s) of a differentiator 31 to produce a motor-accelerating torque component T.sub.mA*, which is caused to pass through a band-pass filter F.sub.comp(s) (vibration suppression control filter) to produce a compensation torque component T.sub.Fcomp, which is fed back to an input torque command T.sub.ref.

(89) Namely, a subtractor 32 subtracts the compensation torque component T.sub.Fcomp from the input torque command T.sub.ref to output an output torque command T.sub.m. Mathematical expression (13) is employed for this bandpass filter F.sub.comp(s). In mathematical expression (13), ?.sub.A is a sole adjustable parameter, and except for this parameter, the natural frequency and damping ratio of mathematical expression (12) are used.

(90) $\begin{array}{cc}{F}_{comp}\left(s\right)=\frac{2.Math.\left({?}_{?}-{?}_r\right).Math.{?}_r.Math.s}{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}& \left(13\right)\end{array}$

(91) The plant side in FIG. 4 (a) can be separated into the integral term G.sub.m(s) of the motor and the filter part G.sub.PTmA(s), and G.sub.m(s) of the actual plant and G.sub.m(s) of the control model are approximated to be equal to each other as shown in FIG. 4 (b). As the filter section G.sub.PTmA(s) is also approximated to G.sub.PTmA2(s), only a feedback F.sub.P-comp(s) and G.sub.m(s) remain as shown in FIG. 4 (c). Accordingly, it is sufficient to approximate F.sub.P-comp(s) as in mathematical expression (14), and design F.sub.comp(s) to have stable characteristics.

(92) $\begin{array}{cc}{F}_{p-\mathrm{comp}}\left(s\right)=\frac{F_p\left(s\right)}{1+F_p\left(s\right).Math.F_{comp}\left(s\right)}\stackrel{.Math.}{\underset{.Math.}{=}}\frac{G_{\mathrm{pTmA}2}\left(s\right)}{1+G_{\mathrm{pTmA}2}\left(s\right).Math.F_{\mathrm{comp}}\left(s\right)}& \left(14\right)\end{array}$

(93) Substituting the mathematical expression (12) for the approximate model and mathematical expression (13) for the compensation filter into mathematical expression (14) yields a second order mathematical expression (15).

(94) $\begin{array}{cc}{F}_{p-\mathrm{comp}}\left(s\right)\stackrel{.Math.}{\underset{.Math.}{=}}\frac{F_{p2}\left(s\right)}{1+F_{p2}\left(s\right).Math.F_{\mathrm{comp}}\left(s\right)}=\frac{\begin{array}{c}{s}^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2\\ s^2+2.Math.{?}_r.Math.{?}_r.Math.s+{?}_r^2\end{array}}{1+\frac{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}{s^2+2.Math.{?}_r.Math.{?}_r.Math.s+{?}_r^2}.Math.\frac{2.Math.\left({?}_A-{?}_r\right).Math.{?}_r.Math.s}{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}}=\frac{s^2+2.Math.{?}_a.Math.{?}_a.Math.s+{?}_a^2}{s^2+2.Math.{?}_A.Math.{?}_r.Math.s+{?}_r^2}& \left(15\right)\end{array}$

(95) Since the adjustable parameter ?.sub.A corresponds to the viscosity ratio of the denominator, setting ?.sub.A=1 makes the denominator have a double root and thereby makes the system become stable, which means that the band pass filter F.sub.comp(S) has been designed suitably.

(96) Actually, model errors exist, so that it is required to set ?.sub.A to a small value. Ideally, it is sufficient to set ?.sub.A as ?.sub.A=1. Mathematical expression (15) is obtained by approximating the filter characteristic part of the plant to mathematical expression (11). The use of the approximate model makes it easy to design the compensator.

(97) According to the first embodiment, by approximating the configuration of FIG. 1 to the model configuration of two-inertia system in FIG. 2, it is possible to reduce the order of the transfer function as in mathematical expression (10) and mathematical expression (11). Furthermore, by modifying the model to output the motor-accelerating torque as shown in FIG. 3, it is possible to express the characteristics by a general system based on a second order filter with a natural frequency and a viscosity ratio of a second order mathematical expression. This makes it possible to easily grasp the characteristics of resonance and anti-resonance of a controlled object.

(98) By using this simplified second order mathematical expression, it is possible to easily design the filter characteristics of the feedback control of mathematical expression (13) required for constructing the vibration suppression control of FIG. 4 (a).

Second Embodiment

(99) The vibration suppression control designed in the first embodiment still has issues. It is required to take countermeasures against gear backlash and tire coefficient (friction coefficient) fluctuations. As a preliminary step, in this section as a second embodiment, a method is proposed for realizing a disturbance torque observer using the approximate model of FIG. 3.

(100) FIG. 5 shows an example of configuration of a general disturbance torque observer. Symbols and variables are defined for components as follows. G.sub.p(s): a model of a plant to be controlled, {circumflex over ()}G.sub.P(s): a model in control, K.sub.g: an observer gain, {circumflex over ()}?.sub.m: a motor speed estimated by control model, T.sub.mdist: a disturbance torque component converted to motor shaft torque, and {circumflex over ()}T.sub.obs: an estimated disturbance torque.

(101) Originally, a gradient such as on a climbing road acts as an external force on the vehicle body, and a decelerating force due to braking acts as a disturbance torque on the tire axle. However, since only the motor speed is measured, these disturbance torque components are collectively defined as T.sub.mdist, which is a quantity produced by conversion to the motor shaft. This disturbance torque is estimated as {circumflex over ()}T.sub.obs by a disturbance torque observer.

(102) FIG. 5 shows a general structure, in which subtracting T.sub.mdist from the output torque command T.sub.m by the subtractor 41 yields a quantity, and the quantity is inputted to the plant model G.sub.p(s) to output a speed corresponding to the measured speed ?.sub.m. On the observer side, a subtractor 44 subtracts {circumflex over ()}T.sub.obs from the output torque command T.sub.m to produce a quantity, which is inputted to the model {circumflex over ()}G.sub.P(s) to calculate the estimated speed {circumflex over ()}?.sub.m; a subtractor 42 calculates a difference between the estimated speed {circumflex over ()}?.sub.m and the measured speed ?.sub.m from the plant; a gain multiplier 43 multiplies the difference by an observer gain Kg to produce the estimated disturbance torque {circumflex over ()}T.sub.obs, and feeds the estimated disturbance torque {circumflex over ()}T.sub.obs back to the subtractor 44 to which the model input torque is inputted.

(103) In the second embodiment, the general configuration of FIG. 5 is further modified to a configuration shown in FIG. 6. In FIG. 4 (a) showing the vibration suppression control according to the first embodiment, the torque accelerating the motor (motor-accelerating torque component) T.sub.mA* is calculated by application of 1/G.sub.m(s)=(TJ.sub.m.Math.s), which corresponds to differentiation, to the measured speed. On the other hand, the model in FIG. 3 also outputs T.sub.mA equivalent to T.sub.mA*. Accordingly, by using the approximate model in FIG. 3 and replacing the speed difference component ({circumflex over ()}?.sub.m-?.sub.m) in FIG. 5 with the difference in motor-accelerating torque ({circumflex over ()}T.sub.mA-T.sub.mA*) (output of a subtractor 51), it is possible to implement a disturbance torque observer that uses T.sub.mA*, which has already been calculated in the vibration suppression control. For actual implementation in a digital controller, the second order transfer function of mathematical expression (12) is used to suppress a discrete time error.

(104) In FIG. 6, the same parts as in FIGS. 3 and 5 are denoted by the same reference numerals. The estimated motor-accelerating torque component {circumflex over ()}T.sub.mA (=({circumflex over ()}TJ.sub.m.Math.s).Math.{circumflex over ()}?.sub.m), which is outputted from a subtractor 11 in the approximate model G.sub.PTmA2(s), is taken into a subtractor 51. The subtractor 51 calculates the difference between the estimated motor-accelerating torque component {circumflex over ()}T.sub.mA and the motor-accelerating torque component T.sub.mA*(=({circumflex over ()}TJ.sub.m.Math.s).Math.?.sub.m) that is produced by causing the motor angular speed ?.sub.m to pass through a differentiator 31. The output ({circumflex over ()}TJ.sub.m.Math.s).Math.??.sub.m of the subtractor 51 is integrated by an integrator 52 and then multiplied by the observer gain K.sub.g of a gain multiplier 43 to produce the estimated disturbance torque {circumflex over ()}T.sub.obs.

(105) Furthermore, in FIG. 6, the slip coefficient D.sub.s and the torsional stiffness coefficient K.sub.d relate to the control model, and accordingly, they are expressed as slip coefficient {circumflex over ()}D.sub.s and torsional stiffness coefficient {circumflex over ()}K.sub.d.

(106) A divider 25 divides the estimated motor-accelerating torque component {circumflex over ()}T.sub.mA by a time constant {circumflex over ()}TJ.sub.m equivalent to the rotational inertia of the motor to produce the motor side acceleration.

(107) A divider 26 divides the shaft torsional torque {circumflex over ()}T.sub.d by the combined rotational inertia {circumflex over ()}TJ.sub.wM of the tires and the vehicle body to produce the vehicle body side acceleration.

(108) A subtractor 27 calculates the difference between the dividers 25 and 26, and an integrator 28 integrates the outputted difference over time to produce the relative speed {circumflex over ()}?.sub.d between the motor and the vehicle body.

(109) By multiplying the shaft torsional torque {circumflex over ()}T.sub.d by the slip coefficient {circumflex over ()}D.sub.s of a D.sub.s block 21, the tire slip speed is calculated.

(110) A subtractor 29 calculates the difference between the tire slip speed and the motor/vehicle relative speed {circumflex over ()}?.sub.d, wherein the calculated difference is time-integrated in a G.sub.d(s) block 14 and thereby converted into the torsional phase of the elastic shaft. The torsional phase is multiplied by the torsional stiffness coefficient {circumflex over ()}K.sub.d of the driveline to produce the shaft torsional torque {circumflex over ()}T.sub.d.

(111) The subtractor 11 and the subtractor 44 may be integrated into a single subtractor that subtracts the estimated disturbance torque {circumflex over ()}T.sub.obs and the shaft torsional torque {circumflex over ()}T.sub.d from the output torque command T.sub.m.

(112) As described above, {circumflex over ()}T.sub.mA from the model G.sub.PTmA2(s) can be used without changed from the output in FIG. 3, wherein there is no need to differentiate the speed on the model side. However, since this difference is a differential component of speed, the integral 1/({circumflex over ()}TJ.sub.m.Math.s) is added after difference calculation in order to restore a speed difference. Finally, the value obtained after the integration is multiplied by the observer gain K.sub.g to produce the estimated disturbance torque {circumflex over ()}T.sub.obs. Thereby, FIG. 6 becomes equivalent to FIG. 5 in terms of characteristics. In the following embodiments, vibration suppressing control is realized by using two types of signals T.sub.mA* and {circumflex over ()}T.sub.mA indicated by broken lines in FIG. 6.

(113) FIG. 7 shows a combination of the disturbance torque observer shown in FIG. 6 and the vibration suppression control shown in FIG. 4 (a), as an example of configuration of the second embodiment. In FIG. 7, the same parts as in FIG. 6 and FIG. 4 (a) are denoted by the same reference numerals.

(114) In FIG. 7, a block 60 is a combination of the functions of the integrator 52 and the gain multiplier 43 shown in FIG. 6.

(115) In FIG. 7, the model section (G.sub.PTmA2(s)) of FIG. 6 is collectively shown as a block {circumflex over ()}G.sub.PTmA2(s). If it is implemented as a model that is not approximated as the model in FIG. 1, calculation takes a longer time. If it is implemented as multiple element blocks as shown in FIG. 3, transformation to a sampled data system may cause errors due to discrete time. However, by transforming to a second order filter form like {circumflex over ()}G.sub.PTmA2(s) of mathematical expression (12) and then transforming to a sampled data system, it is also possible to suppress errors due to discrete time.

(116) According to the second embodiment, by configuring the disturbance torque observer shown in FIG. 6 using the simplified model of FIG. 3, it is possible to estimate the disturbance torque component converted to the motor shaft. Adoption of {circumflex over ()}G.sub.PTmA2(s) for the model section as shown in FIG. 7, serves to simplify the configuration, because the intermediate component of the vibration suppression control of the first embodiment can be used.

(117) Furthermore, when the section of {circumflex over ()}G.sub.PTmA2(s) in FIG. 7 is expressed by a single transfer function, the transfer function has the form of a second order filter as in mathematical expression (12). Accordingly, even with transformation into a sampled data system for implementation in a controller, it is possible to suppress errors due to discrete time.

Third Embodiment

(118) FIG. 8 shows a vibration suppression control according to a third embodiment, which employs the vibration suppression control according to the first embodiment and the disturbance torque observer according to the second embodiment. This differs from FIG. 7 in a feedback signal source, wherein the input to the bandpass filter F.sub.comp(s) is modified from T.sub.mA* on the speed measurement side to the estimated value {circumflex over ()}T.sub.mA on the model side. These signals usually converge to approximately the same value, because the disturbance torque observer operates so as to equate the components T.sub.mA* and {circumflex over ()}T.sub.mA with each other.

(119) However, compared with the method of the first embodiment, the third embodiment is characterized in that it is possible to suppress hunting caused by backlash and disturbance components due to model errors such as when the tire coefficient varies.

