JP2012039730A - Control constant determination method and motor controller - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a control constant determination method that considers response to a torque ripple for rectangular wave control and stability and responsiveness of a torque feedback control system of a motor.SOLUTION: A torque feedback controller calculates a torque deviation of an output torque of the motor that performed low-pass filter processing for a torque command value and performs proportional integral control to calculate a voltage phase. A control constant determination method comprises: a step of determining a torque phase inclination that is an output torque inclination for voltage phase change as a transfer function of the controller; a step of deriving a first determination condition of an integral gain capable of securing a gain margin and a phase margin of a loop transfer function: a step of deriving a second determination condition of an integral gain capable of making responsiveness of a closed loop transfer function faster than a prescribed responsiveness; and a step of determining the integral gain so as to satisfy both the first determination condition and the second determination condition.

Description

  The present invention calculates a voltage phase, which is a phase of a rectangular wave with respect to a rotor angle, so as to reduce a deviation of an output torque with respect to a torque command value, and applies a rectangular wave voltage of the calculated voltage phase to thereby obtain a synchronous AC motor The present invention relates to a method for determining a control constant of a torque feedback controller of an electric motor that rotates and drives an electric motor, and an electric motor control device that includes the determined control constant.

  As the torque feedback controller as described above, a controller described in Patent Document 1 below is already known. In the technique of Patent Document 1, proportional-integral control is performed on the torque deviation so that the deviation of the output torque with respect to the torque command value is reduced, and the voltage phase of the rectangular wave is calculated.

However, the technique of Patent Document 1 does not specifically disclose a method for determining a control constant for proportional-integral control in consideration of stability and responsiveness of a torque feedback control system.
In addition, in the rectangular wave control, the harmonic component is superimposed on the rectangular wave voltage applied to the motor from the fundamental component of the frequency of one rotation cycle, and this harmonic component is compared to the case where the sine wave control is performed. Is also causing a large torque ripple. Therefore, when designing a torque feedback control system for rectangular wave control, it is necessary to design for torque ripple. However, in the technique of Patent Document 1, a control system design for torque ripple and a method for determining a control constant are as follows. Not specifically disclosed.

  In order to set the control constant in consideration of the stability and responsiveness of the torque feedback control system, it is necessary to express the output torque characteristic of the motor to be controlled by a transfer function, but the output torque characteristic of the motor is nonlinear. It is not easy to express with a transfer function.

JP 2000-50689 A

  Therefore, the control constant of the torque feedback controller is considered in consideration of the response to the torque ripple caused by the rectangular wave control and the stability and responsiveness of the torque feedback control system of the motor having a strong nonlinear output torque characteristic. Establishing a decision method is required.

According to the present invention for achieving the above object, a voltage phase that is a phase of a rectangular wave with respect to a rotor angle is calculated so that a deviation of an output torque with respect to a torque command value is reduced, and a rectangular wave voltage of the calculated voltage phase is calculated. The characteristic configuration of the method for determining the control constant of the torque feedback controller of the electric motor that rotates the synchronous AC motor by applying
The torque feedback controller detects the output torque of the electric motor, performs low pass filter processing on the detected output torque to calculate a filtered output torque, and calculates the filtered output torque with respect to the torque command value. A controller that calculates a torque deviation, which is a deviation, and performs proportional integral control including a proportional gain and an integral gain based on the torque deviation, and calculates the voltage phase;
Linearizing the output torque characteristics of the motor at each operating point of the voltage phase to derive a torque phase gradient that is a gradient of the output torque with respect to the change of the voltage phase, and the motor from the voltage phase to the output torque Motor linearization step for determining a transfer function of
A gain margin and a phase margin are ensured in the frequency characteristic of the round transfer function from the torque deviation to the post-filter output torque, which includes the proportional integral control transfer function, the motor transfer function, and the low pass filter transfer function. A first condition deriving step for deriving a first determination condition of the integral gain,
Responsiveness of the output torque to a change in the torque command in a closed loop transfer function from the torque command to the output torque, which includes a transfer function of the proportional integral control, a transfer function of the electric motor, and a transfer function of the low-pass filter. A second condition derivation step for deriving a second determination condition of the integral gain so as to be faster than a predetermined responsiveness;
An integral gain determining step for determining the integral gain so as to satisfy both the first determination condition and the second determination condition.

According to the above characteristic configuration, the output torque characteristic of the motor is linearized with respect to the operating point of the voltage phase, and the transfer function of the motor is determined as a value corresponding to the torque phase inclination, so torque feedback control including the motor Based on the transfer function of the entire system, the control constant can be determined in consideration of the stability and responsiveness of the control system.
In addition, according to the above-described characteristic configuration, the low-pass filter processing is performed on the output torque of the rectangular wave control in which the harmonic torque ripple increases, so that the harmonic ripple component can be removed. It is configured.
The low-pass filter becomes a delay element of the torque feedback control system, and the frequency response of the torque feedback control system greatly changes due to the change in the cut-off frequency, which affects the stability and responsiveness. In addition, since the torque phase gradient of the motor varies greatly depending on the operating point such as voltage phase, rotation speed, and applied voltage, the gain of the torque feedback control system varies greatly due to the variation of the torque phase gradient, and the stability and responsiveness. Affects.
However, according to the above characteristic configuration, the integral gain is such that the gain margin and the phase margin are secured from the frequency characteristic of the one-round transfer function including the transfer function of the proportional integral control, the transfer function of the motor, and the transfer function of the low pass filter. Therefore, even if the cut-off frequency of the low-pass filter and the torque phase gradient change, the first determination condition of the integral gain that can ensure the stability of the torque feedback control system is derived. Can be derived.
Also, the integral gain is such that the response of the output torque to the change in torque command of the closed loop transfer function consisting of the transfer function of proportional integral control, the transfer function of the motor, and the transfer function of the low-pass filter is faster than the predetermined response. Since the second determination condition is derived, the second determination condition of the integral gain that can ensure the responsiveness of the torque feedback control system even if the cutoff frequency of the low-pass filter and the torque phase inclination change. Can be derived.
In addition, since the integral gain is determined so as to satisfy both the first determination condition and the second determination condition, even if the cutoff frequency of the low-pass filter and the torque phase inclination change, the stability and response It is possible to determine an integral gain that ensures both of the characteristics.

  Here, in the first condition deriving step, as the first determination condition, the frequency of an open loop transfer function from the torque deviation consisting of the transfer function of the proportional integral control and the transfer function of the motor to the output torque It is preferable to derive the determination condition of the integral gain such that the gain crossing angular frequency in the characteristic is smaller than the cut-off frequency of the low-pass filter.

  According to this configuration, based on the gain crossing angular frequency of the open-loop transfer function and the cut-off frequency of the low-pass filter, the integral gain is set so that the gain margin and phase margin of the frequency characteristic of the loop transfer function are ensured. One determination condition can be easily determined.

  Here, in the second condition deriving step, as the second determination condition, the integration is performed such that a time constant of the closed-loop transfer function is equal to or less than a predetermined value when the transfer function of the low-pass filter is approximated to 1. It is preferable to derive a gain determination condition.

  According to this configuration, based on the time constant of the closed loop transfer function when the transfer function of the low-pass filter is approximated to 1, the output torque response to a change in the torque command in the closed loop transfer function is faster than a predetermined response. The second determination condition of the integral gain can be easily determined.

  Here, it is preferable that the integral gain determining step determines the integral gain as a variable value that changes according to the torque phase inclination so as to satisfy both the first determination condition and the second determination condition. It is.

  According to this configuration, since the integral gain is determined to be a variable value that changes according to the torque phase inclination, even when the value of the first determination condition and the value of the second determination condition change according to the torque phase inclination. The integral gain that satisfies both the first determination condition and the second determination condition can be determined. Further, an integral gain that satisfies the first determination condition and the second determination condition in a well-balanced manner can be determined according to the operating point of the torque phase inclination.

  Here, in the integral gain determination step, a system voltage that is an amplitude voltage of the rectangular wave voltage is set to a rotor rotational speed so that the integral gain satisfies both the first determination condition and the second determination condition. It is preferable to determine a variable value that changes according to the value divided by.

