CN112783099A - Fractional order composite control method and permanent magnet synchronous motor speed servo system - Google Patents

Fractional order composite control method and permanent magnet synchronous motor speed servo system Download PDF

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CN112783099A
CN112783099A CN202110007791.0A CN202110007791A CN112783099A CN 112783099 A CN112783099 A CN 112783099A CN 202110007791 A CN202110007791 A CN 202110007791A CN 112783099 A CN112783099 A CN 112783099A
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permanent magnet
magnet synchronous
synchronous motor
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CN112783099B (en
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郑伟佳
李欣
黄润权
林梅金
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Foshan University
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Abstract

The invention discloses a fractional order composite control method and a speed servo system of a permanent magnet synchronous motor. The method comprises the following steps: step 1, performing feedforward compensation on a q-axis current loop of a permanent magnet synchronous motor by using an extended state observer; and 2, the fractional order proportional-differential controller carries out order setting on the speed servo system of the permanent magnet synchronous motor through an optimization method based on differential evolution. The system comprises: the system comprises an extended state observer and a fractional order proportional-derivative controller; the invention meets the requirements of tracking performance and anti-interference performance in practical application. The step response performance of the whole permanent magnet synchronous motor speed servo system is improved. The invention is mainly used for the technical field of motor control.

Description

Fractional order composite control method and permanent magnet synchronous motor speed servo system
Technical Field
The invention relates to the technical field of motor control, in particular to a fractional order composite control method and a speed servo system of a permanent magnet synchronous motor.
Background
Modern control theory proposes many control algorithms and design methods with excellent performance and analysis tools, however, the controller designed by the modern control theory is often highly dependent on the accuracy of the established model. In actual engineering, accurate model parameters are difficult to obtain, and even the established mathematical model cannot really reflect all characteristics of the controlled object. Therefore, its practical control performance is often not as superior as that of the theoretical design. In contrast, the classical PID control theory does not depend on the controlled object model, and only depends on the error to perform feedback control on the controlled object. However, the controller is usually only suitable for linear objects, and when the controlled object presents strong coupling and nonlinear characteristics, the performance of the controller designed based on the PID classical control theory is prone to be unsatisfactory.
The active disturbance rejection control algorithm is a nonlinear control algorithm which is provided aiming at the defects of a PID control algorithm. The control idea of eliminating errors based on errors of a PID control algorithm is drawn, and on the basis of the basic idea of the PID control algorithm, the following links are added: 1) a transition process, 2) a nonlinear feedback control law, 3) an extended state observer, and 4) a more reasonable differential signal generator.
The Active Disturbance Rejection Control (ADRC) method is a commonly used composite control method. According to the ADRC scheme, the uncertainty and disturbance of the system are treated as lumped disturbances and estimated by an Extended State Observer (ESO). The composite control strategy adopts the separated design of a feedback controller and feedforward compensation, and can simultaneously ensure good tracking performance and interference suppression performance of a control system.
Fractional order pid (fopid) controllers are derived by extending the integral and derivative order of pid (iopid) controllers from 1 to a real number. FOPID controllers have the potential to achieve better performance of the control system compared to IOPID controllers. However, the tuning of the FOPID controller is more complicated due to the introduction of two additional degrees of freedom, the integration order and the differentiation order μ.
The traditional PID controller is difficult to enable the PMSM servo system to obtain good step response dynamic performance and interference rejection performance. The fractional order PID controller is expected to enable the system to obtain good dynamic performance, but the parameter setting is complex.
Disclosure of Invention
The present invention is directed to a fractional order compound control method and a speed servo system for a permanent magnet synchronous motor, which solve one or more of the problems of the prior art and provide at least one of the advantages.
The solution of the invention for solving the technical problem is as follows: a fractional order compound control method, comprising:
step 1, performing feedforward compensation on a q-axis current loop of a permanent magnet synchronous motor by using an extended state observer;
and 2, the fractional order proportional-differential controller carries out order setting on the speed servo system of the permanent magnet synchronous motor through an optimization method based on differential evolution.
Further, in step 1, the performing feed-forward compensation on the q-axis current loop of the permanent magnet synchronous motor by using the extended state observer includes: the extended state observer satisfies:
Figure BDA0002883755750000031
Figure BDA0002883755750000032
Figure BDA0002883755750000033
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is a fractional order proportional-derivative controller output signal, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer. Further, the order setting of the fractional order proportional-differential controller by an optimization method based on differential evolution comprises: the fractional order proportional-derivative controller satisfies the following conditions:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure BDA0002883755750000034
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure BDA0002883755750000035
