Apparatus and method for separately estimating backlash and compliance of vehicle driving system

Abstract

An apparatus and a method estimate backlash and compliance. The apparatus and the method are configured to distinguish and determine the backlash and the compliance occurring in a vehicle driving system. The method includes providing information related to a driving system model between a motor and a driving wheel for driving a vehicle to a controller, determining a compliance speed, by the controller, by using the information related to the driving system model based on vehicle driving information acquired by a driving information detector while the vehicle is driven, and determining a backlash speed, by the controller, by subtracting the determined compliance speed from an overall speed difference that is a difference between a motor speed and a driving wheel speed. The apparatus is configured to perform the method.

Claims

1. A method for estimating backlash and compliance in a vehicle driving system, the method comprising: providing, to a controller, information related to a driving system model between a motor and a driving wheel for driving a vehicle; determining, by the controller, a compliance speed based on (i) the information related to the driving system model and (ii) vehicle driving information acquired by a driving information detector while the vehicle is driven; and determining, by the controller, a backlash speed by subtracting the determined compliance speed from an overall speed difference, the overall speed difference being a difference between a motor speed and a driving wheel speed.

2. The method of claim 1, wherein determining the compliance speed comprises: using a model equation for the compliance as the information related to the driving system model; determining a rate of change of a driving system transmission torque based on the vehicle driving information; and multiplying a spring constant of the vehicle driving system that is premodeled by the rate of change of the driving system transmission torque.

3. The method of claim 1, wherein determining the compliance speed comprises: using a model equation for the compliance as the information related to the driving system model; determining a rate of change of a motor torque command based on the vehicle driving information; and multiplying a spring constant of the vehicle driving system that is premodeled by the rate of change of the motor torque command.

4. The method of claim 1, further comprising calculating the overall speed difference by using the motor speed and the driving wheel speed that are detected by respective sensors of the driving information detector, wherein the overall speed difference is (i) a difference between the driving wheel speed and a converted speed determined by converting the motor speed to a speed at the driving wheel based on a gear ratio between the motor and the driving wheel, or (ii) a difference between the motor speed and a converted speed determined by converting the driving wheel speed to a speed at the motor based on the gear ratio between the motor and the driving wheel.

5. The method of claim 1, wherein determining the compliance speed comprises: using the vehicle driving information and an ideal compliance model as the information related to the driving system model of the vehicle, and wherein the ideal compliance model is determined assuming no backlash in a driving system.

6. The method of claim 5, wherein the ideal compliance model comprises a model equation of an observer described below: $\mathrm{observer}:\{\begin{array}{c}{\stackrel{.}{\hat{}}}_c={}_{c,\mathrm{meas}}+K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)+K_I\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)\mathrm{dt}\\ {\hat{}}_{\mathrm{backlash}}=-K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)\\ {\hat{}}_c={\stackrel{.}{\hat{}}}_c\end{array},\mathrm{where}\mathrm{each}\{\begin{array}{c}{\stackrel{.}{}}_c={}_c={}_m-{}_w\\ {}_c=\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}\end{array},$ {circumflex over ({dot over ()})}.sub.c is the compliance speed, and {circumflex over ()}.sub.backlash is the backlash speed, .sub.c and .sub.c are a compliance angle and the compliance speed, respectively, assuming no backlash, and the compliance angle is expressed as .sub.c.sub.m.sub.w, and the compliance speed is expressed as .sub.c.sub.m.sub.w, and .sub.m is a motor rotation angle, .sub.m is the motor speed, .sub.w is a driving wheel rotation angle (.sub.w=r.sub.w, raw, where r is a gear ratio between the motor and the driving wheel, and .sub.w, raw is an actual driving wheel rotation angle), .sub.w is the driving wheel speed (.sub.w=r.sub.w, raw where .sub.w, raw is an actual driving wheel speed), K.sub.P and K.sub.I are a P gain and an I gain, respectively, T.sub.in is a motor torque command, K.sub.spr is a spring constant of the vehicle driving system that is premodeled, .sub.c, meas is a difference between a motor speed .sub.m, meas and a driving wheel speed .sub.w, meas that are detected by respective sensors, and {circumflex over ()}.sub.c is a difference in an observation sum angle.