  According to this configuration, the integral gain is determined to be a variable value that changes in accordance with the value obtained by dividing the system voltage by the rotor rotational speed. Therefore, the value of the first determination condition and the value of the second determination condition are Even when the voltage changes according to a value obtained by dividing the voltage by the rotor rotation speed, an integral gain that satisfies both the first determination condition and the second determination condition can be determined. Further, an integral gain that satisfies the first determination condition and the second determination condition in a well-balanced manner can be determined according to the operating point of the value obtained by dividing the system voltage by the rotor rotational speed.

  Here, in the integral gain determining step, it is preferable that the integral gain is determined to be a constant value that satisfies both the first determination condition and the second determination condition over the entire use range of the torque phase gradient. is there.

  According to this configuration, since the integral gain is determined to be a constant value that satisfies both the first determination condition and the second determination condition over the entire range of use of the torque phase gradient, the setting of the integral gain can be simplified. The configuration of the proportional-integral controller can be simplified.

  Here, in the integral gain determining step, the integral gain used in a steady state where the torque deviation is equal to or less than a predetermined value is used, and the responsiveness of the closed-loop transfer function in the second determining condition is the predetermined responsiveness. It is preferable to determine so as to match.

  In a steady state where the torque deviation is equal to or less than a predetermined value, there is little need to improve the responsiveness of the torque feedback control system. According to the above configuration, the responsiveness is lowered to the lower limit, the response sensitivity of the feedback system to the ripple of the output torque composed of the harmonic component is lowered, and the voltage phase can be prevented from oscillating at the steady state.

  Here, in the torque feedback controller, the cutoff frequency of the low-pass filter is changed in proportion to the rotor rotational speed, the torque deviation is proportional to the rotor rotational speed, and the amplitude of the rectangular wave voltage A controller that calculates a corrected torque deviation by multiplying a torque deviation correction coefficient that varies inversely proportional to a system voltage that is a voltage, performs the proportional integral control based on the corrected torque deviation, and calculates the voltage phase. It is preferable.

  According to this configuration, the torque deviation correction coefficient multiplied by the torque deviation is changed in proportion to the rotor rotational speed and inversely proportional to the system voltage that is the amplitude voltage of the rectangular wave voltage, and the cutoff frequency of the low-pass filter is changed. Since the value is changed in proportion to the rotor rotational speed, the value of the first determination condition can be prevented from changing in accordance with the torque phase gradient, and an integral gain setting range that satisfies the first determination condition can be obtained. Can be increased.

  Here, when the proportional integral control is discretized, a control cycle determining step for determining a control cycle of the proportional integral control so that a gain margin and a phase margin in the frequency characteristic of the one-round transfer function are ensured. It is preferable to further provide.

  According to this configuration, for example, when the proportional integral control is discretized for implementation in a digital computer, the control period is determined so that the gain margin and the phase margin in the frequency characteristic of the round transfer function are ensured. Even after discretization, the stability of the torque feedback control system can be ensured.

  Here, it is preferable that the control cycle determining step determines the control cycle so as to be inversely proportional to the integral gain.

  According to this configuration, since the control cycle is determined to be inversely proportional to the integral gain, the stability of the torque feedback control system can be prevented from changing greatly even if the integral gain changes.

According to the present invention for achieving the above object, a voltage phase that is a phase of a rectangular wave with respect to a rotor angle is calculated so that a deviation of an output torque with respect to a torque command value is reduced, and a rectangular wave voltage of the calculated voltage phase is calculated. An electric motor control device including a torque feedback controller for an electric motor that applies rotational force to rotationally drive a synchronous AC electric motor,
The torque feedback controller detects the output torque of the electric motor, performs low pass filter processing on the detected output torque to calculate a filtered output torque, and calculates the filtered output torque with respect to the torque command value. A controller that calculates a torque deviation, which is a deviation, and performs proportional integral control including a proportional gain and an integral gain based on the torque deviation, and calculates the voltage phase;
The output torque characteristic of the electric motor is linearized at the operating point of each voltage phase to derive a torque phase inclination that is an inclination of the output torque with respect to the change of the voltage phase, and the electric motor from the voltage phase to the output torque is derived. The transfer function is a value corresponding to the torque phase gradient,
A gain margin and a phase margin are ensured in the frequency characteristic of the round transfer function from the torque deviation to the post-filter output torque, which includes the proportional integral control transfer function, the motor transfer function, and the low pass filter transfer function. A first determination condition of the integral gain such as
Response of the output torque to a step change of the torque command in a closed-loop transfer function from the torque command to the output torque, which includes a transfer function of the proportional integral control, a transfer function of the electric motor, and a transfer function of the low-pass filter. Based on the second determination condition of the integral gain such that the property is faster than a predetermined response,
The integral gain determined to satisfy both the first determination condition and the second determination condition is provided.

  According to the above characteristic configuration, the torque feedback controller included in the motor control device includes the integral gain determined so as to satisfy both the first determination condition and the second determination condition. Even if the cutoff frequency and the torque phase inclination change, both the stability and the responsiveness of the torque feedback controller are ensured.

It is a block diagram which shows the structure of the torque feedback controller which concerns on 1st embodiment of this invention. It is a block diagram which shows the structure of the torque feedback control which concerns on 1st embodiment of this invention. It is a block diagram which shows the structure of the torque feedback control which concerns on 1st embodiment of this invention. It is a figure which shows the output torque characteristic of the electric motor which concerns on 1st embodiment of this invention. It is a figure which shows the characteristic of the torque phase inclination of the electric motor which concerns on 1st embodiment of this invention. It is a figure which shows the characteristic of the intercept of the electric motor which concerns on 1st embodiment of this invention. It is a figure which shows the driving | operation area | region of the rectangular wave control which concerns on 1st embodiment of this invention. It is a figure which shows the rectangular wave voltage supplied to the electric motor which concerns on 1st embodiment of this invention. It is a Bode diagram explaining the 1st decision conditions concerning a first embodiment of the present invention. It is a Bode diagram explaining the 1st decision conditions concerning a first embodiment of the present invention. It is a figure explaining the 2nd determination conditions which concern on 1st embodiment of this invention. It is a Bode diagram explaining the 2nd decision conditions concerning a first embodiment of the present invention. It is a Bode diagram explaining determination of a control cycle concerning a first embodiment of the present invention. It is a figure explaining the determination of the integral gain which concerns on 1st embodiment of this invention. It is a figure which shows the characteristic of the torque phase inclination which concerns on 1st embodiment of this invention. It is a block diagram which shows the structure of the torque feedback controller which concerns on 2nd embodiment of this invention. It is a block diagram which shows the structure of the torque feedback control which concerns on 2nd embodiment of this invention. It is a figure explaining the determination of the integral gain which concerns on 2nd embodiment of this invention.

[First embodiment]
A first embodiment of the present invention will be described with reference to the drawings. As shown in FIG. 1, the torque feedback controller FB of the electric motor M calculates a voltage phase δ that is a phase of a rectangular wave with respect to the rotor angle θ so that the deviation of the output torque T from the torque command value To decreases. The controller drives the synchronous AC motor M to rotate by applying a rectangular wave voltage of the calculated voltage phase δ. The present invention is characterized by a method for determining a control constant of the torque feedback controller FB.

1. Torque feedback controller A torque feedback controller FB according to the present embodiment detects an output torque T of an electric motor M by an output torque detector Tdt as shown in FIG. 1, and low-passes the output torque T by a low-pass filter LPF. A filtered process is performed to calculate a filtered output torque Tf. Then, the deviation calculator Dv calculates a torque deviation ΔT which is a deviation of the output torque Tf after the filter with respect to the torque command value To, and the proportional integration controller PI provides a proportional gain having a proportional gain Kp and an integral gain Ki based on the torque deviation ΔT. Integration control is performed to calculate the voltage phase δ.

  Further, the torque feedback controller FB includes a rectangular wave generator Wg. The rectangular wave generator Wg performs switching control of the inverter Inv so that a rectangular wave voltage having the voltage phase δ is applied to the motor M based on the calculated voltage phase δ and the detected rotor angle θ. The rotor angle θ is detected by a rotation angle sensor S1 such as a resolver provided in the electric motor M.

