Motor control current sensor loss of assist mitigation for electric power steering

Abstract

A power steering system includes a torque modifier module that generates a modified torque command in response to a current sensor fault, a magnitude of the modified torque command changes over a time period. The power steering system also includes a feedforward selection module that applies a dynamic feedforward compensation to a motor current command, thereby generating a motor voltage that is applied to a motor of the power steering system, the dynamic feedforward compensation modifies a frequency response of the power steering system.

Claims

1. A power steering system comprising: a torque modifier module that generates a modified torque command in response to a current sensor fault, a magnitude of the modified torque command changes over a time period; and a feedforward selection module that applies a dynamic feedforward compensation to a motor current command, the dynamic feedforward compensation based on motor inductance and motor-circuit resistance, thereby generating a motor voltage that is applied to a motor of the power steering system, the dynamic feedforward compensation modifies a frequency response of the power steering system, the motor current command is based on the modified torque command.

2. The power steering system of claim 1, further comprising a stability compensator selector module that selects a stability compensator of a steering torque control loop of the power steering system when a current sensor fault is detected, the stability compensator selector module generates a compensated torque command sent to the torque modifier module.

3. The power steering system of claim 2, the modified torque command is based at least in part on the compensated torque command.

4. The power steering system of claim 2, the dynamic feedforward compensation is based on a transfer function defined by an approximation of a true derivative.

5. The power steering system of claim 4, the approximation of the true derivative is represented by $\tilde{s}=\frac{s}{{\left(\tau s+1\right)}^n}.$

6. The power steering system of claim 1, the modified torque command is reduced to a magnitude of zero when the current sensor fault is detected, the modified torque command is increased from a magnitude of zero over a time period.

7. The power steering system of claim 6, the modified torque command has a steady state value defined by a scale factor applied to the modified torque command during the time period.

8. A power steering system comprising: a stability compensator selector module that selects a stability compensator of a steering torque control loop of the power steering system when a current sensor fault is detected, the stability compensator generates a compensated torque command based on frequency response of a motor control system of a motor of the power steering system; and a torque modifier module that generates a modified torque command from the compensated torque command in response to a current sensor fault, a magnitude of the modified torque command changes over a time period, a motor voltage that is applied to the motor of the power steering system is based on the modified torque command.

9. The power steering system of claim 8, further comprising a feedforward selection module that applies a dynamic feedforward compensation to a motor current command, thereby generating the motor voltage that is applied to a motor of the power steering system, the dynamic feedforward compensation modifies a frequency response of the power steering system, the motor current command is based on the modified torque command.

10. The power steering system of claim 9, the dynamic feedforward compensation is based on a transfer function defined by an approximation of a true derivative.

11. The power steering system of claim 10, the approximation of the true derivative is represented by $\tilde{s}=\frac{s}{{\left(\tau s+1\right)}^n}.$

12. The power steering system of claim 8, the modified torque command is increased from a magnitude of zero when the current sensor fault is detected.

13. The power steering system of claim 12, the modified torque command has a steady state value defined by a scale factor applied to the modified torque command during a time period.

14. A method for controlling a power steering system comprising: generating a modified torque command in response to a current sensor fault, a magnitude of the modified torque command changes over a time period; and applying a dynamic feedforward compensation to a motor current command, the dynamic feedforward compensation based on motor inductance and motor-circuit resistance, thereby generating a motor voltage that is applied to a motor of the power steering system, the dynamic feedforward compensation modifies a frequency response of the power steering system, the motor current command is based on the modified torque command.

15. The method of claim 14, further comprising selecting a stability compensator of a steering torque control loop of the power steering system when a current sensor fault is detected, the stability compensator selector module generates a compensated torque command.

16. The method of claim 14, the modified torque command is increased from a magnitude of zero when the current sensor fault is detected.

17. The method of claim 16, the modified torque command has a steady state value defined by a scale factor applied to the modified torque command during a time period.

18. The method of claim 14, the dynamic feedforward compensation is based on a transfer function defined by an approximation of a true derivative.