7. An apparatus for estimating backlash and compliance in a vehicle driving system, the apparatus comprising: a driving information detector configured to detect vehicle driving information; and a controller configured to acquire the vehicle driving information from the driving information detector and to store information related to a driving system model between a motor and a driving wheel for driving a vehicle, wherein the controller is configured to: while the vehicle is driven, determine a compliance speed based on (i) the information related to the driving system model and (ii) the vehicle driving information acquired by the driving information detector, and determine a backlash speed by subtracting the determined compliance speed from an overall speed difference, the overall speed difference being a difference between a motor speed and a driving wheel speed.

8. The apparatus of claim 7, wherein the controller is configured to determine the compliance speed by: using a model equation for the compliance as the information related to the driving system model; determining a rate of change of a driving system transmission torque based on the vehicle driving information; and multiplying a spring constant of the vehicle driving system that is premodeled by the rate of change of the driving system transmission torque.

9. The apparatus of claim 7, wherein the controller is configured to determine the compliance speed by: using a model equation for the compliance as the information related to the driving system model; determining a rate of change of a motor torque command based on the vehicle driving information; and multiplying a spring constant of the vehicle driving system that is premodeled by the rate of change of the motor torque command.

10. The apparatus of claim 7, wherein the driving information detector comprises sensors configured to detect the motor speed and the driving wheel speed, respectively, wherein the controller is configured to calculate the overall speed difference by using the motor speed and the driving wheel speed that are detected by the sensors of the driving information detector, and wherein the overall speed difference is (i) a difference between the driving wheel speed and a converted speed determined by converting the motor speed to a speed at the driving wheel based on a gear ratio between the motor and the driving wheel, or (ii) a difference between the motor speed and a converted speed determined by converting the driving wheel speed to a speed at the motor based on the gear ratio between the motor and the driving wheel.

11. The apparatus of claim 7, wherein the controller is configured to determine the compliance speed by using the vehicle driving information and an ideal compliance model as the information related to the driving system model of the vehicle, the ideal compliance model being determined assuming no backlash in a driving system.

12. The apparatus of claim 11, wherein the ideal compliance model comprises a model equation of an observer described below: $\mathrm{observer}:\{\begin{array}{c}{\stackrel{.}{\hat{}}}_c={}_{c,\mathrm{meas}}+K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)+K_I\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)\mathrm{dt}\\ {\hat{}}_{\mathrm{backlash}}=-K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)\\ {\hat{}}_c={\stackrel{.}{\hat{}}}_c\end{array},\mathrm{where}\mathrm{each}\{\begin{array}{c}{\stackrel{.}{}}_c={}_c={}_m-{}_w\\ {}_c=\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}\end{array},$ {circumflex over ({dot over ()})}.sub.c is the compliance speed, and {circumflex over ()}.sub.backlash is the backlash speed, .sub.c and .sub.c are a compliance angle and the compliance speed, respectively, assuming no backlash, and the compliance angle is expressed as .sub.c.sub.m.sub.w and the compliance speed is expressed as .sub.c.sub.m.sub.w, and .sub.m is a motor rotation angle, .sub.m is the motor speed, .sub.w is a driving wheel rotation angle (.sub.w=r.sub.w, raw where r is a gear ratio between the motor and the driving wheel, and .sub.w, raw is an actual driving wheel rotation angle), .sub.w is the driving wheel speed (.sub.w=r.sub.w, raw where .sub.w, raw is an actual driving wheel speed), K.sub.P and K.sub.I are a P gain and an I gain, respectively, T.sub.in is a motor torque command, k.sub.spr is a spring constant of the vehicle driving system that is premodeled, .sub.c, meas is a difference between a motor speed .sub.m, meas and a driving wheel speed .sub.w, meas that are detected by respective sensors, and {circumflex over ()}.sub.c is a difference in an observation sum angle.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other objectives, features, and other advantages of the present disclosure will be more clearly understood from the following detailed description when taken in conjunction with the accompanying drawings, in which:

(2) FIG. 1 is a view illustrating a problem that occurs when backlash and torsion (compliance) are not distinguished and are not separated.