  FIG. 8 is a diagram illustrating a rectangular wave voltage supplied to the electric motor M. FIG. 8 shows, as an example, a voltage waveform applied to the U phase among the three-phase AC voltage applied to the electric motor M. The windings of the motor M are star-connected, and the difference between the maximum value and the minimum value in the rectangular wave matches the system voltage Vdc of the inverter Inv. The rectangular wave voltage is a rectangular wave of one pulse per one rotation (360 deg) of the rotor angle θ, and the voltage phase δ corresponds to the leading angle of the falling of the rectangular wave with respect to 0 deg of the rotor angle θ. Yes. The V-phase and W-phase voltage waveforms are rectangular waves similar to the U-phase, delayed by 120 deg and 240 deg from the U-phase voltage waveform, respectively. Note that the rotor angle θ is a lead angle of the q-axis described later with reference to the U-phase winding.

In the present embodiment, the output torque detector Tdt detects the output torque T according to the following equation based on the electric power Pin supplied to the electric motor M and the rotor angular velocity ωe of the electric motor M.
T = Pin / ωe
= (Iu × Vu + Iv × Vv + Iw × Vw) / ωe (1)
Here, Pin represents the electric power supplied to the electric motor M, and ωe represents the rotor angular velocity (electric angular velocity) of the electric motor M. Moreover, Iu, Iv, and Iw show the value of each phase of the three-phase alternating current supplied to the electric motor M, and Vu, Vv, and Vw show the voltage of each phase. In the present embodiment, the three-phase AC currents Iu, Iv, Iw are detected by the current sensor, and the three-phase AC voltages Vu, Vv, Vw are set to voltage command values set in the inverter Inv by the rectangular wave generator Wg. Is done. Note that the three-phase AC voltages Vu, Vv, and Vw may be values detected by a voltage sensor.

  Alternatively, the output torque detector Tdt performs three-phase two-phase conversion (d, q conversion) on the detected three-phase AC currents Iu, Iv, Iw to calculate the d-axis current Id, the q-axis current Iq, and calculates Based on the d-axis current Id and the q-axis current Iq, the magnet torque and the inductance torque may be calculated according to the equation (7) described later, and the sum of these may be calculated as the output torque T. Alternatively, a torque sensor may be provided in the electric motor M, and the output torque detector Tdt may set the detected value of the torque sensor as the output torque T.

In the present embodiment, the low-pass filter LPF is a low-pass filter having a cutoff frequency ωlpf, and the cutoff frequency ωlp is a basic one rotation cycle generated in the output torque T in the rectangular wave control, as will be described later. It is set to remove harmonic vibration components from the wave components. In this example, the low-pass filter is a first-order lag filter.
In the following, the steps for configuring the control constant determination method of the torque feedback controller FB, the motor linearization step, the first condition derivation step, the second condition derivation step, the integral gain determination step, and the discretization The control cycle determination step for setting the control cycle will be described.

2. Motor linearization step Since the output torque characteristic of the motor M is non-linear, it is difficult to determine the control constant of the torque feedback controller FB in consideration of the output torque characteristic of the motor M as it is. Therefore, in the motor linearization step, the output torque characteristic of the motor M is linearized at each operating point of the voltage phase δ to derive the torque phase gradient A that is the gradient of the output torque T with respect to the change of the voltage phase δ, and the voltage phase The transfer function Pm (s) of the electric motor M from δ to the output torque T is a value corresponding to the torque phase gradient A.

2-1. Modeling of control system In this embodiment, a torque feedback control system comprising the torque feedback controller FB and the motor M that is the control target is represented by a transfer function, and the torque feedback controller based on the frequency characteristics of the transfer function. The control constant of FB is determined. As shown in the block diagram of FIG. 2, the torque feedback control system is composed of a transfer function Gpi (s) of proportional integral control, a transfer function Pm (s) of the motor M, and a transfer function Glpf (s) of a low-pass filter. . Here, the transfer function Gpi (s) of proportional-integral control is a transfer function from the torque deviation ΔT to the voltage phase δ, and the transfer function Pm (s) of the motor M is transferred from the voltage phase δ to the output torque T. The low-pass filter transfer function Glpf (s) is a transfer function from the output torque T to the filtered output torque Tf. When the transfer function Pm (s) of the electric motor M is made to correspond to FIG. 1, the rectangular wave generator Wg instructs the inverter Inv according to the voltage phase δ to apply the rectangular wave voltage of the voltage phase δ to the electric motor M. The transfer function until the output torque T of the electric motor M is detected by the output torque detector Tdt.

2-2. Modeling of controller The transfer function Gpi (s) of proportional-integral control is expressed by the following equation.
Gpi (s) = Kp + Ki / s (2)
Here, Kp is a proportional gain, and Ki is an integral gain.
In this embodiment, the low-pass filter is a first-order lag filter, and the transfer function Glpf (s) of the low-pass filter is expressed by the following equation.
Glpf (s) = 1 / (1 + Tlpf × s) (3)
Here, Tlpf is a first-order lag time constant, and the inverse of the time constant Tlpf is the cut-off frequency ωlpf of the low-pass filter (ωlpf = 1 / Tlpf).

2-3. Modeling of the motor Next, the motor M is modeled. The electric motor M is a permanent magnet synchronous motor (PMSM) that operates by alternating current. In the present embodiment, the motor M is a synchronous motor (IPMSM) having an embedded magnet structure that operates with a three-phase AC.
A model for PMSM analysis and design is described. The d-axis is defined in the direction of the N pole of the permanent magnet provided in the rotor (rotor), and the q-axis is defined in a direction advanced by π / 2. The lead angle of the q axis with respect to the U-phase winding is defined as the rotor angle θ. By the d and q conversions, the three-phase windings that are stationary on the stator (stator) are converted into d and q windings that rotate in synchronization with the rotor (rotor).
The voltage equation in steady state can be expressed as:
Vd = −ωe × Lq × Iq
Vq = ωe × Ld × Id + ωe × Φ (4)
Here, Vd and Vq are d-axis and q-axis voltage values, respectively. Id and Iq are current values of the d-axis and q-axis, respectively. Further, Ld and Lq are d-axis and q-axis inductances, and ωe is an electrical angular velocity. Φ is the number of flux linkages.

Here, when Vd and Vq are expressed using the magnitude Va of the voltage vector and the voltage phase δ with reference to the q axis, the following equation is obtained.
Vd = −Va × sinδ (5)
Vq = Va × cosδ (6)

The output torque T of the electric motor M can be expressed as:
T = Pn × Φ × Iq + Pn × (Ld−Lq) × Id × Iq (7)
Here, Pn represents the number of pole pairs. In the above formula, the first term on the right side represents the magnet torque by the permanent magnet, and the second term on the right side represents the reluctance torque.

When the relational expression between the output torque T and the voltage vector is derived from the above expressions (4) to (7), the following expression is obtained.
T = Pn × Φ × Va × sinδ / (ωe × Ld)
+ Pn × (Ld−Lq) × Va ² × sin (2 × δ) / (2 × ωe ² × Lq × Ld) (8)
Similar to Equation (7), the first term on the right side represents the magnet torque by the permanent magnet, and the second term on the right side represents the reluctance torque. FIG. 4 shows an example of the change in the output torque T with respect to the change in the voltage phase δ. In the example shown in FIG. 4, the monotonously increasing range in which the output torque T increases as the voltage phase δ increases is in the range of about −110 deg to +110 deg in the example shown in FIG. 4, and this monotonically increasing range is used for torque feedback control. Scope. The use range of the voltage phase δ is set for each operating point such as the electrical angular velocity ωe and the system voltage Vdc.

Here, the magnitude Va of the voltage vector can be expressed as follows using the system voltage Vdc from the fundamental wave component of the rectangular wave voltage.
Va = (√6 / π) × Vdc (9)
In the rectangular wave control, harmonic components (frequencies of 3 times, 5 times, 7 times,... Of the fundamental wave) are superimposed on the voltage vector, and this harmonic component is torque. Ripple is generated. Therefore, the torque ripple becomes larger than that of the sine wave control.

2-3-1. Linearization of electric motor Since the equation of the output torque characteristic of the electric motor M of the derived equation (8) is non-linear, the transfer function cannot be derived as it is.
Therefore, the output torque characteristic of the motor M is linearized at each operating point of the voltage phase δ, and the torque phase gradient A that is the gradient of the output torque T with respect to the change of the voltage phase δ is derived. The transfer function Pm (s) of the motor M is determined to a value corresponding to the torque phase gradient A.