19. The method of claim 18, the approximation of the true derivative is represented by $\tilde{s}=\frac{s}{{\left(\tau s+1\right)}^n}.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which:

(2) FIG. 1 illustrates a steering control system in accordance with some embodiments;

(3) FIG. 2 illustrates a block diagram of a current regulator configuration in accordance with some embodiments;

(4) FIG. 3 illustrates a block diagram of the motor electrical system in accordance with some embodiments;

(5) FIG. 4 illustrates a typical current sensor fault loss of assist mitigation algorithm in accordance with some embodiments;

(6) FIG. 5 illustrates a plot of a torque command change during a current sensor failure in accordance with some embodiments;

(7) FIG. 6 illustrates a second plot of a torque command change during a current sensor failure in accordance with some embodiments;

(8) FIG. 7 illustrates an open loop current control block diagram with static feedforward compensation in accordance with some embodiments;

(9) FIG. 8 illustrates a comparison plot of the frequency responses of the q-axis direct transfer functions at an operating speed in accordance with some embodiments;

(10) FIG. 9 illustrates a loss of assist mitigation algorithm block diagram in accordance with some embodiments;

(11) FIG. 9A illustrates a loss of assist mitigation algorithm block diagram in accordance with some embodiments;

(12) FIG. 10 illustrates a loss of assist mitigation algorithm block diagram in accordance with some embodiments; and

(13) FIG. 11 illustrates a block diagram for the motor control current loop under a fault condition with dynamic feedforward compensation.

DETAILED DESCRIPTION

(14) Referring now to the Figures, where the invention will be described with reference to specific embodiments, without limiting same, FIG. 1 illustrates a steering control system 10. In the embodiment as shown, the steering control system 10 includes a steering control module 12, a current reference generator 14, a current loop compensator 16, a motor 18 represented by the PMSM motor electrical plant, and a steering system mechanical plant 20. The current loop compensator 16 may include a current regulator 24 along with a static feedforward compensator 22. The outputs of the current regulator 24 and the static feedforward compensator 22 are joined at summation block 26, to form a control signal for the PMSM motor electrical plant. The static feedforward compensator 22 may be active regardless of the feedback provided by the electrical plant. Although a coupled P.I. configuration is shown in FIG. 1, the subject matter disclosed herein is not limited to this configuration.

(15) FIG. 2 illustrates one type of current regulator 200 in accordance with some embodiments. As shown, the control configuration includes several sub-modules—a BEMF compensation module G.sub.F 202, an integration module 204, proportional compensation module C.sub.P 206 and integral compensation module C.sub.I 208, feedforward compensation module G 210, a subtraction module 212, and addition modules 213, 214. FIG. 2 also illustrates the motor 18.

(16) The compensation modules G.sub.F 202, C.sub.P 206 and C.sub.I 208, and the plant P(s) of the motor 18 are 2×2 matrices. Signals I.sub.R, I.sub.E, I.sub.P, I.sub.A, I.sub.M, V.sub.P, V.sub.I, V.sub.C, V.sub.FF, V.sub.F, V.sub.R, V.sub.M are vectors with two values each, corresponding to the d and q axes.

(17) The current mode control configuration implemented in FIG. 2 may be represented by matrix compensators. The following equations defined in the d/q axis coordinate frame describe the plant transfer function (using line to neutral definitions):

(18) $\begin{array}{cc}{V}_d=L_d\frac{d{I}_d}{dt}+{\mathrm{RI}}_d+\frac{N_p}{2}{\omega }_m{L}_q{I}_q& \left(\mathrm{Equation}1\right)\\ V_q=L_q\frac{d{I}_q}{dt}+{\mathrm{RI}}_q-\frac{N_p}{2}{\omega }_m{L}_d{I}_d+K_e{\omega }_m& \left(\mathrm{Equation}2\right)\\ T_e=\frac{3}{2}{K}_e{I}_q+\frac{3}{4}{N}_p\left(L_q-L_d\right)I_d{I}_q& \left(\mathrm{Equation}3\right)\end{array}$

(19) V.sub.d, V.sub.q are the d/q motor voltages (in Volts), I.sub.d, I.sub.q are the d/q motor currents (in Amperes), L.sub.d, L.sub.q are the d/q axis motor inductances (in Henries), R is the motor circuit (motor plus controller) resistance (in Ohms), K.sub.e is the motor BEMF coefficient (in Volts/rad/s), ω.sub.m is the mechanical motor velocity in (in rad/s), and T.sub.e is the electromagnetic motor torque (in Nm).