(3) FIG. 2 is a block diagram illustrating an example of a driving system and a driving system torque control system of a vehicle.

(4) FIG. 3 is a view illustrating an example of a driving system gear model.

(5) FIG. 4 is a view illustrating an example of a drive shaft torsion model.

DETAILED DESCRIPTION

(6) Hereinafter, one or more implementations of the present disclosure will be described in detail with reference to the accompanying drawings. Specific structures and functions stated in the implementation of the present disclosure are exemplified to illustrate an implementation according to the spirit of the present disclosure and implementations according to the spirit of the present disclosure can be achieved in various ways. Furthermore, the present disclosure should not be construed as being limited to the following implementations and should be construed as including all changes, equivalents, and replacements included in the spirit and scope of the present disclosure.

(7) The present disclosure relates to an apparatus and a method that are capable of separately detecting and estimating backlash and torsion (compliance) generated in a driving system of a vehicle.

(8) When torque is compensated without distinguishing between backlash and compliance, a compensation effect compared to the torque compensation amount is insufficient, so that compensating torque without distinguishing between backlash and compliance is inefficient. Therefore, a method for separately responding to backlash and compliance respectively by torque compensation and gradient compensation may be performed.

(9) In some implementations, separately determining backlash and compliance and separately estimating the backlash amount and the compliance amount respectively are performed. When the torque compensation and the gradient compensation are respectively performed based on the result of the separate determining and the separate estimating, backlash impact reduction and torsional vibration reduction may be effectively realized.

(10) FIG. 1 is a view illustrating a problem that occurs when backlash and compliance are not distinguished and are not separated, and factors that impede drivability of a vehicle in a driving system may include backlash and compliance.

(11) In the backlash and the compliance, the backlash includes a tooth space, a gap, a clearance, or the like in driving system components such as a driving system gear, a constant speed joint, and so on. The compliance includes a shaft torsion, a mount variation (a mount stiffness), and so on of the driving system.

(12) The shaft torsion or the mount stiffness that occurs in the driving system while the vehicle is driven may be expressed as compliance, and the terms torsion and compliance are used in the following description in the same meaning.

(13) In the factors that impede the drivability, a problem region where backlash occurs is obvious. That is, there is a torque region in which backlash may occur in the driving system of the vehicle, and such a torque region (a backlash region) may be limited to a torque range between a lower limit value that is a negative value and an upper limit value that is a positive value.

(14) If a direction of motor torque is changed according to a driver's driving input, zero-crossing in which the motor torque passes through zero torque is unavoidable, and one-time impact and noise caused by backlash occur during the zero-crossing of the torque. Such backlash can be counteracted with compensation that reduces the motor torque in a problem region where the backlash may occur.

(15) In some examples, in the case of compliance, a problem may occur in the entire torque region, and compliance induces vibrational shaking. The compliance may be reduced by limiting a gradient of a motor torque, and the vibrational shaking may be reduced by using an anti-jerk control and hardware damping characteristics.

(16) However, the response methods for reducing backlash and compliance as described above are proposed to respond to backlash and torsion respectively based on a pure backlash value and a pure torsion value that are separately extracted and estimated. In some examples, according to the response methods, since a correction that reduces torque is used for backlash and a correction that limits a torque gradient is used for compliance such as shaft torsion and so on, accurate and effective response can be realized when a separated extraction and estimation of backlash and compliance is premised.

(17) When the motor torque is reduced or the gradient of the motor torque is limited in the problem region (the backlash region) in order to reduce the backlash impact, a problem in which the responsiveness of a longitudinal movement of the vehicle is reduced occurs. Furthermore, when the motor torque is rapidly changed to secure the responsiveness equal to the driving input, impact and noise caused by backlash may occur.

(18) In order to solve problems caused by backlash and compliance at the same time, differentiating the torque gradient for each section in which the backlash impact noise is generated may be considered, but this may cause a problem of damaging the linearity of vehicle acceleration and deceleration.