(120) In patent document 1, a prefilter is added to a torque command input section for removing frequency components near resonance. In addition, since an inverse characteristic (1/G.sub.p(s)) of an ideal model in which no disturbance is taken into account is used for vibration suppression, there is a problem that compensation performance is adversely affected by a model error when it is present. Furthermore, since this inverse characteristic has a high gain near an anti-resonant frequency, low-frequency vibration may occur conversely.

(121) In order to solve these problems, in the third embodiment, both the torque command and the measured speed are inputted to the model, and the internal state of the model is used for feedback control for vibration suppression. By ignoring the measured speed component of the two input components to the model, and taking out only the torque command, the model, and the vibration suppression feedback, it is possible to produce an effect equivalent to that of a prefilter. In other words, it acts to suppress a frequency component contained in the torque command which causes resonance. Therefore, the configuration of the third embodiment requires no prefilter inserted as in patent document 1. Furthermore, as the observer gain K g is increased, the prefilter effect becomes smaller, and instead, the effect of vibration suppression control based on speed measurement equivalent to that of the first embodiment becomes larger. By including two types of functions in this way, it is possible to produce an effect of suppressing the vibration component due to resonance, similar to patent document 1 and the first and second embodiments.

(122) Furthermore, patent document 1 and the first and second embodiments have a problem of being susceptible to nonlinearity, model errors, etc. For example, during a period of gear backlash, only the rotational inertia of the motor accelerates, resulting in a large change in the speed of the motor. It is conceivable that this causes excessive compensation of the vibration suppression control, and thereby causes hunting behavior. A model error due to variation in road surface friction (tire coefficient) is conceivable to cause a design error in the compensation filter, thereby cause a deviation in a frequency characteristic for compensation, and thereby distort a response waveform. As described above, the effect of these error components is particularly likely to appear as components in the anti-resonant band where the gain of the compensation filter is high.

(123) On the other hand, when the third embodiment is employed and the observer gain K.sub.g is set so that the operating band of the disturbance torque observer contains the anti-resonant frequency, the low-frequency vibration component near the anti-resonant frequency can be estimated as a disturbance torque. The estimated disturbance torque component is to correct the value of compensation of the vibration suppression control, thereby suppressing low-frequency vibration components from being caused by hunting due to backlash and variation in road surface friction.

(124) Therefore, by employing the disturbance torque observer to use the motor-accelerating torque, which includes the influence of disturbance, for vibration suppression control, it is possible to produce an effect of realizing robustness that can maintain stability even when there are influences of factors such as nonlinearity and model errors.

Fourth Embodiment

(125) FIG. 8 shows a block diagram showing a continuous data system, ignoring a delay in speed measurement. However, actual speed measurement is implemented by periodically sampling phase information obtained from a rotation sensor such as a resolver or encoder, and calculating the speed based on a phase difference and a time difference between samples. Accordingly, speed measurement has a delay due to a sample interval, a calculation time, etc. Furthermore, since the motor drive device employs an electric current control or the like to control the torque, there is also a delay in response of the electric current control. In FIG. 9, these delay times are combined into a dead time component L1 and expressed as a delay 1, e.sup.?L1s (delay part 61). ?.sub.m_dly after this delay is an actually measured speed component.

(126) With respect to the third embodiment, the fourth embodiment further employs a measure for reducing the influence of the dead time. FIG. 9 shows an example of configuration of the fourth embodiment. In FIG. 9, the same parts as in FIG. 6 are denoted by the same reference numerals. In FIG. 9, in order to make the estimated torque of the disturbance torque observer accurate, a dead time component L2 as a delay 2, e.sup.?L2s (delay part 62) is inserted to the disturbance torque observer side, wherein the dead time component L2 is equal to the dead time component L1 on the speed measurement side, to ensure time matching between both components before subtraction by a subtractor 51. The delay part 62 constitutes a delay compensating means of the present invention.

(127) The measured speed component including the delay time L1 is used to calculate a motor-accelerating torque T.sub.mA_dly*, which is outputted from a differentiator 31. Since functions of electric current control and speed measurement are not implemented in the model of the disturbance torque observer, the delay processing (delay part 62) with the delay time (L2) equal to the delay time L1 is inserted to the estimated motor-accelerating torque ({circumflex over ()}T.sub.mA) in the disturbance torque observer, to calculate a quantity ({circumflex over ()}T.sub.mA_dly), and the difference between this quantity ({circumflex over ()}T.sub.mA_dly) and the aforementioned quantity (T.sub.mA_dly*) is calculated to produce the difference component of the motor-accelerating torque of the disturbance torque observer, which is outputted from the subtractor 51.

(128) The fourth embodiment differs from patent document 2 in that the motor-accelerating torque component {circumflex over ()}T.sub.mA of the disturbance torque observer is used as a feedback component of the vibration suppression control (inputted to the bandpass filter F.sub.comp(s)), and {circumflex over ()}T.sub.mA contains no delay. Namely, the component ({circumflex over ()}T.sub.mA) extracted from the preceding stage of the delay 2 (delay part 62) is used for vibration suppression control as indicated by a dashed line from the disturbance torque observer in FIG. 9.

(129) In FIG. 10 showing another example of configuration of the fourth embodiment, it is assumed that there is more noise in speed measurement than in the case of FIG. 9. In general, in order to suppress speed disturbance due to noise, a low-pass filter LPF (high band cutoff filter) is often added to the subsequent stage of the differentiator 31 for filtering the result of speed measurement. This adds an LPF delay the subsequent stage of the dead time component L1, thereby further delaying the component T.sub.mA_dly*. Therefore, it is required to add an LPF to {circumflex over ()}T.sub.mA_dly on the model side for time matching.

(130) However, the configuration of FIG. 10 is such that a low-pass filter 70 is inserted in the subsequent stage of the subtractor 51 in FIG. 9 that calculates the difference between T.sub.mA_dly* and {circumflex over ()}T.sub.mA_dly. In the configuration that the single low-pass filter 70 is inserted in the subsequent stage of calculation of the difference between the motor-accelerating torque components with as little delay as possible and time matching, there is no need to consider time matching for a delay time due to the added low-pass filter 70. This is another example of configuration of the fourth embodiment for realizing delay time matching. It is a The point is that time matching between the actual device side and the model side can be achieved. Although there are various configurations for achieving time matching between the actual vehicle side and the model side, the present disclosure includes only two examples shown in FIGS. 9 and 10.

(131) The fourth embodiment produces the following effects.

(132) In patent document 2, in order to correct the influence of a delay time (dead time) due to speed measurement and others, an equivalent delay is inserted into an input component to the ideal model 1/G.sub.p(s) so as to ensure time matching for a speed difference component between the model and the actual vehicle. However, the signal used for feedback control also contains this dead time delay, so that an error occurs under conditions where a torque command changes rapidly. Therefore, it is required to remove high-frequency components with a prefilter.

(133) In the system of the fourth embodiment, the difference component between the observer model and the actual vehicle is time-matched using a delay, as in patent document 2. However, the vibration suppression control component resulting from the torque command is a signal containing no delay. Accordingly, the effect of suppressing the vibration component caused by change in the torque command includes no delay in compensation.

(134) From a different point of view, the time delay in speed measurement cannot be corrected, but the command of torque to be generated by the motor can be grasped at the time of control calculation. Also, since the time constant of the vehicle body side is large, fluctuations in measured speed due to disturbance torque are relatively slow, but the motor side speed changes greatly depending on the torque command. Therefore, since the compensation component based on speed measurement is less affected by a delay, time matching by delaying is adopted for the compensation component based on speed measurement. In contrast, the compensation component based on the torque command is configured to contain no delay.

(135) Namely, by time-matching the difference in the disturbance torque observer, it is possible to accurately estimate the disturbance torque and to produce an effect of applying predictive compensation for the dead time when the torque command rapidly changes.

Fifth Embodiment

(136) FIG. 11 shows an example of configuration according to a fifth embodiment. For input to the bandpass filter F.sub.comp(s), a function of switching is added between the system based on the differential component of the measured speed in the first and second embodiments and the system based on the disturbance torque observer in the third and fourth embodiments. When the torque command is fixed to zero, such as at the time of starting, it is desirable to suppress the disturbance on the load side as quickly as possible with high priority. In such a case, the first and second embodiments, which use only speed measurement, are more suitable. Furthermore, there may be special conditions in which the road surface condition changes in synchronization with the resonant frequency. In such a case, it is desirable to improve the response of the compensation signal.

(137) Therefore, as shown in FIG. 11, the second embodiment and the third embodiment are combined, and a configuration is added in which both of the motor-accelerating torque components are weighted and added, thereby adding a function of switching between both signals and a function of gain adjustment.

(138) In FIG. 11, the same parts as in FIG. 9 are denoted by the same reference numerals. A multiplier 81 multiplies the motor-accelerating torque component T.sub.mA_dly* on the speed measurement side (on the output side of the differentiator 31) by a weighting factor K.sub.FB1. A multiplier 82 multiplies the motor-accelerating torque component {circumflex over ()}T.sub.mA on the model {circumflex over ()}G.sub.PTmA2(s) side by a weighting factor K.sub.FB2. The weighting factors K.sub.FB1 and K.sub.FB2 are variable. An adder 83 sums the outputs of the multipliers 81 and 82 and inputs the result of summation to the bandpass filter F.sub.comp(s). A signal selection and weight control section 80 is composed of the multipliers 81 and 82 and adder 83.

(139) The function of the fifth embodiment in which the signal selection and weight control section 80 is provided is not limited to FIG. 9, and may be applied to the configurations of FIGS. 7, 8, and 10 as well.

(140) FIG. 11 shows an example of configuration in which a delay 2 (delay part 62) is provided. The configuration of FIG. 11 may be replaced with a configuration without the delay 2.

(141) By relative increase and decrease with time, it is possible to switch slowly between the two types of signals (control systems). Furthermore, by increasing or decreasing the sum of the two types of weighting coefficients, it is possible to adjust the amount of feedback of the vibration suppression control.

(142) According to the example of configuration of the fifth embodiment, immediately after the inverter in the motor drive device is released from its gate cutoff state (in which all switching elements of the inverter are cut off), which corresponds to engine starting, the system is preferably operated to carry out the vibration suppression control based on speed measurement according to the first embodiment, thereby suppressing the disturbance quickly. After the state of the disturbance torque observer is stabilized, the switching weighting coefficients K.sub.FB1 and K.sub.FB2 may be gradually shifted to the system according to the third and fourth embodiments. By shifting the coefficients linearly with time, it is possible to prevent shocks due to switching of the control system.

(143) <Results of Verification of Behavior and Effects of Embodiments>

(144) Since it is an object of the present invention to improve characteristics of vibration suppression control, behavior and effects are verified by investigating transient responses such as step responses through numerical simulations.

(145) FIG. 12 shows a model used as an actual plant. The configuration of FIG. 12 employs a detailed model system G.sub.p(S) based on the configuration of FIG. 1, wherein a load torque caused by the gradient of a road surface is represented by T.sub.Mdist (corresponding to T.sub.F in FIG. 1), and changes in the road surface friction coefficient are simulated by adding a multiplier 85 for multiplication by an adjustment coefficient K.sub.Kt after multiplication by the tire coefficient in the K.sub.t block 18.

(146) Gear backlash is simulated by adding a phase nonlinear function (backlash phase??.sub.BL) part 86 to the torsional phase of the elastic shaft. The G.sub.d(s) (=K.sub.d/s) block 14 in FIG. 1 is composed of an integrator 87 and a K.sub.d block 88 separated from each other. This model is solely employed as the plant, wherein set values are changed for switching of presence/absence of disturbance, presence/absence of coefficient change, and presence/absence of backlash.

(147) The parameters of this plant model are set by the per-unit system, to define a virtual model having a resonant frequency of 10 Hz and an anti-resonant frequency of 1.5 Hz, for investigation of characteristics of compensation. The tire coefficient is set large as K.sub.t=25.0 p.u.

(148) The control system is configured as shown in FIG. 13. The configuration of FIG. 13 is produced by modifying the configuration FIG. 11 partly as follows. The plant model G.sub.p(S) receives input of the backlash phase??.sub.BL, the adjustment coefficient K.sub.Kt for road surface change, and the disturbance force (equivalent torque) T.sub.Mdist(t) applied to the vehicle body. The delay parts 61, 62 are replaced with low-pass filters 91 and 92 (LPF1 and LPF2) with time constants T.sub.LPF1 and T.sub.LPF2. A low-pass filter 93 (LPF3) with a time constant T.sub.LPF3 is provided between the input torque command T.sub.ref(t) and the subtractor 32. Furthermore, the signal selection and weight control section 80 is replaced with a SelFB switch 94 for switching between {circumflex over ()}T.sub.mA and T.sub.mA_dly for input to the bandpass filter F.sub.comp(s). A multiplier 95 is provided on the output side of the bandpass filter F.sub.comp(s) for multiplying by a weighting coefficient (gain correction value) K.sub.FB.

(149) Basically, the first to fourth embodiments can be simulated by this configuration. Feedback compensation can be invalidated by setting K.sub.FB to zero, wherein K.sub.FB is to be multiplied by the vibration suppression control component. Switching between the configuration of the first and second embodiments and the configuration of the third and fourth embodiments can be performed by switching the SelFB switch 94. The time matching of the disturbance torque observer is simulated by the first order delay filters LPF1 (91) and LPF2 (92). The LPF characteristics can be equivalently disabled by setting the time constants T.sub.LPF1 and T.sub.LPF2 to 0 s.