(20) The torque equation may be nonlinear and may represent a sum of the torque developed by leveraging the magnetic field from the permanent magnets, and the reluctance torque generated by rotor saliency (difference between L.sub.d and L.sub.q) and predefined values of I.sub.q and I.sub.d.

(21) Equations 1 and 2 may be rewritten as follows:
V.sub.d=L.sub.dİ.sub.d+RI.sub.d+ω.sub.eL.sub.qI.sub.q  (Equation 4)
V′.sub.q=V.sub.q−K.sub.eω.sub.m=L.sub.qİ.sub.q+RI.sub.q−ω.sub.eL.sub.dI.sub.d  (Equation 5)

(22) In the above equations,

(23) ${\omega }_e=\frac{N_P}{2}{\omega }_m$
is the electrical speed of the machine. To employ standard linear feedback control design techniques, the machine speed is assumed to be a slowly varying parameter. It can be appreciated that due to relatively slow flux dynamics, the quasi-static back-EMF (BEMF) term K.sub.eω.sub.m can be considered to be essentially constant, which is compensated as a disturbance in the feedforward path. These two assumptions allow linearization of equations 4 and 5 for a fixed speed. Note that the apostrophe in the V′.sub.q term is dropped in the equations below.

(24) Equations 4 and 5 can re-written using s-domain representation as follows:

(25) $\begin{array}{cc}U=P_i\left(s\right)X& \left(\mathrm{Equation}6\right)\\ \left[\begin{array}{c}{V}_d\\ V_q\end{array}\right]=\left[\begin{array}{cc}{L}_{d}s+R& {\omega }_e{L}_q\\ -{\omega }_e{L}_d& L_{q}s+R\end{array}\right]\left[\begin{array}{c}{I}_d\\ I_q\end{array}\right]& \left(\mathrm{Equation}7\right)\end{array}$

(26) Note that this description translates plant outputs into inputs via the complex frequency transfer matrix P.sub.i(s), and is thus the inverse of the true plant transfer matrix. The block diagram for the above description (with the additional BEMF term also shown) is shown in the block diagram of the motor shown in FIG. 3. Specifically, FIG. 3 illustrates the quasi-static back-EMF (BEMF) term K.sub.eω.sub.m and the motor 18 includes matrix represented by equation 7.

(27) The closed loop transfer matrix T relating the reference currents I.sub.R to the actual currents I.sub.A for the current control system shown in FIG. 3 may be written in terms of the matrix compensators as:
I.sub.A=TI.sub.R=(P.sup.−1+C).sup.−1(G+C)I.sub.R  (Equation 8)

(28) By inserting the appropriate compensator matrices in the above expressions, the transfer matrix T may be expressed in equation 9 as follows:

(29) $T=\left[\begin{array}{cc}{T}_{\mathrm{dd}}\left(s\right)& T_{\mathrm{dq}}\left(s\right)\\ T_{\mathrm{qd}}\left(s\right)& T_{\mathrm{qq}}\left(s\right)\end{array}\right]=\hspace{1em}\left[\begin{array}{cc}\frac{\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)\left(\left(\tilde{R}+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)+s^2{\tilde{\omega }}_e^2{\tilde{L}}_d{\tilde{L}}_q}{\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)+s^2{\omega }_e^2{L}_d{L}_q}& \frac{\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right){\tilde{\omega }}_e{\tilde{L}}_q-\left(\left(\tilde{R}+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right){\omega }_e{L}_q}{\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)+s^2{\omega }_e^2{L}_d{L}_q}\\ \frac{\left(\left(\tilde{R}+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right){\omega }_e{L}_d-\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right){\tilde{\omega }}_e{\tilde{L}}_d}{\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)+s^2{\omega }_e^2{L}_d{L}_q}& \frac{\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)\left(\left(\tilde{R}+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)+s^2{\tilde{\omega }}_e^2{\tilde{L}}_d{\tilde{L}}_q}{\left(L_d{s}^2+\left(R+K_{\mathrm{pd}}\right)s+K_{\mathrm{id}}\right)\left(L_q{s}^2+\left(R+K_{\mathrm{pq}}\right)s+K_{\mathrm{iq}}\right)+s^2{\omega }_e^2{L}_d{L}_q}\end{array}\right]$

(30) Terms T.sub.dd(s) and T.sub.qq (s) are the direct current to current transfer functions, while T.sub.dq(s) and T.sub.qd (s)represent the cross coupling between the two current loops. For a typical system, the direct transfer functions have extremely high bandwidth.