(19) Therefore, after backlash and compliance are separately extracted and estimated, correcting a torque shape for each element and then deriving a torque command are performed, and then an integration between a functional torque profile and a correction torque profile is performed.

(20) Hereinafter, the separation estimation apparatus and the separation estimation method according to an implementation of the present disclosure will be described in detail with reference to the drawings.

(21) FIG. 2 is a block diagram illustrating a driving system and a driving system torque control system of a vehicle to which the present disclosure is applied. As illustrated in the drawing, the present disclosure may be applied to an electric vehicle in which a motor 30 that is a driving device configured to drive the vehicle is mounted. Typically, a battery is connected to the motor 30 via an inverter such that the battery is capable of being charged and discharged.

(22) The motor 30 is connected to a driving wheel 42 such that the motor 30 is capable of transmitting a power to the driving wheel 42. Torque output from the motor 30 may be transmitted to the driving wheel 42 through driving system elements such as a decelerator and a differential 41, a driving shaft, a vehicle shaft, and so on. Conversely, torque of the driving wheel 42 may be transmitted to the motor 30 through the driving system elements. In such a driving system, backlash and compliance may occur while the vehicle is driven.

(23) In the electric vehicle, the operation (driving and regenerating) of the motor 30 is controlled according to a torque command generated by a controller 20. The controller 20 determines a required torque according to a vehicle driving state, and generates a final torque command based on the required torque.

(24) The final torque command is a motor torque command, and the controller 20 controls the operation of the motor 30 through the inverter based on the final torque command. Generally, when the torque command is a positive value, the torque command is a driving torque command that accelerates the vehicle.

(25) Furthermore, when the torque command is a negative value, the torque command is a regenerative torque command that decelerates the vehicle.

(26) The controller 20 may include a first controller 21 configured to determine a required torque for driving the vehicle based on a driver's driving input value or receive the required torque from another controller such as an Advanced Driver Assistance System (ADAS) controller, and to generate and output a torque command based on the required torque, and may include a second controller 22 configured to control the operation of the motor 30 according to a final torque command input from the first controller 21.

(27) The first controller 21 may be a Vehicle Control Unit (VCU) that determines and generates a torque command required for driving the vehicle in a typical vehicle. Detailed description of the method and the process of determining the torque command in the vehicle will be omitted since the method and the process are well-known technical matters in the relevant technical field.

(28) When the first controller 21 generates and outputs a torque command, the second controller 22 receives the torque command and controls the operation of the motor 30 through the inverter. Accordingly, the torque output from the motor 30 is applied to the driving wheel 42 through the decelerator and the differential 41 of the driving system.

(29) The second controller 22 may be a conventional Motor Control Unit (MCU) that controls the operation of the motor 30 through the inverter according to the torque command output from the VCU in the electric vehicle.

(30) In the description above, the controlling subject is described as the first controller 21 and the second controller 22. However, in the present specification, the controlling subject will be collectively referred to as the controller, and the controller may be set such that the controller performs a backlash and torsion separation estimation process according to the present disclosure.

(31) In the present disclosure, vehicle driving information such as a driver's driving input value and so on input to the controller 20 is information indicating a vehicle driving state, and the vehicle driving information may include sensor detection information which is detected by a driving information detector 10 and which is input to the controller 20 through a vehicle network.

(32) At this time, the driving information detector 10 may include an Accelerator Pedal Sensor (APS) configured to detect an accelerator pedal input value (an APS value, %) of the driver, a Brake pedal Position Sensor (BPS) configured to detect a brake pedal input value (a BPS value, %), a sensor configured to detect a driving system speed, and a sensor for detecting a vehicle speed.

(33) Here, the driving system speed may be a rotation speed of the motor 30 that is the driving device, or may be a rotation speed (a wheel speed) of the driving wheel 42. At this time, the sensor detecting the driving system speed may be a sensor configured to detect the rotation speed of the motor 30, and may be a conventional resolver detecting a rotor position of the motor 30. Alternatively, the sensor detecting the driving system speed may be a conventional wheel speed sensor detecting the rotation speed (the wheel speed) of the driving wheel 42.