(150) Elements in FIGS. 12 and 13 are as follows. T.sub.ref(t): an input torque command, T.sub.mdist(t): a disturbance force applied to vehicle body (equivalent torque), G.sub.p(S): a plant model simulating a vehicle (FIG. 12), ??.sub.BL: a gear backlash phase of an actual model (when set to zero, it means no backlash), K.sub.Kt: an adjustment coefficient for variation in the road surface of the actual model (1.0: the friction of the actual road surface matches the model; <1: when the road surface is in a slip state), {circumflex over ()}G.sub.PTmA2(S): a disturbance torque observer model (mathematical expression (12)), ?TJ.sub.m: a time constant equivalent to the rotational inertia of the model, K.sub.g: a feedback gain of the disturbance torque observer, F.sub.comp(S): a filter section for vibration suppression control (mathematical expression (13), ?.sub.A=1), K.sub.FB: a gain correction for a feedback component of vibration suppression control (when set to zero, it means no compensation), LPF1: a low-pass filter simulating a speed measurement delay (T.sub.LPF1: a time constant; T.sub.LPF1=0 means no delay), LPF2: a low-pass filter inside the observer for matching with the speed measurement delay (T.sub.LPF2: a time constant; T.sub.LPF2=0 means no delay), {circumflex over ()}T.sub.obs: an estimated torque by the disturbance torque observer, T.sub.Fcomp: a compensation torque component by the vibration suppression control, T.sub.mA_dly: a differential component of a measured motor speed on the actual plant side (with a delay), and {circumflex over ()}T.sub.mA, {circumflex over ()}T.sub.mA_dly: a differential component of a measured motor speed on the model side (with no delay; with a delay).

(151) In order to investigate transient response characteristics, an input pattern of input torque command T.sub.ref(t) and load disturbance torque T.sub.Mdist(t) is set as shown in FIG. 14. This is an example of characteristics for evaluating: characteristics of response of the torque command; the vibration component when the reaction force applied to the vehicle body is changed transiently; and effects of backlash when the torque is returned to zero. t=1.0 s to 2.0 s: acceleration with 100% torque, t=2.0 s to 4.0 s: coasting with 0% torque, t=4.0 s to 5.0 s: deceleration by reaction force of 50% torque (uphill gradient), and t=5.0 s?: reaction force of 0% torque; coasting.

(152) However, the actual torque command does not have such a steeply changing step waveform. Accordingly, the low-pass filter 93 (LPF3) (10 ms) is added to soften the rise a little. As described below, the output of this filter 93 is indicated by a waveform labeled as T.sub.refLp.

(153) In order to simulate the characteristics of the first to fourth embodiments, set values are combined as shown in Table 1 below.

(154) TABLE-US-00001 TABLE 1 ??.sub.BL k_Kt TLPF3 SelFB K.sub.FB T.sub.LPF1 T.sub.LPF2 to be studied FIG. 16 0 1.0 5 ms 0 no vibration suppression control FIG. 17 0 1.0 5 ms TmAdet 1.0 0 0 vibration suppression control (speed measurement and differentiation system, without backlash, without tire slip) FIG. 18 ?0.001 1.0 5 ms TmAdet 1.0 0 0 vibration suppression control (speed measurement and differentiation system, with backlash, without tire slip) FIG. 19 ?0.001 0.3 5 ms TmAdet 1.0 0 0 vibration suppression control (speed measurement and differentiation system, with backlash, with tire slip) FIG. 20 0 1.0 5 ms TmAobs 1.0 0 0 vibration suppression control (torque observer system, without backlash, without tire slip) FIG. 21 ?0.001 1.0 5 ms TmAobs 1.0 0 0 vibration suppression control (torque observer system, with backlash, without tire slip) FIG. 22 ?0.001 0.3 5 ms TmAobs 1.0 0 0 vibration suppression control (torque observer system, with backlash, with tire slip) FIG. 23 ?0.001 1.0 0 ms TmAobs 1.0 5 ms 0 vibration suppression control (torque observer system, with backlash, without tire slip, with delay in speed measurement, without time compensation) FIG. 24 ?0.001 1.0 0 ms TmAobs 1.0 5 ms 5 ms vibration suppression control (torque observer system, with backlash, with tire slip, with delay in speed measurement, with time compensation)

(155) <Behavior and Effects of Vibration Suppression Control Using Model Approximated to Two-Inertia System and Speed Measurement Information (First Embodiment)>

(156) FIG. 15 demonstrates validity of the model approximation employed in the first embodiment, where the characteristics of G.sub.TdWw(s) in mathematical expression (2) and the characteristics of G.sub.TdEw2(s) in mathematical expression (7) are compared in Bode diagrams. As can be seen from FIG. 15 (a), a difference in gain occurs at 50 Hz or more. Namely, the difference occurs only in frequency components higher than the resonant frequency of 10 Hz. Furthermore, in FIG. 15 (b), as G.sub.p(S) in mathematical expression (3) and G.sub.p2(S) in mathematical expressions (10) and (11), each of which is a transfer function from the motor input torque to the motor speed, are compared, it can be seen that the characteristics of the two almost overlap with each other, and the error of the approximate model is small, and this approximate model can also be used for control.

(157) FIG. 16 shows characteristics when the vibration suppression control is disabled (K.sub.FB=0) for comparison with the first embodiment. In FIG. 16, the motor rotational speed corn, the relative torsional speed ?.sub.d and torsional torque T.sub.d of the elastic shaft, etc., each show a large vibration around 10 Hz near the resonant frequency, after a change in the torque command, wherein damping is slow.

(158) On the other hand, FIG. 17 shows a response when the vibration suppression control according to the first embodiment and the design method using the approximate model are employed. As compared with FIG. 16, vibration does not occur even when the torque command changes rapidly. Immediately after the start of acceleration at time instant 1 s, the motor speed ?.sub.m increases for a short period of time in order to generate a torsional phase of the elastic shaft corresponding to the input torque. However, when the torsional phase, namely, the transmitted torque T.sub.d, has reached a target value, then the motor speed W m returns to a normal line, and thereafter increases in conformance with the tire speed ?w. From this behavior, it can be confirmed that the vibration due to resonance is suppressed and the acceleration is stabilized. This is also true when the torque command returns to zero at t=2 s.

(159) However, when a disturbance force is applied to the vehicle body at t=4 s, the compensation torque component T.sub.Fcomp oscillates. Vibration occurs in the motor speed corn as well, although the amplitude of the vibration is small. The speed fluctuation is thus amplified by the vibration suppression control. The vibration component caused by this disturbance is a frequency component considerably lower in frequency than that in FIG. 16 and near the anti-resonant frequency of 1.5 Hz.

(160) The following two effects can be confirmed with reference to such change characteristics of the torque command and the disturbance torque. First, even when the vibration suppression control is configured by approximating FIG. 1 as shown in FIG. 2 like a two-inertia system, it is possible to produce an adequate effect of vibration suppression with respect to changes in the torque command. Second, it has a disadvantage of generating low-frequency vibrations near the anti-resonant frequency in response to disturbance torque. This means that it is required to modify the method for designing the compensation filter of mathematical expression (13) or add a disturbance suppression function. Therefore, the latter disturbance suppression function is proposed.

(161) <Behavior and Effects of Load Disturbance Torque Observer (Second Embodiment)>

(162) In FIGS. 16 and 17 shown in the previous section, only the estimation function of the disturbance torque observer in the configuration of FIG. 6 using the approximate model in FIG. 3 is enabled (K.sub.g?0). With reference to behavior of estimation of the estimated disturbance torque {circumflex over ()}T.sub.obs indicated by dashed-dotted lines in FIGS. 16 and 17, it is confirmed that the disturbance torque can be stably estimated, where a small component occurs at t=1 s and at t=2 s but vanishes soon, although there is a response delay when the disturbance torque is started and released at t=4 s and at t=5 s.

(163) As described above, the vibration caused by disturbance torque, which is a problem of vibration suppression control, is affected by the inertia of the vehicle to be a low frequency component. In order to produce a response enough to compensate for the low frequency component, K g is set. Therefore, it can be seen that even with the configuration of the second embodiment, the disturbance torque observer can perform a normal estimating action.

(164) <Behavior and Effects of Vibration Suppression by Disturbance Torque Observer (Third Embodiment)>

(165) Before describing effects of the third embodiment, the following describes examples of waveforms for explaining two types of problems to be solved.

(166) First, the following describes effects of backlash. When the gear backlash component (??.sub.BL?0) is set in the model of the actual plant under the conditions of FIG. 17 in which the first embodiment is employed, the characteristics vary as shown in FIG. 18. When the torque command changes, the vibration can be suppressed in the same manner as in FIG. 17. However, after the disturbance torque occurs at t=4 s, an abnormal vibration, in which hunting continues, occurs. This is because when the torque command is equal to zero, a backlash, namely, a special state, in which tooth faces of the gears are out of contact with each other, occurs. This causes a problem of continuous low-frequency vibration.

(167) Next, the following describes the effect of model errors. When the friction of the road surface is further reduced and only the tire coefficient is changed to 0.3 times (K.sub.Kt=0.3) with respect to the condition of FIG. 18, the characteristics vary as shown in FIG. 19. During the period from t=1 s to t=2 s, it is not in a backlash region, because the torque command is applied, but there is a problem of low frequency vibration due to model errors. Furthermore, when the torque command returns to zero at and after t=2 s, hunting occurs due to backlash with this disturbance as a vibration source.

(168) In summary, the systems of the first and second embodiments have problems of two types of low-frequency vibration phenomena, namely, the hunting phenomenon due to backlash, and the influence of model errors. These problems are addressed by the third embodiment.

(169) Also in FIGS. 18 and 19, only the estimation function of the disturbance torque observer is enabled. Although not yet used for control, the estimated disturbance torque {circumflex over ()}T.sub.obs contains not only the disturbance torque but also the vibration torque component described above. In view of the characteristics of estimation, it is expected that the vibration suppression control using the disturbance torque observer is effective.

(170) The following describes an example of behavior and effects of the third embodiment as compared with characteristics showing the above problems.

(171) First, FIG. 20 shows characteristics when the vibration suppression control system is switched from the first embodiment to the third embodiment under the same ideal plant conditions as in FIG. 17. With respect to changes in the torque command from t=1 s to t=2 s, similar stable characteristics are maintained. Furthermore, the problematic low-frequency vibration near anti-resonance from t=4 s to t=6 s is also suppressed. Therefore, it can be confirmed that the vibration suppression control of the present invention does not cause abnormal low-frequency vibrations.

(172) Next, under the conditions in which only backlash is set as in FIG. 18, stable characteristics are obtained with the system of the present invention as shown in FIG. 21. With respect to changes in the torque command from t=1 s to t=2 s, stable characteristics is maintained. Furthermore, hunting due to backlash that occurs after the input of the disturbance torque after t=4 s is suppressed.

(173) Finally, under the condition where both backlash and model errors exist as in FIG. 19, characteristics shown in FIG. 22 are obtained with the system of the present invention. The low-frequency vibration while the torque command is inputted from t=1 s to t=2 s, which is the issue in the configuration of FIG. 19, is suppressed significantly. No vibration occurs due to backlash after t=2 s. With reference to the estimated disturbance torque {circumflex over ()}T.sub.obs during this period, it can be inferred that the disturbance estimation function contributes to vibration suppression, because the disturbance estimation works in contrast to the situation where there is no model error. After t=4 s, stability is maintained as in FIGS. 20 and 21.

(174) <Behavior and Effects of Vibration Suppression Control where Time Matching with Speed Measurement is Added to Disturbance Torque Observer (Fifth Embodiment)>

(175) FIG. 23 shows an example of characteristics when a delay time in electric current control and speed measurement is simulated as LPF1 (T.sub.LPF1) under the same condition in which only backlash is set as in FIG. 18. The vibration suppression control remains the same as in the third embodiment, and LPF2 is set to no delay (T.sub.LPF2=0) because the time matching measure is not yet adopted on the observer side. In order to clarify the characteristics of the problem, the time constant of LPF3 inserted in the torque command input section is also changed to zero (T.sub.LPF3=10 ms.fwdarw.0 ms), and the torque command is rapidly changed stepwise. Since the effect of improving the characteristics appears when the torque command changes, the waveforms are drawn as enlarged in the time axis direction only during the period of t=0.5 s to 2.5 s. Since there is only a low frequency component at the time of disturbance torque, there is no difference in stability, which is omitted.

(176) In FIG. 23, there is a problem that an error occurs in the estimated torque of the observer due to the influence of the delay time in speed measurement.

(177) After rapid changes in the command at t=1 s and t=2 s, distortion and residual vibration of about one cycle appear in the pulse-like waveform of the estimated disturbance torque {circumflex over ()}T.sub.obs. Accordingly, the waveform of vibration suppression compensation T.sub.Fcomp after t=2 s does not immediately return to zero, and is distorted stepwise in a converging waveform due to an estimation error. As a result, this distortion is also superimposed on the waveform of the torque command T.sub.m that is outputted to the motor drive section.

(178) FIG. 24 shows characteristics when the compensation for the delay in speed measurement as shown in FIG. 9 is adopted to FIG. 23. Specifically, the delay time of LPF2 on the model side is set equal to the delay time of LPF1 on the speed measurement side (T.sub.LPF2=T.sub.LPF1=5 ms). With this time delay matching, the vibration components in the waveforms of the estimated disturbance torque {circumflex over ()}T.sub.obs and the vibration suppression compensation T.sub.Fcomp are suppressed, so that the output torque command T.sub.m has a smooth waveform containing no overshoot, no distortion, and no vibration. Therefore, it can be confirmed that the characteristics of the vibration suppression control can be improved by matching the motor-accelerating torque of the observer and the differential component of the measured speed in terms of time.