(31) A block diagram depicting a typical current sensor fault loss of assist mitigation algorithm 400 is shown in FIG. 4. As described in more detail below, a current regulator selector 402 may be selectively enabled or disabled by a logic input. The current regulator selector 402 may select a mode of feedforward control depending on the fault condition. Algorithms described in more detail below may also be implemented to modify the torque command during the detection of the current sensor fault to ensure smooth transition from feedback control to feedforward control mode.

(32) For example, a first ramp waveform as shown in FIG. 5 may be implemented by the torque command modifier, as described in more detail below, to decrease the torque command during a time t.sub.ramp immediately after a fault detection. FIG. 5 illustrates a torque command change upon detection of a fault. When a fault is detected, the torque command modifier may implement the ramp waveform shown in FIG. 5 by reducing the torque command over a time period t.sub.ramp. After the time period t.sub.ramp, a modified torque command is reduced by a scale factor k to a magnitude of the product of scale factor k and T.sub.org. The modified torque command may be output by the torque command modifier as described in more detail below.

(33) A second torque ramp return waveform 600 is illustrated in FIG. 6. In some cases, the torque ripple caused by the offset error may exceed requirements related to maximum steering effort, so the torque command is set to zero immediately after the current sensor fault is detected. Accordingly, after the torque command is set to a zero value, the torque command is increased over a time period t.sub.ramp. The torque command may return to a steady-state value after time period t.sub.ramp. The modified torque command may be a function of the scale factor k and may be reduced by this scale factor in a steady state condition. The modified torque command may be reduced by a scale factor k as shown in FIG. 6.

(34) Although two specific embodiments of torque ramp return waveforms are shown, the torque command modifier may be configured to implement any number of ramp return waveforms, and the subject application is not limited to the waveforms shown in FIGS. 5 and 6. Further, other algorithms may be added to the torque command to avoid any disturbance the driver may feel during the transition period.

(35) FIG. 7 illustrates an open loop feedback current control block diagram 700 where the feedback loop is opened and only static feedforward compensation is employed. The motor control current loop block diagram can be simplified as shown. For this case, the direct transfer functions become:

(36) $\begin{array}{cc}{T}_{\mathrm{dd}}\left(s\right)=\frac{L_q\tilde{R}s+R\tilde{R}+{\omega }_e{\tilde{\omega }}_e{\tilde{L}}_d{L}_q}{L_d{L}_q{s}^2+R\left(L_d+L_q\right)s+R^2+{\omega }_e^2{L}_d{L}_q}& \left(\mathrm{Equation}9\right)\\ T_{\mathrm{qq}}\left(s\right)=\frac{L_d\tilde{R}s+R\tilde{R}+{\omega }_e{\tilde{\omega }}_e{\tilde{L}}_q{L}_d}{L_d{L}_q{s}^2+R\left(L_d+L_q\right)s+R^2+{\omega }_e^2{L}_d{L}_q}& \left(\mathrm{Equation}10\right)\end{array}$

(37) FIG. 8 represents a comparison plot 800 of a comparison of the frequency responses of the q-axis direct transfer functions at an operating speed of ω.sub.m=200 rad/s. As shown in FIG. 8, static compensation provides undesirable frequency responses in terms of both magnitude and phase, as compared to the feedback compensation.

(38) To compensate for undesirable frequency responses, a stability compensator of the steering control system may be changed at the time the fault occurs. However, a stability compensator would have to be tuned for the motor control loop bandwidth with the static feedforward control configuration. Further, since the stability compensator is a notch filter with various states, when the switching occurs, all the state variables will get re-initialized to zero, causing a lag in response time. Additionally, a modified torque component may be required during the transition.

(39) FIG. 9A shows a steering control system 900A with one type of current loop compensator 925A design. The configuration shown in FIG. 9A may control the PMSM motor electrical plant of the motor 18 by generating an output current from an input voltage command. Specifically, FIG. 9A includes a static feedforward compensation module 922A and a current regulation module 923A.