(34) In addition, the sensor for detecting the vehicle speed may also be the wheel speed sensor. It is a well-known technology to those skilled in the art that the vehicle speed information can be acquired from a signal of the wheel speed sensor, so that the detailed description thereof will be omitted.

(35) As the vehicle driving information for determining the required torque and for generating the torque command in the controller 20, the accelerator pedal input value (the APS value, %) of the driver, the brake pedal input value (the BPS value, %) of the driver, the rotation speed of the motor 30, the rotation speed of the driving wheel 42, and the vehicle speed that are detected by the driving information detector 10 may be selectively used.

(36) In the vehicle driving information described above, the accelerator pedal input value (the APS value) and the brake pedal input value (the BPS value) may be referred to as driving input information of the driver. Furthermore, the rotation speed of the motor 30, the rotation speed of the driving wheel 42, and the vehicle speed may be referred to as vehicle state information.

(37) In addition, in a broad sense, the vehicle driving information may include information determined by the controller 20, or may include information (for example, required torque information) input to the controller 20 through the vehicle network from another controller (for example, the ADAS controller) in the vehicle.

(38) In the present disclosure, two methods of separating and estimating backlash and compliance such as shaft torsion in real time are proposed.

(39) The first method is a method in which a compliance speed (that is, a torsional speed) is first calculated by using a model equation for compliance and then a pure backlash speed is acquired by subtracting the compliance speed from the overall speed difference.

(40) To this end, information related to a driving system model between the motor 30 and the driving wheel 42 for driving the vehicle is provided to the controller 20, and the controller 20 calculates the compliance speed by using the model equation for compliance of the driving model-related information based on the vehicle driving information acquired by the driving information detector 10, and then the pure backlash speed is acquired by subtracting the compliance speed d from the overall speed difference.

(41) In calculating the compliance speed by using the simplified model in the present disclosure, the compliance speed may be acquired by multiplying a spring constant of the vehicle driving system that is premodeled by a rate of change in transmission torque determined based on driving system state information among the vehicle driving information.

(42) The transmission torque may be acquired by the driving system model. FIG. 3 is a view illustrating an example of a driving gear model in the present disclosure [Prajapat, Ganesh P., N. Senroy, and I. N. Kar. Modeling and impact of gear train backlash on performance of DFIG wind turbine system. Electric Power Systems Research 163 (2018): 356-364.].

(43) In addition, FIG. 4 is a view illustrating an example of a drive shaft torsion model in the present disclosure [Margielewicz, Jerzy, Damian Ga ska, and Grzegorz Litak. Modelling of the gear backlash. Nonlinear Dynamics 97.1 (2019): 355-368.].

(44) In the present disclosure, the driving gear model illustrated in FIG. 3 or the drive shaft torsion model illustrated in FIG. 4 may be used as a driving system model for determining the transmission torque that is an output torque from an input torque. Generally, as illustrated in FIG. 3 and FIG. 4, the driving system model considers stiffness or damping existing between connecting parts of gears, and considers backlash that exists in between.

(45) The driving system state information may include an input torque applied to the driving system, a rotation speed of a driving input unit, and a rotation speed of a driving output unit. Furthermore, the rotation speed of the driving input unit is a rotation speed of a motor, and the rotation speed of the driving output unit is a rotation speed of a driving wheel.

(46) The input torque refers to a torque of a torque source which generates the torque for driving the vehicle and which applies the torque to the driving system. At this time, a command value may be used as the input torque.

(47) The main torque source is a driving device for driving the vehicle, and the driving device that is the main torque source in the electric vehicle is the motor, so that the command may be a motor torque command (a final torque command) as an input torque command. At this time, the input torque may be determined based on vehicle driving information.

(48) The transmission torque transmitted between the gears may be estimated by using information such as the input torque command (the motor torque command), the rotation speed of the driving system input unit, the rotation speed of the driving system output unit, and so on based on the driving system model described above. Furthermore, the compliance speed may be determined based on the change rate of the estimated transmission torque.