Problems in First to Fifth Embodiments

(179) (Method for Configuration of Observer, Combination with Speed Measurement System, and Time Matching Measure)

(180) The basic principles described in the first to fifth embodiments are shown with models and transfer functions based on a continuous data system. However, when it is put to practical use, it is required to be implemented to form a digital control. This causes some problems. To implement the system as a program for a digital arithmetic unit, etc., it is required to transform the system to a sampled data system suitable for digital control. When time is approximated to time values that are discrete by a sampling interval, the discretization causes errors. For speed measurement, a filter is used to suppress the effects of phase time difference and measurement noise. Since there is a time delay component due to the filter, an error occurs in the observer estimation due to time mismatching as compared with the speed on the model side with no delay. In particular, during transient response, the error becomes large, so that time matching measures are required.

(181) Although details are described below, examples of resonance characteristics are first shown in FIGS. 39, 40, and 41, to facilitate understanding of the problem. These are examples of resonance and its suppression effect when the torque command is changed in a trapezoidal shape. FIG. 39 (A) shows characteristics of acceleration/deceleration when no vibration suppression control is employed. FIG. 39 (B) is a partial view of FIG. 39 (A) enlarged in time. In FIG. 39 (A), (a) shows the torque command and the torsional torque T.sub.d of the driveline shaft, (b) shows the shaft torsional speed, and (c) shows the motor-accelerating torque component T.sub.mA.

(182) As compared with the data shown in the first to fifth embodiments, the torque command T.sub.ref_LPF is changed to a trapezoidal shape, but breakpoints of the trapezoid still behave as a vibration source to cause overshoots and residual vibrations as resonance phenomena. It can be seen that the steeper the change in the break point, the greater the amplitude of the vibration, which does not attenuate even during acceleration. In the sixth and following embodiments, this is stabilized as shown in FIG. 40 (sixth embodiment) and FIG. 41 (seventh embodiment). When it can be stably controlled, components hidden in the vibration become clear. The waveform of ??.sub.mW in FIG. 40 (b) shows a speed difference between both ends of the driveline mechanism (speed difference between the motor shaft and the tire axle), and corresponds to a time-differential component of the shaft torsional phase (shaft torsional speed), because backlash is not yet considered. When the transmitted torque of the elastic shaft is increased or decreased at a constant gradient, it is required to increase or decrease the shaft torsional phase, so that it can be seen that the amplitude of the shaft torsional speed is constant.

(183) (Countermeasures Against Backlash Elements in Driveline)

(184) Reduction gears are used in a driveline mechanism of a vehicle. Gears have play called backlash. This occurs in the vicinity of zero torque where the polarity of the motor torque switches between positive and negative, wherein the gear teeth are not meshed, so that the transmitted force, namely, the reaction force to the motor shaft, is also equal to zero. Therefore, if the rotational inertia of the motor is small, the motor speed rapidly increases even if the motor torque is not so large. At an end of a backlash period, the teeth of the gears collide with each other, causing an abnormal vibration and sound called rattling shock.

(185) Against this phenomenon, a countermeasure has been adopted, in which, when the motor torque command crosses zero, the rate of change of the motor torque command is reduced to lengthen the period of time during which the torque command is small, thereby allowing the teeth to come into contact with each other softly.

(186) In FIG. 41 (seventh embodiment), backlash is ignored in both the control and the actual vehicle. In contrast, FIG. 42 is presented for investigating the influence of addition of backlash only in the actual plant side without modification of the control system. In FIG. 42, (a) shows the shaft torsional torque T.sub.d that shows a distortion to stick to zero in the vicinity of the zero-crossing point, due to backlash. In FIG. 42, (b) shows the shaft torsional speed on which a pulse-like waveform, which does not appear in FIG. 41, is superimposed. For clearly indicating where in the pulse the backlash period is, a waveform indicated by a broken line is added as a supplement. Only during the backlash period, the waveform of the shaft torsional speed indicated by a solid line is traced, and except for the backlash period, the value is held. During the period when the solid line and the broken line overlap with each other, backlash is occurring.

(187) With reference to the enlarged view of FIG. 42 (B), the shaft torsional speed of (b) has a pulse-like waveform that rapidly increases immediately after the start of backlash and rapidly decreases after the end of backlash. Since there is no reaction force from the elastic shaft, the motor solely rapidly accelerates. When the teeth collide, the accelerated inertial energy is converted into elastic energy of torsion of the shaft, resulting in deceleration. As the amplitude of this pulse waveform increases, the relative speed between teeth at the end of the backlash increases, and the rattling shock also increases.

(188) Patent document 3 discloses a method of backlash control, which is characterized by estimating a period of occurrence of backlash by using a reference model.

(189) According to patent document 3, by increasing the torque command outside of the backlash period and suppressing the torque command to a low level only during the backlash period, it suppresses degradation of the response characteristics as a whole, and reduces the rattling shock.

(190) In the time-enlarged view of FIG. 42 (B), zero-crossing of the torque command T.sub.ref_LPF occurs around 1.5 s and around 2.1 s, wherein the enlarged range is selected so as to include two types, fast change and slow change. Due to fast and slow changes, a difference occurs in behavior of T.sub.m, which is the control output, in the vicinity of zero-crossing. When change of the torque command is gradual, such as around 1.5 s, the control output T.sub.m is throttled to around zero during the backlash, namely, during the period when T.sub.d is equal to zero, so as to produce an effect of backlash control that suppresses rapid changes in the shaft torsional speed shown in the second row.

(191) However, when the torque command changes rapidly, as at 2.1 s in the latter half, the control output T.sub.m is not sufficiently throttled, and the shaft torsional speed becomes large, namely, the motor acceleration becomes rapid, since the disturbance torque observer has a limit of response.

(192) In view of the foregoing, in order to reduce the rattling shock at the time of rapid torque change, which cannot be sufficiently suppressed only by adoption of the sixth and seventh embodiments, the eighth and ninth embodiments are presented to have an extended function of reducing a wide range of rattling shocks.

(193) (Limitation of Sampled Data System)

(194) The configurations of the first to fifth embodiments are each shown in the form of a continuous data system model. However, in recent years, a computer processor called a CPU (Central Processing Unit) is often used as a controller, where a control algorithm is implemented as a digital control handling discrete-time digital values.

(195) Digital control has the following limitations.

(196) (a) Sampled Data System (Discrete Time)

(197) Even a continuous input signal is converted to discrete time sample values and then handled. Internal state quantities are also updated with reference to sample timings. Execution of a program takes time, which causes a delay in an output signal by a maximum of one sampling.

(198) (b) Restrictions on Number of Significant Digits

(199) A quantity on a signal is also treated as an encoded digital value, which causes problems about the number of significant digits and resolution. A dynamic range also varies depending on an encoding method such as fixed point encoding method or floating point encoding method.

(200) (c) Discrete Calculation Error

(201) With a digital control based on a sampled data system, in order to obtain a result close to that of a continuous data system, there is a method of applying iterative operation such as the Runge-Kutta method to approximate an integral. Furthermore, for a configuration that has many integral elements and a feedback loop, there is also a method of transforming into a multivariable state equation or the like and solving a system of simultaneous differential equations. On the other hand, there is also a simple method for implementation using the backward difference method or the like although some errors occur.

(202) In the sixth to ninth embodiments, it is desired to realize a real-time control with a built-in CPU. Therefore, it is required to be implemented to have a simple algorithm and a short calculation time as much as possible. Accordingly, an integral is approximated to a simple backward difference, and a feedback loop is approximated by insertion of a sample delay, and convergence operation is thereby omitted. Therefore, there is a concern that a calculation error may increase with respect to a continuous data system.

(203) In the following embodiments, the foregoing is referred to as a method of transformation to sampled data system, a calculation error in sampled data system, etc.

Sixth Embodiment

(204) The following embodiments also employ the models, variables, and transfer functions, which are defined in the first to fifth embodiments. FIG. 25 is a block diagram showing a basic vehicle model composed of three kinds of inertial bodies (motor, tires, and vehicle body) and spring elements of a torque transmission mechanism (gears, and an elastic shaft).

(205) FIG. 25 differs from FIG. 1 in that the subtractor 10 subtracts the disturbance torque component (equivalent component obtained by conversion to motor shaft) T.sub.dist from the motor torque (output torque command) T.sub.m to output a quantity that is inputted to the subtractor 11. The other configuration is the same as in FIG. 1. Variables and constants in FIG. 25 are the same as those described with FIG. 1.

(206) The model G.sub.p(s) in FIG. 25 is approximated to a model shown in FIG. 26 in which a transfer function has a reduced order, as in the first embodiment (mathematical expressions (1) to (12) are adopted). In FIG. 26, the same parts as in FIG. 25 and FIG. 2 are denoted by the same reference numerals.

(207) FIG. 29 shows a disturbance torque observer constructed using the model of FIG. 26, as described below. The disturbance torque observer estimates the disturbance torque component T.sub.dist of FIG. 25, wherein {circumflex over ()}T.sub.obs and {circumflex over ()}T.sub.d are subtracted from AT m at the same point. Therefore, the estimated disturbance torque {circumflex over ()}T.sub.obs may be regarded as a component for correcting the shaft torsional torque component {circumflex over ()}T.sub.d of the model. In the configuration of FIG. 29, the estimated motor-accelerating torque is calculated as {circumflex over ()}T.sub.mA={circumflex over ()}T.sub.m?({circumflex over ()}T.sub.obs+{circumflex over ()}T.sub.d). The relationship between the estimated motor-accelerating torque {circumflex over ()}T.sub.mA and the estimated motor speed {circumflex over ()}?.sub.m is expressed by differentiation and integration as in mathematical expression (16).

(208) $\begin{array}{cc}{?}^{}{T}_{\mathrm{mA}}=\frac{d}{\mathrm{dt}}{(}^{?}{?}_m){,}^{?}{?}_m=?{(}^{?}{T}_{\mathrm{mA}}).Math.\mathrm{dt}& \left(16\right)\end{array}$

(209) In the following embodiments, examples of configuration are proposed for implementing the foregoing with a sampled data system.

(210) FIG. 27 shows an overall configuration of a continuous data system that is a base of the sixth embodiment. First, the following describes variables and element blocks in FIG. 27.

(211) [Description of Variables] T.sub.ref: an input torque command, which is a value of the shaft output torque of the motor requested by an upper command device, ?T.sub.comp: a compensation torque component, which is an output of the vibration suppression control (outputted from a vibration suppression control filter 150), T.sub.m: an output torque command of the control device, which is also an input to a disturbance torque observer 120. This torque is generated by the motor drive device in the subsequent stage. ?.sub.m: a rotational speed of the actual motor, ?.sub.m, t: a rotational phase and time of the actual motor, which are latched by an RD converter 130 at time instants of sampling, wherein the speed is calculated based on a time difference component by a speed calculation part 140 in the subsequent stage. ?.sub.m_det: a measured motor rotational speed calculated based on the measured values (?.sub.m_det, t_.sub.det) of (?.sub.m, t) by the speed calculation part 140. The sum of (1) a dead time from output of T.sub.m from the control device to torque generation in the actual vehicle, and (2) a dead time from actual rotational speed ?.sub.m to measured rotational speed ?.sub.m_det is described as L1 (delay block 1 is e.sup.?L1s). {circumflex over ()}T.sub.obs: a disturbance torque component estimated by the disturbance torque observer 120 (estimated disturbance torque), which is an estimate of T.sub.dist in FIG. 25, wherein disturbance forces applied to the vehicle body, such as T.sub.F, are converted and estimated herein, {circumflex over ()}?: an estimated motor speed outputted from a reference model (121) in the disturbance torque observer, {circumflex over ()}T.sub.mA: an estimated motor-accelerating torque outputted from the reference model (121) in the disturbance torque observer, {circumflex over ()}?.sub.m_dly: a signal component produced by delaying {circumflex over ()}?m by a delay 2 of e.sup.?L2s in a delay part 62, for matching with a delay 1 of e.sup.?L1s in the speed calculation part 140, and ??.sub.m: a speed deviation component produced by a subtractor 51 as a deviation between the estimated motor speed ({circumflex over ()}?.sub.m_dly) of the model and the measured motor speed (?.sub.m_det), wherein the speed deviation component is multiplied by an observer gain K.sub.g by a gain multiplier 43 to produce the estimated torque {circumflex over ()}T.sub.obs.

(212) [Description of Blocks] (a) Prefilter part (PRE-LPF) 100: a filter that removes high frequency components from an external torque command T.sub.ref, and contains a torque limiter that defines upper and lower limits. The output T.sub.ref_LPF is used as an input to vibration suppression control. (b) Plant (actual vehicle) 110: a plant of an actual vehicle corresponding to G.sub.p(S) in FIG. 25 and mathematical expression (3). Drive devices such as inverters are ignored. The output torque command T.sub.m is inputted, and then the motor rotational speed ?.sub.m is outputted, wherein the motor rotational speed ?.sub.m is time-integrated by an integrator 28 to determine a motor rotational phase ?.sub.m. (c) Disturbance torque observer 120 (T.sub.dist_OBS): a part of vibration suppression control, which is composed of a speed deviation calculation section (delay part 62, subtractor 51), which takes account of a vehicle model part (121) and time matching, and a feedback section based on the observer gain K.sub.g. (d) Vehicle model 121: a model part in the disturbance torque observer 120, which simulates the vehicle corresponding to FIG. 26. The torque command T.sub.m is inputted, and the motor rotational speed {circumflex over ()}?.sub.m corresponding to {circumflex over ()}G.sub.p(S) in mathematical expression (10) is outputted, and the estimated motor-accelerating torque {circumflex over ()}T.sub.mA corresponding to G.sub.TdWw2(s) in mathematical expression (12) is outputted. (e) RD converter 130: a measurement circuit for speed measurement, which outputs a rotational phase ?.sub.m_det using a resolver and a resolver/digital converter (RD converter). In speed measurement, both the phase ?.sub.m_det and time t_.sub.det are sampled simultaneously. (f) Speed calculation part 140: a part that calculates a measured motor speed based on a signal of the RD converter. (g) Vibration suppression control filter 150: a filter F.sub.comp(s) that calculates a vibration suppression control component ?T.sub.comp for suppressing resonance due to the elastic shaft, which corresponds to the bandpass filter of mathematical expression (13).