The linearized output torque characteristic is expressed as the following equation.
T = Aδ + B (10)
Here, A is the torque phase gradient that is the gradient of the output torque T with respect to the change in the voltage phase δ at each operating point of the voltage phase δ, and B is the intercept at that time. FIG. 4 shows an example in which the output torque characteristic is linearized at the operating point δ1 of the voltage phase δ.

The torque phase gradient A is derived as follows by differentiating both sides of the above equation (8) by the voltage phase δ and further eliminating the voltage amplitude Va using the equation (9).
It is expressed.
A = dT / dδ = Pn × Φ × (√6 / π) × Vdc × cosδ / (ωe × Ld)
+ Pn × (Ld−Lq) × (√6 / π) ² × Vdc ² × cos (2 × δ) / (ωe ² × Lq × Ld)
... (11)
Further, the intercept B is represented by the following equation (12) from the equations (8) to (11).
B = Pn × Φ × (√6 / π) × Vdc × (sinδ−δ × cosδ) / (ωe × Ld)
+ Pn × (Ld−Lq) × (√6 / π) ² × Vdc ² × (sin (2 × δ) −2 × cos (2 × δ))
/ (2 × ωe ² × Lq × Ld) (12)
FIG. 5 shows an example of the change in the torque phase gradient A with respect to the change in the voltage phase δ. Since the use range of the torque feedback control is a monotonically increasing range, the torque phase gradient A is a positive value within a predetermined range. Further, the torque phase gradient A varies depending on the operating point of the voltage phase δ. Further, it can be seen from the equation (11) that the torque phase gradient A changes in proportion to the system voltage Vdc / electrical angular velocity ωe. The use range of the system voltage Vdc is determined by the operation range of the booster circuit that supplies the system voltage Vdc to the inverter Inv in the rectangular wave control. Further, the use range of the electrical angular velocity ωe (the rotational speed N of the electric motor M) is determined in advance by the execution range of the rectangular wave control as shown in FIG. Therefore, as shown in FIG. 15, the system voltage Vdc / rotation speed N is used within a predetermined range, and the torque phase gradient A changes approximately in proportion to the system voltage Vdc / rotation speed N within the use range.

Therefore, the transfer function Pm (s) of the electric motor M from the voltage phase δ to the output torque T is determined as the torque phase gradient A based on the linearized output torque characteristic of Equation (10).
Pm (s) = A (13)
From the above, the block diagram of the torque feedback control system is as shown in FIG.

3. First condition deriving step In the first condition deriving step, the transfer function Gpi (s) of proportional integral control determined above, the transfer function Pm (s) of the motor M, and the transfer function Glpf (s) of the low-pass filter are used. The first determination condition of the integral gain Ki is derived so that the gain margin Yg and the phase margin Yp in the frequency characteristic of the one-round transfer function L (s) from the torque deviation ΔT to the filtered output torque Tf are ensured. In other words, the first determination condition is a stability condition for ensuring stability.

The round transfer function L (s) can be expressed by the following equation from the equations (2), (3), and (13).
L (s) = Glpf (s) x Pm (s) x Gpi (s)
= 1 / (1 + Tlpf × s) × A × (Kp + Ki / s) (14)

If the gain margin Yg and the phase margin Yp in the frequency characteristic of the loop transfer function L (s) are secured, the stability of the torque feedback control system can be secured. Therefore, the first determination condition of the integral gain Ki is derived so that the gain margin Yg and the phase margin Yp of the round transfer function L (s) can be secured.
Here, the gain margin Yg is lower than the 0 dB gain of the frequency characteristic of the round transfer function L (s) at the phase crossover frequency when the phase of the frequency characteristic of the round transfer function L (s) is −180 deg. Is defined as the amount that is. Thus, when the gain is 0 dB or less when the phase is -180 deg, the amplitude is stable because it attenuates, and when it is greater than 0 dB, the amplitude increases and becomes unstable. It is also stable when there is no frequency at which the phase of the frequency characteristic of the loop transfer function L (s) becomes −180 deg.
The phase margin Yp is the phase of the frequency characteristic of the round transfer function L (s) at -180 deg at the gain crossover angular frequency when the gain of the frequency characteristic of the round transfer function L (s) crosses 0 dB. It is defined as the amount that exceeds. Thus, when the gain is 0 dB, the phase is stable when it is −180 deg or more, and when it is smaller than −180 deg, the phase becomes unstable.

  In the present embodiment, in order to secure the gain margin Yg and the phase margin Yp in the frequency characteristic of the round transfer function L (s), as a first determination condition, the transfer function Gpi (s) of the proportional integral control and the motor M The gain cross angular frequency ωo in the frequency characteristic of the open loop transfer function Go (s) from the torque deviation ΔT consisting of the transfer function Pm (s) to the output torque T is smaller than the cut-off frequency ωlpf of the low-pass filter. A condition for determining the integral gain Ki is derived.

The open loop transfer function Go (s) can be expressed by the following equation from equations (2), (3), and (13).
Go (s) = Pm (s) x Gpi (s)
= A x (Kp + Ki / s) (15)
Therefore, the round transfer function L (s) of Expression (14) can be expressed by the following expression from the open loop transfer function Go (s) and the transfer function Glpf (s) of the low-pass filter.
L (s) = Glpf (s) × Go (s) (16)
The gain and phase of the frequency characteristic of the loop transfer function L (s) are obtained by comparing the Bode diagram of the open-loop transfer function Go (s) and the Bode diagram of the low-pass filter transfer function Glpf (s) By adding them together, the approximate curve can be obtained. Therefore, by considering the Bode diagram of the open-loop transfer function Go (s) and the Bode diagram of the transfer function Glpf (s) of the low-pass filter, the gain margin Yg and phase margin Yp of the loop transfer function L (s) The conditions for securing the can be determined.

Since the open loop transfer function Go (s) is a proportional element by linearizing the transfer function Pm (s) of the motor M, the open loop transfer function Go (s) is proportional to the equation (15). It can be composed of proportional elements and integral elements that are the same as the transfer function Gpi (s) of the integral control. Therefore, as shown in FIG. 9, the phase of the open loop transfer function Go (s) is delayed by −90 deg in the frequency band lower than the gain crossing angular frequency ωo, but is 0 deg in the frequency band higher than the gain crossing angular frequency ωo. It becomes the phase characteristic which advances to. In the open loop transfer function Go (s), the proportional gain Kp is set to a predetermined value such that A × Kp, which is the gain of the proportional term, is sufficiently smaller than 1. Therefore, as shown in FIG. 9, the gain of the open loop transfer function Go (s) in the high frequency band where the gain of the open loop transfer function Go (s) is 20 log ₁₀ | A × Kp | Yes.
Further, since the transfer function Glpf (s) of the low-pass filter is a first-order lag filter, the phase thereof is −45 deg at the cutoff frequency ωlpf as shown in FIG. 9, and is a frequency lower than the cutoff frequency ωlpf. Although it progresses from -45 deg to 0 deg in the band, the phase characteristic is delayed from -45 deg to -90 deg in the frequency band higher than the cut-off frequency ωlpf.

  From these characteristics, when the gain crossing angular frequency ωo of the open loop transfer function Go (s) is made smaller than the cutoff frequency ωlpf of the low pass filter transfer function Glpf (s), the gain crossing angular frequency ωo is The frequency band is lower than the cut-off frequency ωlpf in the transfer function Glpf (s) of the low-pass filter. Therefore, at the gain crossover angular frequency ωo, the phase of the transfer function Glpf (s) of the low-pass filter can be advanced by at least −45 deg. Therefore, even if the phase of the low-pass filter transfer function Glpf (s) is added to the phase of the open-loop transfer function Go (s), the phase of the loop transfer function L (s) is the highest at the gain crossover angular frequency ωo. There is no delay greater than -45 deg from the phase of the open loop transfer function Go (s) with a retard angle of -90 deg. Therefore, the phase margin Yp of the loop transfer function L (s) can be ensured to be greater than 45 degrees, and the stability of the torque feedback control system can be sufficiently ensured in terms of the phase margin Yp.