(49) In the present disclosure, the transmission torque may refer to a torque transmitted from a rear end (an output side) of compliance elements when it is assumed that the compliance elements are combined with each other in the driving system and the compliance elements are present in one place.

(50) Under an assumption that backlash is not considered, the models in FIG. 3 and FIG. 4 may be used as the driving system model for acquiring the transmission torque in the present disclosure, and may be used as the driving system model for inducing the compliance model equation.

(51) Alternatively, the compliance speed may be acquired by multiplying the spring constant by the torque command that is the driving system control command determined based on the vehicle driving information, in which the torque command is a slope (a derivative of the command value) of the motor torque command.

(52) The overall speed difference is the difference between the motor speed and the driving wheel speed. Here, the motor speed and the driving wheel speed (the wheel speed) are the rotation speed of the motor 30 and the rotation speed of the driving wheel 42 that are detected by each sensor of the driving information detector 10.

(53) Of course, it is assumed that the difference between the motor speed and the driving wheel speed is in a state in which a difference due to a reduction gear ratio or a gear ratio has already been corrected. That is, the speed difference between the motor and the driving wheel may be a difference between the motor speed and a speed in which the driving wheel speed is converted to a speed at the motor by using the reduction gear ratio or the gear ratio between the motor and the driving wheel. Alternatively, the speed difference between the motor and the driving wheel may be a difference between the driving wheel speed and a speed in which the motor speed is converted to a speed at the driving wheel by using the reduction gear ratio or the gear ratio.

(54) In addition, the overall speed difference may be understood as a sum of the backlash speed and the compliance speed. Therefore, the pure backlash speed may be acquired by subtracting the calculated compliance speed from the overall speed difference. In this manner, it is possible to separately estimate backlash and compliance (torsion) in real time.

(55) The second method is a method of using an ideal compliance (torsion) model and using a measured speed difference between a motor and a driving wheel. Furthermore, in the ideal compliance model, it is assumed that there is no backlash in the driving system. In the description below, the measured speed difference between the motor and the driving wheel is a difference between a motor speed and a driving wheel speed that are detected by the sensor of the driving information detector 10.

(56) Since the model is constructed assuming that there is no backlash, an error occurs between a model value and an actual value when a speed difference between a motor and a driving wheel acquired from a driving system plant in which backlash actually exists is substituted into the model.

(57) Since this error is likely to be an error caused by backlash that is intentionally not implemented in the model, the corresponding error value may be defined as a pure backlash speed. Therefore, a pure compliance speed may be acquired by subtracting the calculated backlash speed from the speed difference (that is, the overall speed difference) between the motor and the driving wheel measured in real time.

(58) In the method described above, the speed difference between the motor and the driving wheel measured in real time is acquired, and a model value is acquired from the model at the same time, so that setting information designed in the form of an observer may be used.

(59) That is, an observation value finally acquired through the model is a difference in an observation sum speed, and a method of acquiring the difference is summing a feedback term value and the measured speed difference between the motor and the driving wheel. Here, the feedback term value may be acquired by a function of a difference value between a difference in a model angle and a difference in an observation sum angle.

(60) The difference in the observation sum angle may be acquired by integrating the difference in the observation sum speed acquired as a final result from the observer, and the difference in the model angle may be acquired by multiplying the torque command by a reciprocal of the spring constant that is predetermined.

(61) According to this method, a differentiator in the first method that is described above may be deleted, robustness against noise may be secured, and robustness against the model error such as the reduction gear ratio may be additionally secured by converging to the feedback term.

(62) An implementation of designing such an observer is as follows.

(63) First, when a motor rotation angle (a motor angle) is set to .sub.m, a motor speed (a rotation speed) is set to .sub.m, a driving wheel rotation angle (a wheel angle) is set to .sub.w, and a driving wheel speed (a wheel speed) is set to .sub.w the wheel angle .sub.w converted to a rotation angle at the motor by using a gear ratio r may be expressed as a value acquired by multiplying an actual driving wheel rotation angle .sub.w, raw before conversion by the gear ratio r (that is, .sub.wr.sub.w, raw).