(213) Next, the following describes the configuration of FIG. 27. First, the prefilter part 100 removes a high frequency band from the input torque command T.sub.ref, and apply limitation with the upper and lower limits, to calculate T.sub.ref_LPF. The compensation torque ?T.sub.comp, which is produced by the vibration suppression control, is subtracted from T.sub.ref_LPF, to produce the control output torque T.sub.m. T.sub.m is also an input to the disturbance torque observer 120 in the vibration suppression control system.

(214) The motor speed is calculated based on the measured values (?.sub.m_det, t_.sub.det) of the rotational phase ?.sub.m and the time t by the speed calculation part 140. For example, the measured speed ?.sub.m_det is determined by dividing a phase difference from a past sample value by a time difference.

(215) Although the detailed configuration of the disturbance torque observer 120 (Tdist_OBS) is described below, the output of the disturbance torque observer 120 is the estimated component {circumflex over ()}T.sub.mA of the motor-accelerating torque that is used for vibration suppression control. The estimated component {circumflex over ()}T.sub.mA is caused to pass through the vibration suppression control filter 150 (F.sub.comp(s)) to produce a compensation torque ?T.sub.comp, which is subtracted from T.sub.ref_LPF to produce T.sub.m.

(216) FIG. 28 shows a control section that is produced by transforming the control section shown in FIG. 27 into a sampled data system. FIG. 28 shows the whole of the control section, wherein only the prefilter part 100 is shown in detail. The prefilter part 100 includes a low-pass filter K.sub.LPF that suppresses a high frequency band of the input torque command T.sub.ref, and is also provided with a torque limiter 101 (TLIM0) (first torque limiter) that defines a maximum value. FIG. 28 shows a simple example of configuration that is produced by transformation by the backward difference method, wherein a delay operator of a delay part 103 is represented by z.sup.?1, and a sample period thereof is represented by T.sub.c.

(217) The output of torque limiter 101 (T.sub.ref_LPF) is delayed by a delayer 103, and the output of delayer 103 is subtracted from the input torque command T.sub.ref by a subtractor 104, and the output of subtractor 104 is caused to pass through the low-pass filter K.sub.LPF, and is thereafter added to the output of the delayer 103 by an adder 105. The output of addition of the adder 105 is inputted to the torque limiter 101.

(218) In FIG. 28, the output T.sub.m of the vibration suppression control is produced by subtracting the compensation torque ?T.sub.comp, which is the output of the vibration suppression control filter 150, from the output T.sub.ref_LPF of the prefilter part 100. The output T.sub.m is also an input torque command to the disturbance torque observer 120. It is required to insert a delay z.sup.?1 into the feedback section, so that a delayer 161 is inserted in the subsequent stage of the vibration suppression control filter 150. As the number of delayers increases, errors increase. Therefore, the delayer 161 is inserted in this position in consideration of reduction of the number of delayers.

(219) FIG. 29 shows an example of configuration of the disturbance torque observer 120. FIG. 29 shows a base continuous data system model, which employs the reduced order model of FIG. 26. The model G.sub.p2(s) in FIG. 29 has the same configuration as the disturbance torque observer model {circumflex over ()}G.sub.PTmA2(S) according to the second embodiment shown in FIG. 6, where the delay part 62, subtractor 51, gain multiplier 43, and subtractor 44 are also shown.

(220) FIG. 30 shows a sampled data system produced by transformation from FIG. 29, showing an example of configuration in which time integration is replaced with integration by backward difference.

(221) FIG. 30 differs from FIG. 29 in that: the output ({circumflex over ()}T.sub.mA) of the subtractor 11 is caused to pass through an integral coefficient multiplier T.sub.c/TJ.sub.m and an integrating part 122, which composed of a delayer having a delay operator z.sup.?1, and an adder, to produce the estimated motor rotational speed {circumflex over ()}?.sub.m; the estimated shaft torsional speed {circumflex over ()}?.sub.d is caused to pass through an integration coefficient multiplier {circumflex over ()}K.sub.d.Math.T.sub.c, an integrating part 123, which is composed of a delayer having a delay operator z.sup.?1, and an adder, and a delayer 124 having a delay operator z.sup.?1, to produce an estimated shaft torsional torque {circumflex over ()}T.sub.d; the estimated shaft torsional torque {circumflex over ()}T.sub.d is caused to pass through the integral coefficient multiplier T.sub.c/TJ.sub.m, and an integrating part 125, which is composed of a delayer having a delay operator z.sup.?1, and an adder, to produce {circumflex over ()}?.sub.WM; and a delayer 126 having a delay operator z.sup.?1 is inserted in the subsequent stage of the gain multiplier 43.

(222) By subtracting the estimated value of the disturbance torque {circumflex over ()}T.sub.obs from the torque command inputted to the model, the speed deviation converges to decrease so that the disturbance torque and the estimated value match each other.

(223) The delay part 62 (e.sup.?L2s block) in FIG. 30 is inserted for time matching, as described below in detail with reference to FIG. 32.

(224) FIG. 31 shows another form of FIG. 30. The motor model part of {circumflex over ()}DG.sub.p2 in FIG. 30 may be implemented by using the second order transfer function of mathematical expression (12). Therefore, coefficients of a second order IIR filter 127 (Infinite Impulse Response Filter) are designed directly from mathematical expression (12) and implemented as {circumflex over ()}DG.sub.pTmA2_IIR2 ({circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block of the present invention). {circumflex over ()}?.sub.m, which is used for calculating the estimated disturbance torque {circumflex over ()}T.sub.obs, is produced by time-integrating the output component {circumflex over ()}T.sub.mA of the second order IIR filter 127 by an integral coefficient multiplier T.sub.c/TJ.sub.m and an integrating part 122.

(225) Referring back to FIG. 28, the torque command T.sub.ref is processed by the prefilter part 100 that is a first order LPF based on backward difference, to produce T.sub.ref_LPF whose rapid changes are suppressed. The prefilter part 100 is not required to perform a function to remove the resonant frequency component as a notch filter, and but removes high frequency components that cannot be compensated for by the vibration suppression control at the subsequent stage.

(226) The disturbance torque observer 120 receives input of the output torque command component T.sub.m, which is produced by subtracting the compensation torque component ?T.sub.comp of the vibration suppression control from the output T.sub.ref_LPF of the prefilter part 100, and the measured speed component ?.sub.m_det, which is calculated by the speed calculation part 140, and outputs the estimated motor-accelerating torque component {circumflex over ()}T.sub.mA that is calculated by the vehicle model. The vibration suppression control filter 150 calculates the vibration suppression compensation torque component ?T.sub.comp, wherein the vibration suppression compensation torque component ?T.sub.comp is subtracted from T.sub.ref_LPF to produce the torque command T.sub.m as a quantity that is produced by application of the vibration suppression control compensation, wherein the torque command T.sub.m is used as an output of the controller. In the drive system, this torque command T.sub.m is fed to the drive device at the subsequent stage, to cause the actual motor to generate a motor torque corresponding to the torque command T.sub.m.

(227) The vibration suppression control thus configured using the disturbance torque observer 120 is expected to produce three types of effects in accordance with the input signal, as already described in the third embodiment.

(228) The following discusses the transfer function from the torque command T.sub.ref_LPF to the output T.sub.m where the speed measurement side input to the disturbance torque observer 120 is fixed to zero and thereby invalidated. As the feedback section including the disturbance torque observer 120 and the vibration suppression control filter 150 is transformed into an integrated transfer function, this transfer function is equivalent to a kind of band elimination filter. Namely, this produces an effect of outputting a torque command produced by removing a torque component in the resonant band contained in the torque command T.sub.ref_LPF.

(229) On the other hand, the following discusses the effect of vibration suppression based on speed measurement where the torque command side input to the disturbance torque observer 120 is fixed at zero and thereby invalidated. Then, as a second effect, an effect of vibration suppression control based on speed differential feedback is produced, which is known as an effect of general PID control or the like. With reference to the example of FIG. 31, the disturbance torque observer 120 operates so that the speed deviation becomes zero, namely, the model speed and the measured speed become equal to each other. Since {circumflex over ()}T.sub.mA is the input signal to the integrator that generates the model speed {circumflex over ()}?.sub.m, {circumflex over ()}T.sub.mA corresponds to the differential of {circumflex over ()}?.sub.m, and may be regarded as an approximation of the differential component of measured speed under convergence behavior by the observer. Since {circumflex over ()}T.sub.mA is used for vibration suppression control via the vibration suppression control filter 150, this produces an effect similarly to a differential feedback type vibration suppression control based on speed measurement. This serves to suppress the resonant component caused by the disturbance forces applied to the vehicle body and driveline mechanism.

(230) Furthermore, the disturbance torque observer is configured to feed back the deviation component between the information from the reference model and the information from the speed measurement to the model input, so that even if there is a difference in parameters between the reference model and the actual vehicle, this produces an effect of suppressing an error component resulting from the difference. This effect is a third effect, wherein robustness is ensured to suppress deterioration of performance of the vibration suppression control even if errors or fluctuations occur in parameters.

(231) FIG. 32 shows a configuration of the speed measurement section (RD converter 130 and speed calculation part 140) and the section that calculates the deviation ??.sub.m between the estimated speed {circumflex over ()}?.sub.m and the detected speed ?.sub.m_det, which is used in the disturbance torque observer. The delay block e.sup.?L2s (delay part 62) corresponding to the delay time L2 is inserted on the estimated speed ??.sub.m side for time matching.

(232) Although omitted in FIGS. 27 and 28, many delay components exist in this control system. A calculation time is required until a control output is produced in response to an interrupt signal from the CPU. There is also a delay in electric current control and others in the drive device at the subsequent stage. Furthermore, in a configuration in which the speed is measured using a position sensor, it is required to calculate the speed using the phase difference in a certain amount of time difference, which causes a delay in measurement. If an LPF is inserted for noise removal, this adds a further delay component. In FIG. 27, the delay time due to speed measurement is represented by Ln, and the sum of the delay times including others is represented by L1.

(233) On the other hand, since the model section of the disturbance torque observer calculates the model using sample values of the torque command, the estimated speed of the model can be regarded as a component at a sample time instant. Therefore, if the deviation is calculated without correction, the deviation is produced as a difference between the components shifted in time by the time L1 from each other. This time mismatch causes an error during transient response.

(234) In view of the foregoing, in calculation of the speed deviation of the disturbance torque observer as shown in FIG. 32, for matching with the delay time L1, the delay block e.sup.?L2s corresponding to the time L2 equal to the delay time L1 is inserted to the model side. Regarding the correction for delay times, a delay component due to electric current control from an interrupt time instant to a phase measurement time instant, etc., and a delay component in the speed measurement calculation section are shown separately. The calculation time and the response time of the electric current control are relatively short and vary little, but the speed measurement delay varies depending on the calculation method, LPF, etc. This is because these are discussed separately. The following proposes a time matching method adapted to the speed measurement method.

(235) In FIG. 32 (a), the speed measurement section (RD converter 130) samples the rotational phase ?.sub.m and its corresponding time t by a measurement circuit, and reads values by the CPU as the phase ?.sub.m_det and time t_.sub.det. Then, a delayer 141 having a delay operator z.sup.?n delays the phase ?.sub.m_det, and a subtractor 142 subtracts a value of ?.sub.m_det n-samplings before, which is outputted from the delayer 141, from the value of ?.sub.m_det at the current time. Also, a delayer 143 having a delay operator z.sup.?n delays t_.sub.det, and a subtractor 144 subtracts a value of t_.sub.det n-samplings before, which is outputted from the delayer 143, from the value of t_.sub.det at the current time.

(236) Then, a calculator 145 divides a phase difference, which outputted from the subtractor 142, by a time difference, which is outputted from the subtractor 144, to calculate the measured speed ?.sub.m_det. Here, the z.sup.?n block corresponds to n-cascaded z.sup.?1 blocks. With the z.sup.?n block, the difference between the value at the current time and the value n-samplings before is calculated.

(237) FIG. 32 shows an example of configuration of the deviation calculation section (subtractor 51) for calculation of a deviation between the model and the speed measurement calculation section (140), and the time matching section e.sup.?L2s (delay part 62). The delay time due to the current control of the motor drive device is assumed to be substantially constant, and is compensated for by ?-time delay calculations by a delayer 65 (z.sup.??). In the subsequent stage, correction is made for the delay time due to speed measurement. There are various methods for speed measurement. When the phase difference at n-sample interval is used as shown in FIG. 32 (a), a delay time equivalent to that in speed measurement can be generated by inserting (n+1) samples moving average calculation.