  In this case, since the gain of the low-pass filter transfer function Glpf (s) is close to 0 dB at the gain crossover angular frequency ωo, the loop transfer function L (s ) Is approximately equal to the open loop transfer function Go (s). For this reason, it is possible to prevent the gain crossing angular frequency ωl of the loop transfer function L (s) from becoming smaller than the gain crossing angular frequency ωo of the open loop transfer function Go (s), and to substantially match them. Therefore, it is possible to prevent a decrease in the frequency bandwidth (bandwidth), which is a frequency band equal to or lower than the gain crossing angular frequency ωl, and it is possible to prevent deterioration of the quick response. In this frequency bandwidth, as shown in FIG. 12, the gain becomes 0 dB, and the followability of the output torque T to the change of the torque command To becomes good.

  Also, when the gain crossing angular frequency ωo is smaller than the cutoff frequency ωlpf, there is no frequency at which the phase of the loop transfer function L (s) is -180 deg. Can be secured.

  Further, when the gain crossing angular frequency ωo is made sufficiently smaller than the cut-off frequency ωlpf, as shown in FIG. 9, at the gain crossing angular frequency ωo, the phase of the transfer function Glpf (s) of the low-pass filter is 0 deg. You can go closer. Therefore, the phase margin Yp of the round transfer function L (s) can be secured up to 90 deg.

  FIG. 10 shows a case where the gain crossing angular frequency ωo of the open loop transfer function Go (s) is made sufficiently higher than the cutoff frequency ωlpf, contrary to the present embodiment. At the gain crossover angular frequency ωo, the phase of the transfer function Glpf (s) of the low-pass filter is delayed to near -90 deg. Therefore, the phase of the loop transfer function L (s) is delayed to approximately −180 deg at the gain crossover angular frequency ωo. At the gain crossover angular frequency ωo, the gain of the transfer function Glpf (s) of the low-pass filter is smaller than 0 dB, so this gain is added to the open-loop transfer function Go (s) to make a round transfer function L (s ) Is smaller than the open loop transfer function Go (s). Therefore, the gain crossing angular frequency ωl of the loop transfer function L (s) is smaller than the gain crossing angular frequency ωo of the open loop transfer function Go (s), the frequency bandwidth (bandwidth) is reduced, and the speed response is reduced. It is getting worse. Further, the phase margin Yp at the gain crossing angular frequency ωl of the loop transfer function L (s) is reduced, and the stability is lowered.

  Therefore, as in the present embodiment, as a first determination condition, the integral gain Ki is determined such that the gain crossing angular frequency ωo of the open-loop transfer function Go (s) is smaller than the cut-off frequency ωlpf of the low-pass filter. By satisfying the conditions, the gain margin Yg and phase margin Yp in the frequency characteristic of the loop transfer function L (s) are ensured to ensure stability, and the reduction of the frequency bandwidth (bandwidth) is prevented and the speed is reduced. Decrease in responsiveness can be prevented.

Next, the first determination condition is derived.
First, the gain crossing angular frequency ωo of the open loop transfer function Go (s) is derived. Substituting s = jω into the open-loop transfer function Go (s) in equation (16) to obtain the gain in decibels, the following equation is obtained.
20log ₁₀ | Go (jω) | = 20log ₁₀ (A × √ (Kp ² + Ki ² / ω ² )) (17)
From the equation (17), when the gain crossing angular frequency ωo when the gain is 0 dB (1 in the true number) is obtained, the following equation is obtained.
A × √ (Kp ² + Ki ² / ωo ² ) = 1
ωo = A × Ki × √ (1 / (1-A ² × Kp ² )) (18)
Note that the cutoff frequency ωlpf of the low-pass filter is 1 / Tlpf from the time constant Tlpf of the first-order lag filter.
The condition that the gain crossing angular frequency ωo of the open loop transfer function Go (s) is smaller than the cut-off frequency ωlpf of the low-pass filter is as follows.
ωo <ωlpf (19)
Substituting equation (18) into equation (19) and rearranging the integral gain Ki, the first determination condition of the following equation is obtained.
Ki <ωlpf / A × √ (1-A ² × Kp ² ) (20)

4. Second condition deriving step In the second condition deriving step, a torque command comprising a transfer function Gpi (s) of proportional-integral control, a transfer function Pm (s) of the motor M, and a transfer function Glpf (s) of the low-pass filter. In the closed loop transfer function Gfb (s) from To to the output torque T, the second determination condition of the integral gain Ki is such that the response of the output torque T to the change of the torque command To becomes faster than a predetermined response. To derive. In other words, the second determination condition is a responsiveness condition for ensuring responsiveness.

The closed loop transfer function Gfb (s) can be expressed by the following equation.
Gfb (s) = Pm (s) x Gpi (s) / (1 + Glpf (s) x Pm (s) x Gpi (s))
= Go (s) / (1 + Glpf (s) x Go (s)) (21)

  In the present embodiment, the transfer function Glpf (s) of the low-pass filter is used as the second determination condition so that the response of the output torque T to the torque command To in the closed-loop transfer function Gfb (s) is faster than a predetermined response. ) Is approximated to 1, a condition for determining the integral gain Ki is derived so that the time constant τ of the closed-loop transfer function Gfb (s) is equal to or less than a predetermined value.

The closed-loop transfer function Gfb (s) in the equation (21) is expressed by the following equation when the transfer function Glpf (s) of the low-pass filter is approximated to 1.
Gfb (s) = Go (s) / (1 + Glpf (s) × Go (s)) ≈Go (s) / (1 + Go (s)) (22)
When the integral gain Ki is determined by the first determination condition of the equation (20) and the condition of ωo <ωlpf of the equation (19) is satisfied, as shown in FIG. 12, the closed-loop transfer function Gfb (s) before and after the approximation. The frequency characteristics of are almost the same. As shown in FIG. 9, in the band where the frequency ω is smaller than the cutoff frequency ωlpf of the low-pass filter (ω <ωlpf), the gain of the transfer function Glpf (s) of the low-pass filter is almost 0 dB (true number ( Since the non-logarithm) is 1), the frequency characteristic of the round transfer function L (s) (= Glpf (s) x Go (s)) is assumed to be equal to the frequency characteristic of the open-loop transfer function Go (s) Can do. Therefore, the transfer function Glpf (s) of the low-pass filter can be approximated to 1 in the band. In the band where the frequency ω is equal to or higher than the cut-off frequency ωlpf of the low-pass filter (ω ≧ ωlpf), the loop transfer function L (s) (= Go (s) × Glpf (s)) and the open-loop transfer function Go (s ) Gain is lower than 0dB. Here, since the gain is reduced in dB, these gains are true (non-logarithmic) and are significantly smaller than 1. Therefore, the denominator of the closed-loop transfer function Gfb (s) in Equation (22) is almost 1 regardless of before and after the approximation (that is, 1 + Glpf (s) × Go (s) ≈1 + Go (s) ≈1). The transfer function Glpf (s) of the low-pass filter can be approximated to 1. Accordingly, the closed-loop transmission in which the transfer function Glpf (s) of the low-pass filter is approximated to 1 over both the band where the frequency ω is smaller and larger than the cut-off frequency ωlpf of the low-pass filter, that is, the entire range of the frequency ω. Using the function Gfb (s), the responsiveness of the closed-loop transfer function Gfb (s) can be considered.

The closed-loop transfer function Gfb (s) in the equation (22) becomes the following equation when the equation (15) is substituted.
Gfb (s) ≒ Go (s) / (1 + Go (s)) = (Kp / Ki × s + 1) / (τ × s + 1)
τ = (1 + A × Kp) / (A × Ki) (23)
Here, τ is the time constant of the closed loop transfer function Gfb (s).
The initial response which is the time response of the output torque T under the initial value 0 when the torque command To of the unit step function u (t) is input to the closed loop transfer function Gfb (s) of the equation (23). f (t) is derived as follows.
f (t) = L ⁻¹ (Gfb (s) × U (s)) = L ⁻¹ ((Kp / Ki × s + 1) / (τ × s + 1) × 1 / s)
= 1− (1−Kp / (1 + A × Kp)) × exp (−1 / τ × t) (24)
Here, L ⁻¹ () represents the inverse Laplace transform, and U (s) represents the Laplace transform of the unit step function u (t), which is 1 / s.
FIG. 11 shows the initial response f (t) of the output torque T in Expression (24). It can be seen that the exponential change of the first-order lag is dominant in the transient response of the indental response f (t) of the closed loop transfer function Gfb (s). After the step change of the torque command To, the response time of the step response until the output torque T reaches the torque command To (approx. 99% of To) is about 5 times the time constant τ of the equation (23). Become.