(40) FIG. 9A also includes a steering control module 912A with a stability compensator module 913A, a torque modifier module 914A, a stability compensator selector module 915A and a current reference generator module 916A. A feedforward selection module 918A changes the mode of the current regulator module 923A in the event a current sensor failure is detected. The feedforward selection module 918A selects a mode of the current regulator module 923A for the electric motor of the system, which is sent to the PMSM motor electrical plant of the motor 18.

(41) The system may further include a current sensor fault detector module 920A that detects an operational state of a current sensor (not shown). The current sensor fault detector module 920A may send an enable command to the stability compensator selector module 915A, the torque modifier module 914A, and the feedforward selection module 918A.

(42) In response to the detection of a current sensor fault by current sensor fault detector module 920A, the stability compensator selector module 915A may implement a loss of assist mode in the steering system by selecting a loss of assist mode output from the stability compensator module 913A, and therefore generate a compensated torque command that is sent to the torque command modifier module 913A. The selection of the loss of assist mode output changes a function provided by the stability compensator module 913A upon the detection of the current sensor fault. The stability compensator module 913A may be tuned as a function of the motor control bandwidth, while the static feedforward control configuration implemented in the current loop compensator 925A may not change when the feedforward selection module 918A receives the enable command from the current sensor fault detector module 920A.

(43) The stability compensator module 913A is, in some embodiments, a notch filter that can be programmed with a plurality of states. During the change of the function of the stability compensator module 913A as controlled by the stability compensator selector module 915A, state variables of the stability compensator module 913A may be re-initialized to zero values, and over time, transition to values that represent the actual state of the steering system 900A.

(44) Specifically, the torque modifier module 914A may implement the first and second ramp waveforms as shown in FIG. 5 and FIG. 6, respectively, to assist with mitigation of any disruptions caused by the current sensor fault.

(45) The torque modifier module 914A may generate a modified torque command in response to a current sensor fault. A magnitude of the modified torque command may change over time and be consistent with the waveforms shown in FIG. 5 and FIG. 6. As emphasized above, the torque modifier module 914A is not limited to the implementation of the waveforms shown in FIGS. 5 and 6.

(46) Turning to FIG. 9, this figure includes a steering control module 912, a torque modifier module 914, and a current reference generator module 916. FIG. 9 further includes a feedforward selection module 918 that enables a dynamic feedforward compensation in the event of a detection of a sensor failure. The feedforward selection module 918 modifies the torque command sent to the electric motor of the system, which is represented by the PMSM motor electrical plant of the motor 18.

(47) The system may further include a current sensor fault detector module 920 that detects an operational state of a current sensor (not shown). The current sensor fault detector module 920 may send an enable command to the torque modifier module 914 and to the feedforward selection module 918.

(48) The torque modifier module 914 may implement the first and second ramp waveforms as shown in FIG. 5 and FIG. 6, respectively, to assist with mitigation of any disruptions caused by the current sensor fault. The torque modifier module 914 may generate a modified torque command in response to a current sensor fault. A magnitude of the modified torque command may change over time and be consistent with the waveforms shown in FIG. 5 and FIG. 6. As emphasized above, the torque modifier module 914 is not limited to the implementation of the waveforms shown in FIGS. 5 and 6.

(49) The feedforward selection module 918 may select a dynamic feedforward compensation mode that processes a motor current command. The motor current command may be generated by the current reference generator 916 in response to the current reference generator 916 receiving the torque command modifier. The processing of the motor current command may change the voltage commands sent to the electric motor in response to the current sensor fault detection.

(50) The dynamic feedforward compensation algorithm applied by the feedforward selection module 918 may be performed by the dynamic feedforward compensator module 922. The dynamic feedforward compensator module 922 may use a derivative transfer function implemented by a derivative estimation submodule (not shown). The dynamic feedforward compensator module 922 may modify a frequency response of a motor control loop of the power steering system. Ideally, the derivative transfer function is a true derivative that may be denoted by Laplace transform variable s, however in some embodiments, the transfer function may be represented by an approximation of the derivative, {tilde over (s)}, as follows:

(51) $\begin{array}{cc}\tilde{s}=\frac{s}{{\left(\tau s+1\right)}^n}& \left(\mathrm{Equation}12\right)\end{array}$

(52) The derivative estimation submodule may be a high pass filter in some embodiments, but in other embodiments the derivative estimation submodule may be a discrete time derivative filter with specific magnitude and phase characteristics.