(64) Similarly, the driving wheel speed .sub.w converted to a speed at the motor by using the gear ratio r may be expressed as a value acquired by multiplying an actual driving wheel speed .sub.w,raw before conversion by the gear ratio r (that is, .sub.wr.sub.w, raw).

(65) In addition, when it is assumed that there is no backlash, a compliance angle .sub.c may be expressed as an angle difference between the motor and the driving wheel (that is, .sub.c.sub.m.sub.w), and a compliance speed We may be expressed as a speed difference between the motor and the driving wheel (that is, .sub.c.sub.m.sub.w).

(66) In addition, an observer model as the ideal compliance model assuming that there is no backlash is illustrated as follows. As described below, error factors are observed by using a model in which backlash is intentionally not considered.

(67) $\mathrm{perfectly}\mathrm{backlashless}\mathrm{model}:\{\begin{array}{c}{\stackrel{.}{}}_c={}_c={}_m-{}_w\\ {}_c=\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}\end{array}$$\mathrm{difference}\mathrm{actual}\mathrm{plant}:{\stackrel{.}{}}_c\left({}_{c,\mathrm{meas}}={}_{m,\mathrm{meas}}-{}_{w,\mathrm{meas}}\right)\mathrm{instead},{\stackrel{.}{}}_c={}_{m,\mathrm{meas}}-{}_{w,\mathrm{meas}}-{}_{\mathrm{backlash}}$$\mathrm{observer}:\{\begin{array}{c}{\stackrel{.}{\hat{}}}_c={}_{c,\mathrm{meas}}+\underset{P-\mathrm{term}}{\underset{}{K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)}}+\underset{I-\mathrm{term}}{\underset{}{K_I\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right)\mathrm{dt}}}\\ \begin{array}{c}{\hat{}}_{\mathrm{backlash}}=-K_p\left(\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}-{\hat{}}_c\right):P-\mathrm{term}\mathrm{error}\mathrm{serves}\\ \mathrm{as}\mathrm{unmodeled}\mathrm{backlash}\mathrm{speed}\end{array}\\ {\hat{}}_c={\stackrel{.}{\hat{}}}_c:\mathrm{backlash}\mathrm{eliminated}\end{array}$

(68) In the equation described above, K.sub.P and K.sub.I represent a P gain and an I gain, respectively.

(69) As can be seen from the equation described above, in the model assuming that there is no backlash, the compliance speed ({dot over ()}.sub.c=c) may be expressed as the speed difference (.sub.m.sub.w) between the motor and the driving wheel, and the compliance angle .sub.c may be expressed as a value acquired by multiplying a reciprocal of a spring constant K.sub.spr of a premodeled vehicle driving system by a torque command T.sub.in that is a motor torque command.

(70) However, in an actual driving system plant in which backlash and compliance are present together, the compliance speed {dot over ()}.sub.c is different from the measured speed difference between the motor and the driving wheel. That is, the compliance speed {dot over ()}.sub.c is different from a difference between a motor speed .sub.m, meas measured by a sensor and a driving wheel speed .sub.w, meas measured by a sensor, and the compliance speed {dot over ()}.sub.c is a value acquired by subtracting a backlash speed from the speed difference (.sub.c, meas=.sub.m, meas.sub.w, meas) between the motor and the driving wheel (that is, the speed difference between the motor and the driving wheel is the sum of the compliance speed and the backlash speed).

(71) In the observer model described above, which is the ideal compliance model without backlash, {circumflex over ({dot over ()})}.sub.c is the difference in the observation sum speed, .sub.c, meas is the measured speed difference (the speed difference between the motor and the driving wheel, .sub.c, meas=.sub.m, meas.sub.w, meas),

(72) $\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}$
is a model angle difference, and {circumflex over ()}.sub.c is a difference in an observation sum angle.

(73) In addition, since {circumflex over ()}.sub.backlash is a pure backlash speed to be estimated and the model assumes that there is no backlash, the difference in the observation sum speed of the observer model is a compliance speed to be estimated. That is, the compliance speed to be estimated is a pure compliance speed {circumflex over ()}.sub.c={circumflex over ({dot over ()})}.sub.c in which the backlash speed is subtracted.