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I represents fractional order proportional-derivative controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure BDA0002883755750000041
where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
Further, the step setting of the permanent magnet synchronous motor speed servo system by the fractional order proportional-derivative controller through an optimization method based on differential evolution comprises the following steps:
step 1, initialization: randomly select N μ values to construct the population, then according to the design specification (ω)c，
Figure BDA0002883755750000042
) Calculating a fractional order proportional-differential controller for each individual;
step 2, mutation: randomly selecting several individuals as target objects according to mutation rate, applying self-adaptive mutation rate, and overlapping for m timesMutation Rate P in generationsmIs defined as:
Pm＝P0·2γ,
Figure BDA0002883755750000043
wherein, P0Is the initial mutation rate, msThe upper limit of the iteration times is adopted, and after a target individual is selected, a mutant individual is generated, so that a fractional order proportional-differential controller of the mutant individual is obtained;
step 3, step response simulation: controlling the speed of the permanent magnet synchronous motor by using the fractional order proportional-derivative controller of each individual, and executing step response simulation;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the change of the overall average fitness in the last 10 iterations is less than delta or the iteration number reaches the upper limit, the optimization is terminated, the individual with the maximum fitness is regarded as the optimal individual, and the final fractional order proportional-derivative controller is obtained.
In another aspect, a permanent magnet synchronous motor speed servo system includes: the system comprises an extended state observer and a fractional order proportional-derivative controller; the extended state observer is used for performing feedforward compensation on a q-axis current loop of the permanent magnet synchronous motor; the fractional order proportional-differential controller is used for carrying out order setting on a speed servo system of the permanent magnet synchronous motor through an optimization method based on differential evolution.
Further, the speed servo system of the permanent magnet synchronous motor also comprises a first processing unit; the first processing unit is configured to perform operations including: determining feedforward compensation using an extended state observer, comprising: the extended state observer satisfies:
Figure BDA0002883755750000051
Figure BDA0002883755750000052
Figure BDA0002883755750000053
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is a fractional order proportional-derivative controller output signal, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer.
Further, the speed servo system of the permanent magnet synchronous motor further comprises a second processing unit, wherein the second processing unit is used for executing the following steps: the fractional order proportional-derivative controller satisfies the following conditions:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure BDA0002883755750000061
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure BDA0002883755750000062
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I denotes Fractional Order Proportional Derivative (FOPD) controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure BDA0002883755750000063
where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
Further, the second processing unit is further configured to perform:
step 1, initialization: randomly select N μ values to construct the population, then according to the design specification (ω)c，
Figure BDA0002883755750000071
) Calculating a fractional order proportional-differential controller for each individual;
step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure BDA0002883755750000072
wherein, P0Is the initial mutation rate, msThe upper limit of the iteration times is adopted, and after a target individual is selected, a mutant individual is generated, so that a fractional order proportional-differential controller of the mutant individual is obtained;
step 3, step response simulation: controlling the speed of the permanent magnet synchronous motor by using the fractional order proportional-derivative controller of each individual, and executing step response simulation;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the change of the overall average fitness in the last 10 iterations is less than delta or the iteration number reaches the upper limit, the optimization is terminated, the individual with the maximum fitness is regarded as the optimal individual, and the final fractional order proportional-derivative controller is obtained.
The invention has the beneficial effects that: the invention provides a fractional order composite control scheme aiming at a Permanent Magnet Synchronous Motor (PMSM) speed servo system so as to meet the requirements of tracking performance and anti-interference performance in practical application. An Extended State Observer (ESO) is used to compensate for uncertainty in the current loop and convert a Permanent Magnet Synchronous Motor (PMSM) speed servo device to a dual integrator model. A Fractional Order Proportional Derivative (FOPD) controller is used as the velocity controller of the servo system. The FOPD controller is adjusted by an optimization method based on Differential Evolution (DE) to ensure that the control system obtains the best step response performance. The step response performance of the whole permanent magnet synchronous motor speed servo system is improved.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the example serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a diagram of a dynamic model of a q-axis current loop based on an extended state observer;
FIG. 2 is a diagram of a dynamic model of a PMSM speed servo system based on a q-axis current loop of an Extended State Observer (ESO);
fig. 3 is a main step of a Fractional Order Proportional Derivative (FOPD) controller for order tuning of a permanent magnet synchronous motor speed servo system by an optimization method based on Differential Evolution (DE).
Detailed Description