(238) The reason why the multiple (n-times) sampling interval is set for speed measurement is that the measured phase data contains measurement errors and noise, and the accuracy of speed measurement is to be improved by reducing the noise component ratio (measurement error) by increasing the phase difference and time difference for difference calculation. However, increasing the number n raises a problem of an increase in time delay (expressed as e.sup.?Lns) in exchange for accuracy. Therefore, a delay corresponding to Ln is also inserted for the estimated speed on the disturbance torque observer side for time matching.

(239) FIG. 33 (b) illustrates an equivalent delay time by the moving average calculation in FIG. 33 (a). When n=4, the measured speed is calculated based on the phase difference of 4?T.sub.c between sample timings d0 (n=0) and d4 (n=4), so that the delay time is equal to (?T.sub.Ln=2?T.sub.c), where a time instant of measurement is defined as a central time instant of the measurement time period. Therefore, when a moving average of (n+1) times is inserted into the model side, in case of (n+1)=5, the average value ma(5) of d0 to d5 is outputted, and this central time instant defines a delay time (2?T.sub.c) equivalent to the delay in speed measurement.

(240) Inserting a delay in the model side for time matching may seem to reduce the effect of vibration suppression. However, the vibration suppression to the torque command, which is required to respond quickly, employs ?T.sub.mA at the preceding stage of the delay block, and thereby is not affected by the time matching. The speed deviation information containing the delay is only used for estimating the disturbance torque that changes relatively slowly, so that the performance is not adversely affected so much.

(241) The speed measurement section in FIG. 32 (a) is based on the assumption that the phase measurement is implemented by a CPU interrupt signal and software, etc., and the interrupt interval T.sub.c, which is constant, contains a variation of ?.sub.T. Therefore, a time instant is measured simultaneously with measurement of the phase, for calculating an accurate time difference. If the speed measurement is implemented as a digital logic circuit, the sample time instant t_det can be accurately synchronized with the sample period T.sub.c, so that the time difference may be replaced with a constant sample period of n.Math.T.sub.c as shown in FIG. 32 (b).

(242) In FIG. 32(b), the phase difference outputted from the subtractor 142 is divided by the constant sample period n.Math.T.sub.c by a divider 146 to output the measured speed ?.sub.m_det

(243) The speed measurement section in FIG. 32(c) is an example in which the time difference and the filter are configured by a technique called incomplete differentiation or pseudo differentiation. By a first order filter by backward difference (first order delay filter based on sampled data system), a component before being added to a previous value is extracted, and divided by time T.sub.c, to produce a component based on combination of speed measurement by time difference and first order filtering (LPF). On the other hand, by using a first order filter having the same configuration on the model side for time matching, it is possible to insert a delay equivalent to that on the speed measurement side.

(244) In FIG. 32 (c), the first order filter based on backward difference on the speed measurement side includes: a subtractor 152 that subtracts the output of a delayer 151 from the phase measured by the RD converter 130 (speed measurement circuit); a multiplier 153 having a filter coefficient K.sub.LP, through which the output of the subtractor 152 passes; and an adder 154 that sums the output of the multiplier 153 and the output of the delayer 151. The delayer 151 delays the output of the adder 154.

(245) A divider 155 divides the output of the multiplier 153, which is before being added to the previous value by the adder 154, by the time T.sub.c.

(246) The first order filter based on backward difference on the model side includes: a delayer 65 that delays ??.sub.m by a-times delay calculation; a subtractor 163 that subtracts the output of the delayer 162 from the output of the delayer 65; a multiplier 164 having a filter coefficient K.sub.LP, through which the output of the subtractor 163 passes; and an adder 165 that sums the output of the multiplier 164 and the output of the delayer 162. The delayer 162 delays the output of the adder 165.

(247) In the case of backward difference, the multiplication coefficient K.sub.LP of the multipliers 153 and 164 is set as K.sub.LP=T.sub.c/(T.sub.c+T.sub.LPF), where T.sub.LPF is a filter time constant.

(248) The sixth embodiment described above produces the following effects. (a) The accuracy of calculation of the reference model can be improved. (b) Since various time matching measures are made with respect to speed measurement and LPF, the accuracy of the deviation (difference) between the reference model and the speed measurement is improved, and the accuracy of disturbance torque estimation is improved.

(249) In this way, it is possible to improve the accuracy and response performance of the disturbance torque observer, and thereby improve the stability of vibration suppression control using the disturbance torque observer.

Seventh Embodiment

(250) FIG. 34 shows a seventh embodiment that employs the system using the deviation of the motor-accelerating torque as in the third and fourth embodiments. FIG. 34 shows an overall configuration of a continuous data system. The continuous data system is transformed into a sampled data system, which has the same overall configuration as in FIG. 28. In this embodiment, only the disturbance torque observer and the speed calculation are modified. In FIG. 34, the same parts as in FIG. 27 are denoted by the same reference numerals.

(251) FIG. 34 differs from the example of configuration of the sixth embodiment in that the input to the deviation part (subtractor 51) of the disturbance torque observer 120 is modified to a difference {circumflex over ()}T.sub.mA between the estimated motor-accelerating torque component {circumflex over ()}T.sub.mA_dly and the time-differential component T.sub.mA_det calculated by a speed calculation part 141.

(252) The deviation component {circumflex over ()}T.sub.mA of the motor-accelerating torque, which is the output of the subtractor 51, is finally returned to the speed deviation component ??.sub.m by time integration (integrator 52), so that the disturbance torque observer can be configured as in the sixth embodiment. Thereby, the output of the vehicle model 121 in the disturbance torque observer 120 can be used for both vibration suppression control and disturbance torque estimation. This eliminates the need to calculate the estimated motor speed {circumflex over ()}?.sub.m.

(253) In FIG. 34, the prefilter part 100 shown in FIGS. 27 and 28 is omitted for illustration purposes.

(254) FIG. 35 (a) shows an example of configuration produced by transforming the disturbance torque observer 120 of FIG. 34 into a sampled data system, and corresponds to FIG. 30 of the sixth embodiment. Since the estimated motor speed ??.sub.m is not required, the number of items corresponding to integration can be reduced by moving the integrating parts (122, 125), which are positioned at the subsequent stage of the integral coefficients of ?TJ.sub.m and {circumflex over ()}TJ.sub.WM in the model {circumflex over ()}DG.sub.p2 shown in FIG. 30, to a position subsequent to the subtractor 27 in the model {circumflex over ()}DG.sub.p1, and combining the integrating parts into a single integrating part 128.

(255) The difference output from the subtractor 51 is caused to pass through an integration coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m and the integrating part 122, which is composed of a delayer having a delay operator z.sup.?1, and an adder, and is thereafter inputted to the gain multiplier 43, to estimate the disturbance torque.

(256) FIG. 35 (b) corresponds to FIG. 31 of the sixth embodiment, wherein the integration (integration coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m and integrating part 122) in the model {circumflex over ()}DG.sub.p2 is moved to the subsequent stage of the deviation calculation by the subtractor 51, and accordingly, the model {circumflex over ()}DG.sub.p2 of FIG. 31 is simply implemented by only a second order IIR filter 127 (DG.sub.pTmA2_IIR2) ({circumflex over ()}T.sub.m-{circumflex over ()}T.sub.mA transformation block of the present invention).

(257) The reason why the output of the vehicle model is set to the estimated motor-accelerating torque {circumflex over ()}T.sub.mA in the seventh embodiment is that it is desirable that the two integral terms {circumflex over ()}TJ.sub.m and {circumflex over ()}TJ.sub.WM are moved to the subsequent stage of the difference calculation and thereby reduced to one integral term.

(258) For digital calculation of the sampled data system, it is expected that as the number of integrators decreases, errors decrease, and the accuracy gets enhanced.

(259) FIG. 36 shows details of the difference calculation of the motor-accelerating torque and the configuration of the part for integrating the difference in the seventh embodiment. FIG. 36 (a) corresponds to FIG. 32 (a) of the sixth embodiment, in which the output from the model side is changed to the motor-accelerating torque only, and on the other hand, a time differentiation is added to the speed measurement side while being approximated to a time difference calculation.

(260) The speed measurement side of FIG. 36 (a) differs from that of FIG. 32 (a) in that the time differentiation is added. The measured motor rotational speed ?.sub.m_det outputted from a calculator 145 is caused to pass through a delayer 132 having a delay operator z.sup.?1; a subtractor 133 calculates a difference between the output of the delayer 132 and ?.sub.m_det; and the difference outputted from the subtractor 133 is caused to pass through a differentiator 134 having a coefficient TJ.sub.m/T.sub.c. The addition of the time differential calculation to the speed measurement side causes an increase in the delay time component. In order to compensate for this increase, an output of a moving average calculation part 66 is caused to pass through a two-samples moving average calculation part 67 to obtain T.sub.mA_dly, and the output of the subtractor 51 is caused to pass through the integration coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m and the integrating part 122 composed of a delayer having a delay operator z.sup.?1, and an adder, to obtain ??.sub.m.

(261) Although not shown, the calculation part for ?.sub.m_det in FIG. 36 (a) may be replaced with a configuration corresponding to FIG. 32 (b) of the sixth embodiment. Namely, the RD converter 130, the delayers 141 and 143, the subtractors 142 and 144, and the calculator 145 in FIG. 36 (a) may be replaced with the RD converter 130, the delayer 141, the subtractor 142, and the divider 146 in FIG. 32 (b).

(262) FIG. 36 (b) shows a configuration in which an IIR filter (first order filter with a filter coefficient K.sub.LP) is employed for filtering after speed measurement and time differentiation as shown in FIG. 32 (c). Since the IIR filter is expected to produce an LPF effect, and some noise is allowed to occur in speed measurement, the sample interval for speed measurement is set to n=1.

(263) FIG. 36 (b) differs from FIG. 32 (c) in that a differentiating function is provided between the RD converter 130 and the subtractor 152, wherein the differentiating function is composed of a delayer 135 having the delay operator z.sup.?1, a subtractor 136 for calculating a deviation from the output of the delayer 135, and a multiplier 137 for multiplying the output of the subtractor 136 by a coefficient 1/T.sub.c. In order to cancel this differentiation, an integral coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m and an integrator 122 are provided on the output side of the subtractor 51.

(264) Furthermore, the divider 155 in FIG. 32(c) is a part of the speed calculation section, and is therefore moved as an element 137 to a position immediately subsequent to the subtractor 136.

(265) While the speed measurement side of FIG. 36 (a) employs the delayer 132 for difference calculation in the time differentiation section, a function of the first order delay filter is employed instead in FIG. 36 (b).

(266) Although the first order delay filter serves originally for the speed, the time differential component of the speed can be extracted by extracting {circumflex over ()}T.sub.mA_det from the input part of the integrating part inside the filter. In other words, the function of the delayer 132 is included in the delayer 151, resulting in a slightly simplified configuration.

(267) On the other hand, in the model side of FIG. 36 (b), the input signal itself is changed from the model estimated speed {circumflex over ()}?.sub.m to its differential component, the motor-accelerating torque {circumflex over ()}T.sub.mA. Others are the same as in FIG. 32 (c), where as in the sixth embodiment, the first order delay filter is inserted, and the moving average calculator 67 is provided subsequent to the delayer 65 for matching with an increase in the delay time in the speed measurement side which is caused by the differential calculation.

(268) As described above, according to the seventh embodiment, various time matching measures are made with respect to speed measurement and LPF as in the sixth embodiment, so that the accuracy of the deviation (difference) between the reference model and the speed measurement is improved, and the accuracy of disturbance torque estimation is improved.

(269) In this way, it is possible to improve the accuracy and response performance of the disturbance torque observer, and thereby improve the stability of vibration suppression control using the disturbance torque observer.

Eighth Embodiment

(270) In order to suppress the rattling shock due to gear backlash, it is desirable to reduce the motor torque during the backlash period, to suppress rapid changes in speed. However, if the motor torque is limited to zero, the backlash phase does not change, so that it takes longer time to eliminate the play. Therefore, it is desirable to accelerate the motor at an upper limit speed corresponding to an allowable shock level, and pass through a condition of backlash as quickly as possible, and thereby shorten the period during which the torque command is limited. For this purpose, it is required to accurately estimate the start and end of backlash.

(271) In view of the foregoing, with respect to the configurations of the sixth and seventh embodiments, the eighth embodiment is additionally provided with a function of estimating the backlash period and a function of suppressing the torque command to a small value during the backlash period.

(272) FIG. 37 shows an example of overall configuration of the eighth embodiment, and FIG. 38 shows an example of configuration of a backlash period detection section 200. The elements already described in the sixth and seventh embodiments are the speed calculation part 140, the disturbance torque observer (Tdist_OBS) 120, the vibration suppression control filter 150 (F.sub.comp), etc. Furthermore, as indicated by the one-dot chain line in the disturbance torque observer 120 in FIGS. 27 and 34, a function is added to output the component (Tm-{circumflex over ()}T.sub.mA) as the estimated shaft torsional torque {circumflex over ()}T.sub.d, and is used for estimation.

(273) In FIG. 37, a compensation torque subtractor 201 (subg) is provided for subtracting the compensation torque component ?T.sub.comp for vibration suppression from the output of the adder 105 in the prefilter part 100.

(274) On the output side of the compensation torque subtractor 201, torque limiters are provided for limiting the output torque command T.sub.m, wherein a first torque limiter 101 (TLIM0) has a first torque limit value, and a second torque limiter 102 (TLIM1) has a second torque limit value that has a narrower width between upper and lower limits than the first torque limit value.

(275) On the output side of the torque limiters 101 and 102, there is a switch swA for selecting the output of the torque limiters 101 and 102, and when the backlash period detection section 200 described below detects backlash, selecting the output of the second torque limiter 102.