(53) In should be appreciated that although the static feedforward module 922 is shown in FIG. 9, the static feedforward module 922 is not essential for operation of the system of FIG. 9 upon implementation of the dynamic feedforward algorithm.

(54) The stability compensator of the steering control module 912 is, in some embodiments, a notch filter that can be programmed with a plurality of states. During the change of the function of the stability compensator as controlled by the stability compensator selector module, state variables of the stability compensator may be re-initialized to zero values, and over time, transition to values that represent the actual state of the steering system.

(55) FIG. 10 includes a steering control module 1012 with a stability compensator module 1013, a torque modifier module 1014, a stability compensator selector module 1015 and a current reference generator module 1016. A feedforward selection module 1008 changes the mode of the current regulator module 1023 in the event a current sensor failure is detected. The feedforward selection module 1008 selects a mode of the current regulator module 1023 for the electric motor of the system, which is sent to the PMSM motor electrical plant of the motor 18.

(56) Specifically, the torque modifier module 1014 may implement the first and second ramp waveforms as shown in FIG. 5 and FIG. 6, respectively, to assist with mitigation of any disruptions caused by the current sensor fault.

(57) Similar to the description provided in FIG. 9A, in response to the detection of a current sensor fault by current sensor fault detector module 1020, the stability compensator selector module 1015 may implement a loss of assist mode in the steering system by selecting a loss of assist mode output from the stability compensator module 1013. The selection of the loss of assist mode output changes a function provided by the stability compensator module 1013 upon the detection of the current sensor fault.

(58) In addition, a feedforward selection module 1008 enables a dynamic feedforward compensation in the event of a detection of a sensor failure. The feedforward selection module 1008 modifies the torque command sent to the electric motor of the system, which is represented by the PMSM motor electrical plant of the steering system mechanical plant 1018.

(59) FIG. 11 is a simplified block diagram for the motor control current loop under fault condition with dynamic feedforward compensation employed. The derivative term is shown as {tilde over (s)}. The derivative compensator included in the derivative estimation module is an approximation of a true derivative. In general, many different types of derivative filter designs may be used, from simple high pass filters to more sophisticated discrete time derivative filters with specific magnitude and phase characteristics, depending on the application.

(60) For FIG. 11, the direct transfer functions become:

(61) $\begin{array}{cc}{T}_{\mathrm{dd}}\left(s\right)=\frac{L_q{\tilde{L}}_{d}s\tilde{s}+L_q\tilde{R}s+{\tilde{L}}_{d}R\tilde{s}+{\omega }_e{\tilde{\omega }}_e{\tilde{L}}_d{L}_q}{L_d{L}_q{s}^2+R\left(L_d+L_q\right)s+R^2+{\omega }_e^2{L}_d{L}_q}& \left(\mathrm{Equation}13\right)\\ T_{\mathrm{qq}}\left(s\right)=\frac{L_d{\tilde{L}}_{q}s\tilde{s}+L_d\tilde{R}s+{\tilde{L}}_{q}R\tilde{s}+{\omega }_e{\tilde{\omega }}_e{\tilde{L}}_q{L}_d}{L_d{L}_q{s}^2+R\left(L_d+L_q\right)s+R^2+{\omega }_e^2{L}_d{L}_q}& \left(\mathrm{Equation}14\right)\end{array}$

(62) It can be appreciated from equations 13 and 14 that if the derivative filter were ideal, both the transfer functions would simply become unity. The derivative filter is contained within the derivative estimation module 1110 in FIG. 11.

(63) If the current loop has a different configuration, and does not have a complete feedforward compensator during normal operation, then the full dynamic feedforward compensation terms can be calculated continuously, but applied only during the fault condition.

(64) As used above, the term “module” or “sub-module” refers to an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that executes one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. When implemented in software, a module or a sub-module can be embodied in memory as a non-transitory machine-readable storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method. Moreover, the modules and sub-modules shown in the above Figures may be combined and/or further partitioned.

(65) While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments. Rather, the invention can be modified to incorporate any number of variations, alterations, substitutions or equivalent arrangements not heretofore described, but which are commensurate with the spirit and scope of the invention. Additionally, while various embodiments of the invention have been described, it is to be understood that aspects of the invention may include only some of the described embodiments. Accordingly, the invention is not to be seen as limited by the foregoing description.