(74) In addition, in the ideal compliance model without backlash, .sub.c, meas is a feedforward term. Furthermore, in the model equation, a P-term and an I-term are feedback terms.

(75) Since the observer model is the ideal compliance model constructed assuming that there is no backlash, an error occurs between the model value and the actual value when the measured speed difference between the motor and the driving wheel in the driving system plant in which backlash actually exists is substituted into such a model.

(76) Since this error is caused by backlash that is intentionally not implemented in the model, the corresponding error value may be defined as the pure backlash speed {circumflex over ()}.sub.backlash. Therefore, the pure compliance speed {circumflex over ()}.sub.c={circumflex over ({dot over ()})}.sub.c may be acquired by subtracting the calculated backlash speed {circumflex over ()}.sub.backlash from the speed difference .sub.c, meas between the motor and the driving wheel measured in real time.

(77) The observation value {circumflex over ({dot over ()})}.sub.c finally acquired through the model is a difference in the observation sum speed, and a method of acquiring the difference is summing the feedback term values and the measured speed difference (.sub.c, meas, the feedforward term) between the motor and the driving wheel. Here, the feedback term values may be acquired a function of a difference value between the difference in the model angle

(78) $\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}$
and the difference in the observation sum angle {circumflex over ()}.sub.c.

(79) The difference in the observation sum angle {circumflex over ()}.sub.c may be acquired by integrating the difference in the observation sum speed {circumflex over ({dot over ()})}.sub.c acquired as a final result from the observer, and the difference in the model angle

(80) $\frac{T_{\mathrm{in}}}{k_{\mathrm{spr}}}$
may be acquired by multiplying the torque command T.sub.in by the reciprocal of the spring constant K.sub.spr that is predetermined.

(81) In the present disclosure, the pure backlash amount, which is the pure backlash speed, is estimated based on the actually measured speed difference between the motor and the driving wheel by using the ideal compliance model without backlash.

(82) At this time, a linear spring model may be used as the ideal compliance model, a linear spring model value may be defined as a pure compliance speed, and a value acquired by subtracting the pure compliance speed from the actually measured speed difference between the motor and the driving wheel may be defined as a pure backlash value.

(83) Alternatively, the measured speed difference between the motor and the driving wheel in the ideal compliance model may be used. Furthermore, when the compliance speed model is constructed, the measured speed difference between the motor and the driving wheel may be used as a feedforward term, and the angle difference acquired based on the linear spring model and the angle difference acquired by integrating the compliance speed model may be used as feedback terms.

(84) At this time, a proportional error feedback term is formed by multiplying the feedback term by a gain, and the proportional error feedback term may be added and used in the compliance model.

(85) In addition, the proportion error feedback term is formed by multiplying the feedback term by the gain, an integral error feedback term is formed by multiplying the feedback term by a gain, and the proportional error feedback term and the integral error feedback term may be added and used in the compliance model.

(86) In addition, a value acquired by multiplying the proportional error feedback term by an appropriate sign may be determined as a pure backlash speed, or a value acquired by multiplying the summed value of the proportional error feedback term and the integral error feedback term by an appropriate sign may be defined as a pure backlash speed. Alternatively, a value acquired by multiplying the integral error feedback term by an appropriate sign may be defined as a pure backlash speed.

(87) Here, the reason for multiplying the appropriate sign is that the sign of the backlash speed may be different according to whether a value acquired by subtracting a physical amount of a wheel side from a physical amount of a motor side is defined as a positive direction backlash or a negative direction backlash.

(88) In addition, a value acquired by subtracting the pure backlash speed from the measured speed difference between the motor and the driving wheel may be determined as the pure compliance speed. Here, it is assumed that the difference value between the motor speed and the driving wheel speed is a value in which the difference due to the reduction gear ratio or the gear ratio has already been corrected.

(89) Although the implementations of the present disclosure have been described in detail, the scope of the prevent disclosure is not limited to these implementations, and various modifications and improvements devised by those skilled in the art using the fundamental concept of the present disclosure, which is defined by the appended claims, further fall within the scope of the present disclosure.