(276) The output (T.sub.m) of the switch swA is added by an adder 108 (addg) to the pre-delay compensation torque component ?T.sub.comp directly outputted from the vibration suppression control filter 150, and the output of addition of the adder 108 is inputted to a delayer 103 that is used for holding the previous value.

(277) The disturbance torque observer 120 receives input of the output torque command T.sub.m limited by the torque limiter selected by the switch swA and the motor rotational speed ?.sub.m_det measured by the speed calculation part 140, and outputs the estimated motor-accelerating torque component {circumflex over ()}T.sub.mA, and the estimated shaft torsional torque {circumflex over ()}T.sub.d that is the component of T.sub.m-{circumflex over ()}T.sub.mA.

(278) The backlash period detection section 200 receives input of the output torque command T.sub.m outputted from the torque limiter selected by the switch swA and the estimated shaft torsional torque {circumflex over ()}T.sub.d outputted from the disturbance torque observer 120, estimates the backlash period, and outputs a logic signal S_BL (backlash detection signal) indicating the status of the backlash period.

(279) When the logic signal S_BL is used for manipulation of the torque command, it corresponds to a feedback signal. Therefore, a backlash detection signal S_BLz, which is produced by delaying the input signal by one sampling by a delayer 202, is used as an operation signal for the switch swA.

(280) In this embodiment, the backlash detection signal S_BLz is configured to output 1 during the backlash period, so that the switch swA selects a =1 side, namely, selects the torque limiter 102 having a smaller width between upper and lower limits. This limits the magnitude of the torque command during the backlash period to prevent rapid acceleration of the motor.

(281) FIG. 38 shows a main part of the backlash period detection section 200, which includes: a switch swB that is fixed to a =d side to receive input of the estimated torsional torque {circumflex over ()}T.sub.d; a divider 210 (torque-to-phase transformation section) configured to perform transformation into an estimated shaft torsional phase {circumflex over ()}?.sub.d; a backlash start timing detection section 220 configured to detect a zero cross point of the estimated shaft torsional phase ({circumflex over ()}?.sub.d) as a start timing of the backlash period; a torsional speed estimation section 230 configured to estimate the shaft torsional speed {circumflex over ()}?d_divTd by time-differentiating the estimated shaft torsional phase {circumflex over ()}?.sub.d; a speed change estimation section 240 configured to estimate a change component {circumflex over ()}?d_.sub.BL of the motor speed during the backlash period by time-integrating the output torque command T.sub.m in FIG. 37 by a time constant {circumflex over ()}TJ.sub.m equivalent to the rotational inertia of the motor; a torsional displacement estimation section 250 configured to calculate an estimated phase change amount {circumflex over ()}??.sub.BL corresponding to backlash by: calculating by an adder 251 a sum of the shaft torsional speed, which is estimated by the torsional speed estimation section 230, an initial torsional speed {circumflex over ()}?d_.sub.ini, which is stored in a latch circuit sh1 at the start timing of the backlash period detected by the backlash start timing detection section 220, and the speed change component {circumflex over ()}?d_.sub.BL during the backlash period, which is estimated by the speed change estimation section 240; and time-integrating the sum; and a backlash end detection section 260 configured to detect an end of the backlash period by comparing the phase change amount ??.sub.BL, which is estimated by the torsional displacement estimation section 250, with an absolute value of backlash phase width ?.sub.BL and a margin width ?? as set values; and wherein the backlash period is detected based on the backlash start timing (trigger signal E_Set) detected by the backlash start timing detection section 220 and the backlash end (S_Rst) detected by the backlash end detection section 260.

(282) Next, the following describes details of FIGS. 37 and 38. The switch swB in FIG. 38 is fixed to the =d side in the eighth embodiment, and is fixed to a =r side in the ninth embodiment. Accordingly, in the eighth embodiment, {circumflex over ()}T.sub.d is used as an input to the shaft torsional phase estimation calculation (divider 210).

(283) A backlash period prediction section is divided into two sections, the backlash start timing detection section 220 and the backlash end detection section 260. Based on the detection signals (E_Set, S_Rst) indicating the start timing and end, the logic signal S_BL indicating the status of the backlash period is outputted by a flip-flop sr1 composed of an SR-FF (set-reset flip-flop). In the shown example, it is configured to output =1 during the backlash period. Next, the following describes configuration of the backlash start timing detection section 220. {circumflex over ()}T.sub.d obtained by the disturbance torque observer 120 in FIGS. 27 and 34 corresponds to a reaction force from the elastic shaft, and is therefore converted to the shaft torsional phase {circumflex over ()}?.sub.d by dividing by the stiffness coefficient K.sub.d in the divider 210 (torque-to-phase converter). The backlash start timing detection section 220 detects the zero cross timing at which the polarity of the phase {circumflex over ()}?.sub.d switches between positive and negative, and outputs the start timing in the form of trigger signals. The trigger signals have two types according to the direction of phase change, wherein E_For is outputted for the direction from negative to positive, and E_Rev is outputted for the direction from positive to negative. These signals are combined into the single backlash start timing trigger signal E_Set by a logical sum circuit 221 (OR), and outputted from the backlash start timing detection section 220. This start timing is inputted and used as a trigger signal for the flip-flop sr1 (SR-FF). Furthermore, for detecting the end of the backlash, information on the direction of change in the phase is required. Therefore, the E_For and E_Rev trigger signals are latched, and the status signal S_FR indicating the polarity of the direction is also outputted.

(284) Next, the following describes a method for detecting the end of backlash. The component {circumflex over ()}T.sub.d cannot be used for this purpose. The component {circumflex over ()}T.sub.d is constantly compensated by the vibration suppression control based on disturbance estimation by the disturbance torque observer, so that the motor-accelerating component during the backlash period is also compensated to change the output torque command T.sub.m. In other words, since {circumflex over ()}T.sub.d also changes rapidly, it becomes impossible to accurately estimate the shaft torsional phase based on {circumflex over ()}T.sub.d. Therefore, estimation of the end of backlash is implemented by combination with another prediction method. The configuration thereof is depicted at the bottom of FIG. 38.

(285) If there is no backlash and vibration is suppressed as in the waveform of the shaft torsional speed ??.sub.mW shown in FIG. 40 (b), the shaft torsional speed becomes almost constant when the polarity changes while the shaft torque changes at a constant gradient. Since this speed is required for estimating the backlash period, a function is added for estimating the shaft torsional speed from the component {circumflex over ()}T.sub.d.

(286) For this purpose, the shaft torsional phase {circumflex over ()}?.sub.d, which is produced by conversion from the component {circumflex over ()}T.sub.d by the divider 210, is used, and time-differentiated by the torsional speed estimation section 230, to calculate the shaft torsional speed {circumflex over ()}?d_divTd.

(287) This estimated shaft torsional speed is held as the initial torsional speed value {circumflex over ()}?d_.sub.ini by the backlash start timing trigger signal E_Set outputted from the backlash start timing detection section 220, using the latch circuit sh1.

(288) The torsional speed estimation section 230 is composed of a delayer 231, a subtractor 232 and a divider 233 for time differentiation.

(289) However, since the torque command T.sub.m on the motor side changes even during the backlash period, the speed change component {circumflex over ()}??d_.sub.BL is also estimated by time-integrating T.sub.m with the time constant {circumflex over ()}TJ.sub.m of the motor.

(290) The time integration with the time constant TJ.sub.m is performed by an integration coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m and an integrator 241 composed of a delayer having a delay operator z.sup.?1 and an adder. The speed change component {circumflex over ()}??d_.sub.BL is reset to zero by a switch sw3, which is switch-controlled by the backlash detection signal S_BLz estimated at the previous sampling timing until start of the backlash period. During the backlash period, the switch sw3 is switched to the adder side to the integrating part 241 to estimate the change component only.

(291) Then, the change component {circumflex over ()}??d_.sub.BL is added and corrected by the adder 251 to the initial speed {circumflex over ()}?d_.sub.ini latched by the latch circuit sh1, to produce a quantity that is regarded as the shaft torsional speed {circumflex over ()}?d_.sub.BL during the backlash period. Finally, in the torsional displacement estimation section 250, the shaft torsional speed {circumflex over ()}?d_.sub.BL is time-integrated to estimate the phase change amount {circumflex over ()}??.sub.BL corresponding to the backlash. This time integration is performed by a multiplier 252 with the sample period T.sub.c, and an integrator 253 composed of a delayer having a delay operator z.sup.?1 and an adder.

(292) The initial value of the phase change amount {circumflex over ()}??.sub.BL at the start of backlash is also reset to zero by a switch sw4 whose switching is controlled by the backlash detection signal S_BLz. During the backlash period, the switch sw4 is switched to the adder side to the integrating part 253 to estimate the phase change.

(293) The integral coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m, the integrating part 241, and the switch sw3 constitute the changing speed estimation section 240. The adder 251 corresponds to a compensating section for correcting the initial speed by the change component. In the position subsequent to the adder 251, the multiplier 252, the integrator 253, and the switch sw4 constitute the torsional displacement estimation section 250.

(294) Next, the following describes configuration of the backlash end detection section 260.

(295) The direction (positive/negative signs, positive/negative polarity) of the phase displacement to be estimated depends on the positive/negative polarity (S_FR) of the initial shaft torsional speed. Accordingly, a reference phase to be compared for determination of the end of backlash is required to be shifted depending on the positive/negative polarity. In view of the foregoing, reference phase setting parts 261p and 261n are provided for setting two kinds of determination reference phases in accordance with the positive/negative polarity. Switches sw2f and sw2r are switch-controlled by the status signal S_FR outputted from the backlash start timing detection section 220, to shift the determination reference phases, which are latched by latch circuits sh2f and sh2r at the timing of the backlash start timing trigger signal E_Set.

(296) A determination phase width ?p as a reference, which is latched by the latch circuit sh2f, is inputted to a b input terminal of a comparator cmpf. This is compared with the estimated phase change amount ??.sub.BL inputted to an a input terminal, to detect a state of ({circumflex over ()}??.sub.BL>?p).

(297) A determination phase width ?n as a reference, which is latched by the latch circuit sh2r, is inputted to an a input terminal of a comparator cmpr. This is compared with the estimated phase change amount {circumflex over ()}??.sub.BL inputted to a b input terminal, to detect a state of (?n>{circumflex over ()}??.sub.BL).

(298) Outputs of determination of the comparators cmpf and cmpr are caused to pass through the logical sum circuit 262 to produce the backlash end signal S_Rst, and reset the flip-flop sr1.

(299) In the reference phase setting parts 261p and 261n, a reference phase width of backlash is set as an unsigned absolute value ?.sub.BL, and a determination value is set by adding the margin width ?? and then setting the positive/negative sign depending on the direction of change. Furthermore, even during the backlash period, the polarity of the torque command T.sub.m may change to reverse the direction of rotation. Accordingly, for the reverse direction, the determination level is set to about the margin width ?? close to zero, thereby making it possible to output the end of backlash immediately in response to reverse. The determination phase widths ?p and ?n are compared with the estimated phase change amount {circumflex over ()}??.sub.BL to determine the end, and the signal S_BL of SR-FF (flip-flop sr1) is reset.

(300) The above is an example of configuration of the backlash period estimation section.

(301) The reference phase setting parts 261p and 261n, the switches sw2f and sw2r, the latch circuits sh2f and sh2r, the comparators cmpf and cmpr, and the logical sum circuit 262 constitute the backlash end detection section 260.

(302) The flip-flop sr1 outputs the backlash detection signal S_BL during the period from being set by the backlash start timing trigger signal E_set to being reset by the backlash end signal S_Rst.

(303) The estimated phase change amount {circumflex over ()}??.sub.BL is a change amount of the difference between the motor phase and the tire phase from the start of the backlash, and corresponds to an estimated phase of gear backlash play. When the play phase reaches the set backlash phase (?p, ?n), the end of the backlash period is determined by the comparators cmpf, cmpr and logical sum circuit 262.

(304) Referring back to FIG. 37, the following describes a method of limiting the torque command based on the backlash detection signal S_BL.

(305) There are two types of upper and lower limit blocks in the prefilter part 100. The first upper and lower limit block TLIM0 (torque limiter 101) is a conventional one, and the other second upper and lower limit block TLIM1 (torque limiter 102) serves for limitation during the backlash period and sets a torque width (torque limit value) to a second torque limiter value smaller than the first upper and lower limit block TLIM0 (torque limiter 101). The switch swA is switched to a backlash limit side (TLIM1 side) only when the backlash detection signal S_BLz is indicating the backlash period. This limits the magnitude of the torque command during the backlash period, and thereby prevents acceleration of the motor.

(306) However, if the compensation component ?T.sub.comp of the vibration suppression control is subtracted at the subsequent stage of the upper/lower limit block, the compensation component ?T.sub.comp is not subject to this limiting function. Therefore, the subtracting compensation part (compensation torque subtractor 201) is moved to the preceding stage of the limiter. With this configuration, when the switch swA is switched back from the backlash side (=1) to the normal side (=0), the output of the prefilter part 100 changes rapidly, thereby causing resonance.

(307) Therefore, in order to ensure a bumpless feature, a system is adopted in which the compensation component ?T.sub.comp is subtracted at subg (compensation torque subtractor 201) and the same compensation component ?T.sub.comp is added at addg (adder 108) immediately before holding of the previous value (delayer 103).