  Accordingly, the time constant τ of the closed loop transfer function Gfb (s) when the target response time of the step response is 5 × τo and the transfer function Glpf (s) of the low-pass filter is approximated to 1 is set to be equal to or less than the target time constant τo. The condition for determining the integral gain Ki is derived. Accordingly, it is possible to derive the second determination condition of the integral gain Ki such that the response of the output torque T to the torque command To in the closed loop transfer function Gfb (s) is faster than a predetermined response.

In the following, the second determination condition is derived.
The condition for the time constant τ of the closed-loop transfer function Gfb (s) to be equal to or less than a predetermined target time constant τo is as follows.
τ ≦ τo (25)
Substituting equation (23) into equation (25) and rearranging the integral gain Ki, the second determination condition of the following equation is obtained.
Ki ≧ 1 / τo / A × (1 + A × Kp) (26)
Here, the time constant τ corresponds to the reciprocal of the cutoff frequency ωfb (≈ωl, ≈ωo) of the closed-loop transfer function Gfb (s). Therefore, if the reciprocal of the target time constant τo is the target value ωfbo of the cutoff frequency of the closed-loop transfer function Gfb (s), the second determination condition of Expression (26) can be expressed by the following expression.
Ki ≧ ωfbo / A × (1 + A × Kp) (27)

5. Integral Gain Determination Step In the integral gain determination step, the integral gain Ki is determined so as to satisfy both the first determination condition and the second determination condition.
In the present embodiment, the condition that the integral gain Ki should satisfy is determined as the following expression so that both the first determination condition of Expression (20) and the second determination condition of Expression (27) are satisfied.
ωlpf / A × √ (1−A ² × Kp ² )> Ki ≧ ωfbo / A × (1 + A × Kp) (28)

The value of the first determination condition in Expression (28) is proportional to the cutoff frequency ωlpf of the low-pass filter, and as described above, A × Kp is set smaller than 1, and A ² × Kp ² is 1. Since it becomes sufficiently smaller, it is inversely proportional to the torque phase gradient A as shown in FIG.

Here, the setting of the cutoff frequency ωlpf in the present embodiment will be described. Since the rectangular wave voltage is applied to the electric motor M, a harmonic vibration component is superimposed on the output torque T of the electric motor M from the fundamental wave component of one rotation period of the electric motor M. Therefore, in the present embodiment, the cut-off frequency ωlpf of the low-pass filter is set so that the fundamental component of the output torque T is transmitted and the harmonic component is removed. Therefore, the cut-off frequency ωlpf is set to a frequency that is higher than the frequency of the fundamental wave and lower than a frequency that is six times the fundamental wave frequency, which is the lowest harmonic. In this example, the cut-off frequency ωlpf of the low-pass filter is set to 1.6 times the fundamental frequency and is set according to the rotational speed N [rpm] of the electric motor M, as in the following equation.
ωlpf = 2 × π × N / 60 × 1.6 (29)
Here, 2 × π × N / 60 is a frequency of one rotation cycle that is a frequency of the fundamental wave, and is equal to the rotor angular velocity ωe of the electric motor M.

  Therefore, the value of the first determination condition changes in proportion to the rotational speed N of the electric motor M. Since the rotation speed N changes between the lower limit rotation speed N1 and the upper limit rotation speed N2 that are the execution range of the rectangular wave control as shown in FIG. 7, the value of the first determination condition is as shown in FIG. In addition, the value between the value at the lower limit rotational speed N1 and the value at the upper limit rotational speed N2 changes according to the rotational speed N. Therefore, if the integral gain Ki is determined to be smaller than the value of the first determination condition corresponding to the lower limit rotation speed N1, the first determination condition can be satisfied in the entire use range of the rotation speed N.

  The value of the second determination condition in Expression (28) is proportional to the target cutoff frequency ωfbo (= 1 / τo) of the closed-loop transfer function Gfb (s), and A × Kp is smaller than 1 as described above. Therefore, it is inversely proportional to the torque phase gradient A as shown in FIG. Since the change timing of the voltage phase δ in the rectangular wave voltage is every electrical angle of 60 degrees, the target response time is set sufficiently later than one rotation cycle. Therefore, the target cutoff frequency ωfbo corresponding to 1/5 of the target response time is set to be smaller than the frequency of one rotation period. Therefore, the target cut-off frequency ωfbo is set to be smaller than the cut-off frequency ωlpf of the low-pass filter set between 1 and 6 times the frequency of one rotation cycle (ωfbo <ωlpf).

  Therefore, the value of the second determination condition is smaller than the value of the first determination condition. As shown in FIG. 14 with hatching, the first determination condition and the second determination condition in Expression (28) are used. There is a settable region of the integral gain Ki that satisfies both of the above.

In the present embodiment, the integral gain Ki is determined to be a variable value Kia that changes according to the torque phase gradient A so as to satisfy both the first determination condition and the second determination condition. For example, as shown in FIG. 14, the integral gain Ki is determined to be a value Kia that is intermediate between the first determination condition (lower limit rotational speed) and the second determination condition for each operating point of the torque phase gradient A.
Alternatively, the integral gain Ki may be determined to be a constant value Kib that satisfies both the first determination condition and the second determination condition over the entire use range of the torque phase gradient A.
Alternatively, as described above with reference to FIG. 15, the torque phase gradient A changes approximately in proportion to the system voltage Vdc / rotational speed N in the usage range. That is, as the system voltage Vdc / rotational speed N increases, the torque phase gradient A also increases. Therefore, the integral gain Ki changes according to the value obtained by dividing the system voltage Vdc, which is the amplitude voltage of the rectangular wave voltage, by the rotor rotational speed N so as to satisfy both the first determination condition and the second determination condition. A variable value may be determined.

Further, the integral gain Ki used in the steady state where the torque deviation ΔT is equal to or less than a predetermined value is determined so that the response of the closed-loop transfer function Gfb (s) in the second determination condition matches the predetermined response. It may be. That is, the integral gain Ki is determined by changing the second determination condition of the equation (26) as the following equation.
Ki = (1 + A × Kp) / A / τo (30)
As a result, in a steady state in which the torque deviation ΔT is equal to or less than a predetermined value, there is little need to increase the responsiveness of the torque feedback control system. It is possible to reduce the response sensitivity of the system and prevent the voltage phase δ from oscillating in a steady state.

6. Control cycle determination step In the control cycle determination step, when proportional-integral control is discretized, the control cycle Tc of proportional-integral control is set to gain margin Yg and phase margin Yp in the frequency characteristic of the round transfer function L (s). Is determined to be secured.

  When implementing torque feedback control designed in a continuous system in a control device using a digital computer, it is necessary to discretize the torque feedback control with a control cycle Tc (sampling interval). Therefore, a control cycle Tc in which stability is ensured is determined from the discretized transfer function of torque feedback control.

  As described in relation to Expression (22) in the second determination condition, the integral gain Ki is determined by the first determination condition in Expression (20), and the condition of ωo <ωlpf in Expression (19) is satisfied. In the case where the frequency ω is smaller than the cut-off frequency ωlpf of the low-pass filter (ω <ωlpf), the transfer function Glpf (s) of the low-pass filter can be approximated to 1 and ignored. Therefore, in this embodiment, the open-loop transfer function Go (s) that matches the one-round transfer function L (s) when the transfer function Glpf (s) of the low-pass filter is approximated to 1 is stable when discretized. The control cycle Tc is determined so as to ensure the performance. Since the open loop transfer function Go (s) is obtained by multiplying the proportional integral control by the torque phase gradient A, the control cycle Tc is a control cycle when the proportional integral control is discretized.