(308) The foregoing is an example of configuration of the detection of the backlash period and the method of limiting the torque command during the backlash period. The torque limitation during the backlash period does not need to be activated in all situations where the torque crosses zero, specifically, in situations where the rate of change of the torque command inputted from the outside is gradual. The vibration suppression control with the disturbance torque observer also operates to limit the torque command during the backlash period. Therefore, it is sufficient to cause the limitation by the backlash detection signal S_BL and TLIM1 (torque limiter 102) to be activated only when the limitation by the vibration suppression control is inadequate.

(309) Next, the following describes the principles of the phase estimation. As described above, in the systems to which the sixth and seventh embodiments are applied, {circumflex over ()}T.sub.d cannot be used to detect the end of backlash. Therefore, since the combined rotational inertia of the tires and the vehicle body is large, and the torque command is also near zero, it is assumed that a speed change of the tire side during a short time is small, and the method described above is adopted.

(310) If the rotational speeds of both ends of the gearing can be measured, the speed difference ??.sub.mW(t) is calculated based on the motor side speed ?.sub.m(t) and the tire side speed ?.sub.w(t) as in mathematical expression (17), and the relative phase ?.sub.BL(?t) between the gear teeth during the backlash period can be calculated by time integration for the elapsed time ?t from the backlash start time t0 as in mathematical expression (18).

(311) $\begin{array}{cc}?{?}_{\mathrm{mw}}\left(t0+?t\right)\stackrel{.Math.}{\underset{.Math.}{=}}{?}_m\left(t0+?t\right)-{?}_w\left(t0+?t\right)& \left(17\right)\end{array}$$\begin{array}{cc}{?}_{\mathrm{BL}}\left(?t\right)={?}_{t0}^{t0+?t}\left(?{?}_{\mathrm{mw}}\left(t\right)\right)\mathrm{dt}& \left(18\right)\end{array}$

(312) ??.sub.mW(t) is a time derivative of the sum of two types of phase components, i.e. a phase component of shaft torsion and a phase component of backlash. ??.sub.mW(t) indicates the shaft torsional speed until immediately before the occurrence of backlash, and indicates the relative speed during the period of gear play because the shaft torque during the backlash period is equal to zero.

(313) However, since the tire side speed cannot be measured, the tire side speed is approximated using other information as in mathematical expression (19).

(314) $\begin{array}{cc}\begin{array}{c}{?}^{}?{?}_{\mathrm{mw}}\left(t0+?t\right)\stackrel{.Math.}{\underset{.Math.}{=}}{?}_m\left(t0+?t\right)-{?}^{}?{?}_w\left(t0\right)\\ \stackrel{.Math.}{\underset{.Math.}{=}}?{?}_m\left(?t\right)+\left({?}_m\left(t0\right)-{?}^{}?{?}_w\left(t0\right)\right)\\ =?{?}_m\left(?t\right)+{\mathrm{??}}_{\mathrm{mw}}\left(t0\right)\end{array}& \left(19\right)\end{array}$

(315) First, on the assumption that the tire speed changes little, an initial value is held and substituted as {circumflex over ()}?w(t0+?t)?{circumflex over ()}?w(t0). Next, the motor side speed is separated into a speed change ??.sub.m(?t) and an initial speed ?.sub.m(t0) as ?.sub.m(t0+?t)=??.sub.m(?t)+?.sub.m(t0). Then, as in the third line of the mathematical expression (19), the right side is reduced into two elements, namely, the first term of the right side is reduced to the motor side speed change ??.sub.m(?t), and the second term of the right side is reduced to the initial value of the torsional speed ??.sub.mw(t0)=(?.sub.m(t0)?{circumflex over ()}?.sub.w(t0)). Thus, this is handled in a form where a variable term and a constant term are separated from each other.

(316) For the constant term, the speed, which is produced by time-differentiating the phase {circumflex over ()}?.sub.d by the torsional speed estimation section 230, is used, wherein the phase {circumflex over ()}?.sub.d is estimated from {circumflex over ()}T.sub.d. For the variable term, the motor speed change ??.sub.m(?t) during the backlash is estimated by integrating the torque command T.sub.m by mathematical expression (20).

(317) 0$\begin{array}{cc}?{?}_m\left(?t\right)=\frac{1}{TJm}{?}_0^{?t}\left(T_m\left(t\right)\right)dt& \left(20\right)\end{array}$

(318) Advantageously, all of the input torque to the motor serves as a torque component that accelerates the motor, because no reaction force is applied to the motor output shaft. Therefore, the rotational inertia TJ.sub.m of the motor may be used as the integral time constant as in the integral coefficient multiplier T.sub.c/{circumflex over ()}TJ.sub.m of the speed change estimation section 240.

(319) By mathematical expression (19) and the approximation of mathematical expression (20), it is possible to calculate an approximate value of the shaft torsional speed that changes during the backlash period. Then, by applying the integral calculation of mathematical expression (18) to the approximate value, it is possible to calculate an estimated value of the backlash phase. Then, by comparing the estimated value of the backlash phase with the preset backlash phase width, the end of the backlash is detected.

(320) For description based on correspondence between the mathematical expressions described above and FIG. 38, the input signal {circumflex over ()}T.sub.d is divided by the stiffness coefficient K.sub.d to calculate the torsional phase {circumflex over ()}?.sub.d; the torsional phase {circumflex over ()}?.sub.d is time-differentiated to calculate {circumflex over ()}?d_divTd corresponding to ??.sub.mw(t); and {circumflex over ()}?d_divTd is sampled by the latch circuit sh1 to obtain {circumflex over ()}?d_.sub.ini corresponding to the initial value ??.sub.mw(t0). The torque command T.sub.m, which is the other input signal, is time-integrated to calculate {circumflex over ()}??d_.sub.BL corresponding to the motor side speed change ??.sub.m(?t); the sum of {circumflex over ()}??d_.sub.BL and {circumflex over ()}?d_.sub.ini is calculated by the adder 251 to determine {circumflex over ()}?d_.sub.BL corresponding to (t0+?t); and {circumflex over ()}?d_.sub.BL is time-integrated by the torsional displacement estimation section 250 to estimate {circumflex over ()}?.sub.BL corresponding to {circumflex over ()}?.sub.BL(?t). The initial value of ??.sub.m(?t) in mathematical expression (20) and the initial value of {circumflex over ()}?.sub.BL(?t) in mathematical expression (18) are zero at the start time t0. Accordingly, while the backlash detection signal S_BLz is at 0, namely, during a standby period where no backlash occurs, {circumflex over ()}?d_.sub.BL and {circumflex over ()}?.sub.BL are reset to zero values by the switches sw3 and sw4.

(321) In this way, it is possible to estimate the amount of change in the backlash phase by the configuration of FIG. 38. Then, the estimated amount of change is compared with the phase widths ?p, ?n, which are set by the reference phase setting parts 261p, 261n, to detect the end of backlash.

(322) As described above, the backlash phase widths, which are set comparison references, have two kinds corresponding to torque change directions, namely, a kind corresponding to the positive direction, and a kind corresponding to the negative direction. Accordingly, selection is made by the switches sw2f and sw2r and latch circuits sh2h and sh2r.

(323) The system of the eighth embodiment requires some assumptions and measures. First, at the start of estimation, the actual torque is required to be estimated wherein the estimated value of the disturbance torque observer is sufficiently converged. If large torque changes occur repeatedly in a short period of time, it is impossible to accurately estimate the start timing of backlash, so that an error occurs in the estimation of the initial speed, and the detection of the end becomes inaccurate. In this regard, it is conceivable that it is when the torque command is small that the torque polarity repeatedly changes in a short time. As described with reference to FIG. 42, the systems of the sixth and seventh embodiments are effective for suppressing the torque command, so that when the torque command is small, there is no problem even if the estimation operation of the eighth embodiment is stopped and the limiter switching is not performed.

(324) Furthermore, since the phase of backlash varies from one machine to another, the estimated period varies. In this regard, it is preferable that the response be quiet even if the response is slightly delayed, rather than the period during which the torque is reduced is shortened to allow the occurrence of the rattling shock. Therefore, the backlash start determination is set to a level such that a backlash start can be detected a little earlier than zero-crossing of the torque (zero-cross edge detection by the backlash start timing detection section 220). This may be implemented by adding ?? as an appropriate margin phase to the set values of the reference phase setting parts 261p, 261n, to delay detection.

(325) FIG. 43 is a time chart showing an example of characteristics when the system of the eighth embodiment is additionally applied to the seventh embodiment. This is an example of behavior under the same conditions as in FIG. 42. The behavior regarding the prediction operation during the backlash period is shown in the time chart of FIG. 44.

(326) In FIGS. 43 (A) and 43 (B) where waveforms (b) show the shaft torsional speed, it can be confirmed that the speed change width of the shaft torsional speed during the backlash period can be significantly suppressed as indicated by a section where the solid line and the dashed line overlap with each other. Furthermore, the control output T.sub.m is forcibly suppressed to a small value, and as shown in waveforms (c), the motor-accelerating torque T.sub.mA and the correction amount ?T.sub.comp of the vibration suppression control are both suppressed to small values. Since the estimated shaft torque {circumflex over ()}T.sub.d in waveforms (d) has a waveform similar to the actual torsional torque until the backlash starts, it can be seen that the start timing can be detected by zero-cross detection. However, during the subsequent backlash period, the component {circumflex over ()}T.sub.d is suppressed to be small, but it is not suppressed to near zero. Therefore, the torque limiter is added. Regarding the estimated torque {circumflex over ()}T.sub.obs of the disturbance torque observer, an estimation error occurs due to a pulsation remaining even after the backlash. However, the estimated torque {circumflex over ()}T.sub.obs converges to a normal estimated value within 0.1 s. Therefore, it is conceivable that the backlash estimation can be thereafter performed again.

(327) FIG. 44 shows behavior of the function of estimating the backlash period, wherein in waveforms (a), a dashed line indicates the torsional speed estimated based on the input of {circumflex over ()}T.sub.d. Here, {circumflex over ()}?.sub.d_ini held at the start is drawn with a solid line.

(328) In waveforms (b), a solid line indicates the component ??.sub.m(?t) ({circumflex over ()}??.sub.d_BL) estimated by integrating the motor torque command, and a dashed line indicates the sum of the component ??.sub.m(?t) ({circumflex over ()}??.sub.d_BL) and the initial value {circumflex over ()}?.sub.d_ini ({circumflex over ()}?.sub.d_BL) It can be confirmed that even if the torque command is limited, it is possible to generate a speed sufficient to terminate the backlash in a short time.

(329) In waveforms (c), solid lines indicate the phase {circumflex over ()}?.sub.d calculated from the torque estimation {circumflex over ()}T.sub.d, and the component {circumflex over ()}??.sub.BL estimated using the mathematical expression (18), a dashed line indicates ?p, and a broken line indicates ?n, wherein ?p and ?n are to be compared with {circumflex over ()}??.sub.BL.

(330) Waveforms (d) indicate the timing signals E_Set and S_Rst, and the backlash detection signal S_BL produced by latching the timing signals E_Set and S_Rst. For comparison, the backlash period detected from the actual plant model is also drawn with a dashed line at the bottom. It can be seen that the backlash period can be estimated almost accurately.

Ninth Embodiment

(331) In the eighth embodiment, the slip phase and speed are estimated using the input/output difference component {circumflex over ()}T.sub.d of the disturbance torque observer. In the ninth embodiment, the torque command T.sub.m is used instead for input information. Specifically, the switch swB of FIG. 38 is set to the =r side to input T.sub.m, which is caused to pass through the divider 210 to be transformed into the shaft torsional phase {circumflex over ()}?.sub.d, thereby providing the torque command T.sub.m as a substitute of an information source for estimating {circumflex over ()}?.sub.d.

(332) Since the torque command is near zero, this approximation can be adopted if the compensation component of the vibration suppression control has converged.

(333) Since a backlash occurs when the torsional torque of the shaft is near zero, the estimated shaft torque {circumflex over ()}T.sub.d calculated by the disturbance torque observer and T.sub.m are approximately equal to each other. Therefore, with regard to backlash prediction, there is little difference even if the signal is replaced.

(334) Other operations are the same as in the eighth embodiment. FIGS. 45 and 46 show an example of characteristics in correspondence to FIGS. 43 and 44. The characteristics of FIGS. 45 and 46 are almost the same as those of FIGS. 43 and 44. It has been confirmed that the operation is possible even with the approximation.

(335) Comparing the examples of characteristics of the eighth embodiment and the ninth embodiment, it seems that there is little superiority or inferiority due to variation in system. Accordingly, for practical use, it is conceivable that which is to be selected is determined according to the amount of noise contained in speed measurement.

(336) By expanding the configuration of the sixth and seventh embodiments with addition of the functions of the eighth and ninth embodiments, it is possible to estimate the backlash start time and end time, and furthermore, reduce the torque command during the backlash period, and thereby suppress the amount of acceleration of the motor. This reduces the kinetic energy resulting from acceleration, and reduce the shock when the gear teeth collide at the end of the backlash.

(337) In this system, backlash cannot be accurately estimated in a region where the torque command is small or when the torque changes slowly. However, the vibration suppression control using the disturbance torque observer of the sixth and seventh embodiments also has a function of reducing the output torque command when the motor rapidly accelerates during the backlash period. Therefore, the eighth and ninth embodiments are not required to operate over the entire region, and are only required to operate only when the rate of change of the torque command is large enough to facilitate estimation of the backlash period.

(338) In other words, by combining the sixth or seventh embodiment with the eighth or ninth embodiment, it is possible to suppress rattling shocks caused by a wide range of backlash.