The discretized open-loop transfer function God (s) when the open-loop transfer function Go (s) in Equation (15) is discretized using a sampler that samples at every sampling interval Tc and the 0th-order hold is expressed by the following equation: Show.
God (s) = Go (s) x (1-exp (-s x Tc)) / s
= A * (Kp + Ki / s) * (1-exp (-s * Tc)) / s (31)
Expression (31) is z-transformed to obtain a pulse transfer function of the following expression.
God (z) = A × (Kp + Ki × Tc / (z−1)) (32)
In order to obtain the frequency characteristics of the pulse transfer function, substituting z = exp (j × ω × Tc) into the equation (32) and rearranging, the following equation is obtained.
God (jω) = α + j × β
α = A × (Kp−Ki × Tc / 2)
β = −A × Ki × Tc × sin (ω × Tc) / 2 / (1-cos (ω × Tc)) (32)
The phase crossover frequency ωp when the phase of the frequency characteristic of Expression (32) is −180 deg is obtained.
∠God (jω) = tan ^-1 (β / α) = − π
β / α = 0
sin (ω × Tc) = 0
Ω ωp = π / Tc (33)

Next, the gain of the frequency characteristic of Expression (32) when the phase becomes −180 deg (ω = π / Tc) is obtained.
| God (j × π / Tc) | = √ (α ² + β ² ) = A × (Ki × Tc / 2−Kp) (34)

Therefore, the condition for determining the control period Tc in which the gain of the equation (34) when the phase becomes −180 deg is smaller than 0 dB (1 in the true number), that is, the gain margin Yg is secured is as follows.
| God (j × π / Tc) | = A × (Ki × Tc / 2−Kp) <1
Tc <Tco
Tco = 2 × (1 + A × Kp) / A / Ki (35)
Here, Tco is the control cycle of the stability limit.
Therefore, the control cycle Tc is determined so as to satisfy the equation (35).
FIG. 13 shows the frequency characteristics of the discretized open loop transfer function God. When the control cycle Tc is set to the stability limit control cycle Tco (Tc = Tco), the gain margin Yg1 is 0 dB, which is the stability limit. Further, the phase margin Yp1 at the gain crossover angular frequency ωo is greatly reduced from 90 deg. Next, when the control cycle Tc is set smaller than the stability limit control cycle Tco (Tc <Tco), the gain margin Yg2 is secured, and the stability is secured. In addition, the phase margin Yp1 at the gain crossover angular frequency ωo is hardly reduced from 90 degrees, and the stability is ensured.

Therefore, in order to sufficiently secure the gain margin Yg and the phase margin Yp, the control cycle Tc may be determined to be sufficiently smaller than the control cycle Tco of the stability limit. For example, the control cycle Tc may be determined to be 1/10 of the stability limit control cycle Tco as in the following equation.
Tc = Tco / 10 (36)

  Further, it can be seen from the equation (35) that the control cycle Tco of the stability limit is inversely proportional to the integral gain Ki. Therefore, the control cycle Tc may be determined so as to be inversely proportional to the integral gain Ki. In this way, the control cycle Tc is changed so that the stability of the torque feedback system does not change according to the integral gain Ki determined so as to satisfy both the first determination condition and the second determination condition. can do. Further, it can be seen from the equation (35) that the control period Tco of the stability limit is inversely proportional to the torque phase gradient A. Therefore, the control cycle Tc may be determined so as to be inversely proportional to the torque phase gradient A.

  When the integral gain Ki is determined so as to be inversely proportional to the torque phase gradient A as in the case of the Kia example in FIG. 14 or in the case of the equation (30), A × Kp in the equation (35) is sufficiently larger than 1. Therefore, the control cycle Tco at the stability limit of the equation (35) can be set to a constant value. Therefore, when the integral gain Ki is determined so as to be inversely proportional to the torque phase gradient A, the stability of the discretized feedback control system can be maintained even if the control cycle Tc is constant as shown in the equation (36). It can be prevented from changing.

7. Motor control device The motor control device including the torque feedback controller FB as shown in FIG. 1 has control constants such as the integral gain Ki and the control cycle Tc of the torque feedback controller FB determined in each step described above. It is comprised so that it may comprise. Further, the torque feedback controller FB is configured to include a map or an arithmetic expression in which the integral gain Ki and the control cycle Tc are preset according to the torque phase gradient A or the system voltage Vdc / rotational speed N. Then, the torque feedback controller FB calculates the torque phase gradient A or the system voltage Vdc / rotation speed N based on various sensor detection values and control parameters, and calculates the calculated torque phase gradient A or the system voltage Vdc / rotation speed N. Accordingly, the integral gain Ki and the control cycle Tc are calculated.

[Second Embodiment]
Next, a second embodiment will be described with reference to the drawings. In the first embodiment, as shown in FIGS. 1 to 3, the torque feedback controller FB performs proportional-integral control based on the torque deviation ΔT. However, in the present embodiment, as shown in FIGS. 16 and 17, the torque feedback controller FB further includes a torque deviation corrector Ct, and the rotor deviation speed N with respect to the torque deviation ΔT by the torque deviation corrector Ct. The corrected torque deviation ΔTn is calculated by multiplying the torque deviation correction coefficient Kc that varies in proportion to the system voltage Vdc and inversely proportional to the system voltage Vdc, and proportional integral control is performed based on the corrected torque deviation ΔTn. Is different. Below, the determination method of the control constant of the torque feedback controller FB which concerns on this embodiment is demonstrated centering on difference with said 1st embodiment. Note that points not particularly described are the same as those in the first embodiment.

As described above, in this embodiment, the torque feedback controller FB is further provided with a torque deviation corrector Ct. The torque deviation corrector Ct calculates the corrected torque deviation ΔTn by multiplying the torque deviation ΔT by the torque deviation correction coefficient Kc. The torque deviation correction coefficient Kc is configured to change in proportion to the rotational speed N of the electric motor M and in inverse proportion to the system voltage Vdc. That is, the torque deviation corrector Ct performs a calculation represented by the following equation.
ΔTn = Kc × ΔT
Kc = K1 × N / Vdc (37)
Here, K1 is a predetermined constant.

Also in this embodiment, the low-pass filter LPF is a low-pass filter having a cutoff frequency ωlpf, and the cutoff frequency ωlpf is the rotational speed of the electric motor M as shown in the equation (29). It is set to change in proportion to N. Equation (29) is shown again below.
ωlpf = 2 × π × N / 60 × 1.6 (29)

With the addition of the torque deviation corrector Ct, the open loop transfer function Go (s) from the torque deviation ΔT to the output torque T in this embodiment is a torque deviation correction transfer function with respect to the right side of the equation (15). A certain Kc is multiplied to obtain the following equation.
Go (s) = A × (Kp + Ki / s) × Kc (38)
Along with this, the first determination condition of the equation (20) according to the present embodiment is changed as the following equation.
Ki <ωlpf / (Kc × A) × √ (1-Kc ² × A ² × Kp ² ) (39)
Here, unlike the equation (20) of the first embodiment, in the equation (39), the cutoff frequency ωlpf is changed to be divided by the torque deviation correction coefficient Kc × the torque phase gradient A. As shown in FIG. 15, since the torque phase gradient A is proportional to the system voltage Vdc / rotational speed N, the torque phase gradient A is corrected by K1 × (N / Vdc) in order to keep the torque phase gradient A constant.
Therefore, in the present embodiment, by providing the torque deviation corrector Ct that corrects the torque phase gradient A by K1 × (N / Vdc), the first determination condition is different from that of the first embodiment. The torque phase gradient A can always be a constant value.

  Accordingly, in the present embodiment, as shown in FIG. 18, unlike the first embodiment shown in FIG. 14, the first determination condition does not change according to the torque phase gradient A, and the integral gain Ki can be set easily.

Further, the second determination condition of the equation (27) according to the present embodiment is changed as the following equation.
Ki ≧ ωfbo / (Kc × A) × (1 + Kc × A × Kp) (40)
Here, the torque deviation correction coefficient Kc is corrected by K1 × (N / Vdc) so that the torque phase gradient A is always a constant value, as in the equation (37).

  Thus, unlike the first embodiment, the torque deviation corrector Ct that corrects the torque phase gradient A by K1 × (N / Vdc) is provided in the second determination condition of the equation (40). A constant value can always be set for any torque phase gradient A. Accordingly, it is possible to prevent the value of the second determination condition in the equation (40) from changing according to the torque phase gradient A. Therefore, the integral gain Ki can be set easily.

[Other Embodiments]
(1) In each of the above-described embodiments, the case where the low-pass filter is a first-order lag filter having the cutoff frequency ωlpf has been described as an example. However, the embodiment of the present invention is not limited to this. That is, it is also a preferred embodiment of the present invention that the low-pass filter is composed of a higher-order low-pass filter having a cutoff frequency ωlpf.

(2) In the second embodiment, the torque feedback controller FB includes the torque deviation correction mechanism Ct. In the first embodiment, the torque feedback controller FB does not include the torque deviation correction mechanism Ct. The case has been described as an example. However, the embodiment of the present invention is not limited to this. That is, in the first embodiment, the torque feedback controller FB includes a torque deviation correction unit Ct having a torque deviation correction coefficient Kc set to a constant value for gain adjustment, as shown in FIGS. It is also one of the preferred embodiments of the present invention to provide at the same position as in the second embodiment.

(3) In each of the above embodiments, the transfer function and the frequency characteristics are obtained by multiplying each of the torque phase gradient A and the integral gain Ki by a predetermined coefficient in consideration of the resolution design when the controller is mounted. It is also one preferred embodiment of the present invention that the first determination condition and the second determination condition are derived.

  The present invention calculates a voltage phase, which is a phase of a rectangular wave with respect to a rotor angle, so as to reduce a deviation of an output torque with respect to a torque command value, and applies a rectangular wave voltage of the calculated voltage phase to thereby obtain a synchronous AC motor The method can be suitably used for a method for determining a control constant of a torque feedback controller of an electric motor that rotationally drives the motor, and an electric motor control device that includes the determined control constant.

To: Torque command value T: Output torque ΔT: Torque deviation θ: Rotor angle S1: Rotation angle sensor N: Motor rotation speed δ: Voltage phase M: Electric motor (synchronous AC motor)
FB: Torque feedback controller PI: Proportional integral controller Tdt: Output torque detector LPF: Low pass filter Dv: Deviation calculator Tf: Filtered output torque Wg: Rectangular wave generator Inv: Inverter Kp: Proportional gain Ki: Integral Gain A: Torque phase slope B: Intercept Pm (s): Motor transfer function Gpi (s): Proportional integral control transfer function Glpf (s): Low-pass filter transfer function L (s): Round transfer function Gfb (s) ): Closed loop transfer function Go (s): open loop transfer function God (s): discretized open loop transfer function Yg: gain margin Yp: phase margin ωo: gain cross angular frequency of open loop transfer function ωlpf: cut of low-pass filter Off-frequency ωl: gain cross angular frequency ωp of a round transfer function ωp: phase crossover frequency τ of a discretized open loop transfer function τ: closed loop transfer function Number Tauo: target time constant (a predetermined value)
Vdc: system voltage ωe: rotor rotational speed (electrical angular speed)
Ct: torque deviation correction mechanism Kc: torque deviation correction coefficient ΔTn: corrected torque deviation Tc: control cycle (sampling interval)
Tco: Stability limit control cycle

Claims (11)

The voltage phase, which is the phase of the rectangular wave with respect to the rotor angle, is calculated so that the deviation of the output torque with respect to the torque command value is reduced, and the synchronous AC motor is rotationally driven by applying the rectangular wave voltage of the calculated voltage phase. A method for determining a control constant of a torque feedback controller of an electric motor,
The torque feedback controller detects the output torque of the electric motor, performs low pass filter processing on the detected output torque to calculate a filtered output torque, and calculates the filtered output torque with respect to the torque command value. A controller that calculates a torque deviation, which is a deviation, and performs proportional integral control including a proportional gain and an integral gain based on the torque deviation, and calculates the voltage phase;
Linearizing the output torque characteristics of the motor at each operating point of the voltage phase to derive a torque phase gradient that is a gradient of the output torque with respect to the change of the voltage phase, and the motor from the voltage phase to the output torque Motor linearization step for determining a transfer function of
A gain margin and a phase margin are ensured in the frequency characteristic of the round transfer function from the torque deviation to the post-filter output torque, which includes the proportional integral control transfer function, the motor transfer function, and the low pass filter transfer function. A first condition deriving step for deriving a first determination condition of the integral gain,
Responsiveness of the output torque to a change in the torque command in a closed loop transfer function from the torque command to the output torque, which includes a transfer function of the proportional integral control, a transfer function of the electric motor, and a transfer function of the low-pass filter. A second condition derivation step for deriving a second determination condition of the integral gain so as to be faster than a predetermined responsiveness;
An integral gain determining step of determining the integral gain so as to satisfy both the first determination condition and the second determination condition;   In the first condition deriving step, the gain in the frequency characteristic of the open loop transfer function from the torque deviation to the output torque consisting of the transfer function of the proportional integral control and the transfer function of the motor is set as the first determination condition. The method for determining a control constant according to claim 1, wherein a condition for determining the integral gain is derived so that a crossing angular frequency is smaller than a cutoff frequency of the low-pass filter.   In the second condition deriving step, as the second determination condition, the integral gain is determined such that a time constant of the closed-loop transfer function when the transfer function of the low-pass filter is approximated to 1 is equal to or less than a predetermined value. The method for determining a control constant according to claim 1, wherein the condition is derived.   The integral gain determination step determines the integral gain as a variable value that changes according to the torque phase gradient so as to satisfy both the first determination condition and the second determination condition. 4. A method for determining a control constant according to any one of 3 above.   In the integral gain determination step, the system voltage that is the amplitude voltage of the rectangular wave voltage is divided by the rotor rotational speed so that the integral gain satisfies both the first determination condition and the second determination condition. The method for determining a control constant according to any one of claims 1 to 3, wherein a variable value that changes according to the value is determined.   6. The integral gain determination step determines the integral gain to a constant value that satisfies both the first determination condition and the second determination condition over the entire use range of the torque phase gradient. A method for determining a control constant according to any one of the above.   In the integral gain determining step, the responsiveness of the closed-loop transfer function in the second determination condition matches the predetermined responsiveness with respect to the integral gain used in a steady state where the torque deviation is a predetermined value or less. The method for determining a control constant according to claim 1, wherein the control constant is determined as follows.   In the torque feedback controller, the cutoff frequency of the low-pass filter is changed in proportion to the rotor rotational speed, and the torque deviation is proportional to the rotor rotational speed and becomes the amplitude voltage of the rectangular wave voltage. A controller that calculates a corrected torque deviation obtained by multiplying a torque deviation correction coefficient that varies inversely proportional to a system voltage, and calculates the voltage phase by performing the proportional-integral control based on the corrected torque deviation. The method for determining a control constant according to any one of 1 to 7.   In the case where the proportional integral control is discretized, a control cycle determining step for determining a control cycle of the proportional integral control so as to ensure a gain margin and a phase margin in the frequency characteristic of the one-round transfer function is further provided. The method for determining a control constant according to any one of claims 1 to 8.   The control constant determining method according to claim 9, wherein the control cycle determining step determines the control cycle so as to be inversely proportional to the integral gain. The voltage phase, which is the phase of the rectangular wave with respect to the rotor angle, is calculated so that the deviation of the output torque with respect to the torque command value is reduced, and the synchronous AC motor is rotationally driven by applying the rectangular wave voltage of the calculated voltage phase. An electric motor control device including an electric motor torque feedback controller,
The torque feedback controller detects the output torque of the electric motor, performs low pass filter processing on the detected output torque to calculate a filtered output torque, and calculates the filtered output torque with respect to the torque command value. A controller that calculates a torque deviation, which is a deviation, and performs proportional integral control including a proportional gain and an integral gain based on the torque deviation, and calculates the voltage phase;
The output torque characteristic of the electric motor is linearized at the operating point of each voltage phase to derive a torque phase inclination that is an inclination of the output torque with respect to the change of the voltage phase, and the electric motor from the voltage phase to the output torque is derived. The transfer function is a value corresponding to the torque phase gradient,
A gain margin and a phase margin are ensured in the frequency characteristic of the round transfer function from the torque deviation to the post-filter output torque, which includes the proportional integral control transfer function, the motor transfer function, and the low pass filter transfer function. A first determination condition of the integral gain such as
Response of the output torque to a step change of the torque command in a closed-loop transfer function from the torque command to the output torque, which includes a transfer function of the proportional integral control, a transfer function of the electric motor, and a transfer function of the low-pass filter. Based on the second determination condition of the integral gain such that the property is faster than a predetermined response,
An electric motor control device comprising the integral gain determined so as to satisfy both the first determination condition and the second determination condition.

Images