The conception, the specific structure, and the technical effects produced by the present invention will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings to fully understand the objects, the features, and the effects of the present invention. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and those skilled in the art can obtain other embodiments without inventive effort based on the embodiments of the present invention, and all embodiments are within the protection scope of the present invention. In addition, all the coupling/connection relationships mentioned herein do not mean that the components are directly connected, but mean that a better coupling structure can be formed by adding or reducing coupling accessories according to specific implementation conditions. All technical characteristics in the invention can be interactively combined on the premise of not conflicting with each other.
Embodiment 1, referring to fig. 1 and 2, a fractional order compound control method applied to a speed servo system of a permanent magnet synchronous motor includes:
step 1, performing feedforward compensation on a q-axis current loop of a permanent magnet synchronous motor by using an Extended State Observer (ESO);
and 2, a Fractional Order Proportional Differential (FOPD) controller carries out order setting on the speed servo system of the permanent magnet synchronous motor by an optimization method based on Differential Evolution (DE).
For the q-axis current loop of an existing Permanent Magnet Synchronous Motor (PMSM), this is generally defined as follows:
the three-phase rotating PMSM can be described by equations (1) and (2) by using the d-q coordinate as a reference coordinate and adopting a magnetic field orientation vector control method,
Figure BDA0002883755750000091
Figure BDA0002883755750000092
wherein iqIs the q-axis stator current, uqIs the q-axis stator voltage, LqIs q-axis stator inductance, R is stator resistance, npIs the number of pole pairs, ΨfIs the flux linkage, ω is the angular velocity (in rad/s), J is the moment of inertia of the PMSM, CmIs the torque coefficient, TdIs the total disturbance torque.
When designing a q-axis current controller, the back electromotive force (EMF) npωΨfCan be approximated as a constant perturbation. Using PI controlThe controller is used as a q-axis current controller,
Figure BDA0002883755750000101
wherein e ═ iqr-iq，iqrIs a q-axis reference current, KsBeing the proportional gain of the current PI controller, the q-axis current loop may be approximately represented in the form:
Figure BDA0002883755750000102
in some preferred embodiments, in step 1, the performing feed-forward compensation on the q-axis current loop of the permanent magnet synchronous motor by using an Extended State Observer (ESO) includes: determining that a q-axis current loop after feedforward compensation using an Extended State Observer (ESO) satisfies:
Figure BDA0002883755750000103
Figure BDA0002883755750000104
Figure BDA0002883755750000105
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is a fractional order proportional-derivative controller output signal, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer, KsIs the proportional gain, x, of the current PI controller1＝iq，x2＝h，h＝-b0iq+ ε, ε is an introduced interference term, which is constant, iqIs the q axisStator current, LqIs the q-axis stator inductance.
The method specifically comprises the following steps: the Extended State Observer (ESO) based q-axis current loop is:
Figure BDA0002883755750000111
wherein, b0＝Ks/LqWhere e represents the influence of unmodeled dynamics and uncertainties, and where the terms of interference introduced are generally constant, different values are selected, in particular for different PMSM, and h-b0iq+ epsilon is the concentrated interference. x is the number of1＝iq，x2H, then formula (5) may be represented as:
Figure BDA0002883755750000112
Figure BDA0002883755750000113
a common linear ESO is derived to estimate the lumped disturbance of the control system,
Figure BDA0002883755750000114
Figure BDA0002883755750000115
where z1 and z2 are estimates of iq and h, respectively. In addition, the gain of ESO is set to β1＝2ω0，β2＝ω0 2，ω0Representing the bandwidth of an Extended State Observer (ESO). If ω is0> 0 and h is bounded, then linear ESO is Bounded Input Bounded Output (BIBO) stable. The control law is expressed by equation (10).
Figure BDA0002883755750000121
Thus, an ESO based q-axis current loop may be represented as shown in fig. 1. Using the ESO-based feed forward compensation, the q-axis current loop device can be converted to an integrator,
Figure BDA0002883755750000122
a PMSM speed servo system with an ESO-based q-axis current loop is shown in FIG. 2, where nrAnd n represents reference and actual motor speeds (in revolutions per minute (rpm)), respectively, n being 60 ω/(2 π), Cv(s) is a speed controller. According to fig. 2, the PMSM speed servo device can be represented as a dual integrator model,
Figure BDA0002883755750000123
wherein K is 60b0Cm/(2πJ)。
It can be seen that the PMSM speed servo device can be converted to a dual integrator model by introducing an ESO based feed forward compensation. Since the gain K in equation (12) can be directly compensated by the feedback controller, the ESO based control scheme offers the possibility to design a universal feedback controller for different PMSM speed servo systems.
In some embodiments, the Fractional Order Proportional Derivative (FOPD) controller performing an order tuning of a permanent magnet synchronous motor speed servo system by a Differential Evolution (DE) based optimization method comprises: the fractional order proportional-derivative controller (FOPD) satisfies:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure BDA0002883755750000131
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure BDA0002883755750000132
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I represents fractional order proportional-derivative controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure BDA0002883755750000133
where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
The fractional order proportional-derivative (FOPD) controller carries out order setting on a permanent magnet synchronous motor speed servo system through an optimization method based on Differential Evolution (DE) and comprises the following steps:
step 1, initialization: n μ values were randomly selected to construct the population. Then according to the design specification (omega)c，
Figure BDA0002883755750000134
) A Fractional Order Proportional Derivative (FOPD) controller is calculated for each individual.
Step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure BDA0002883755750000141
wherein P is0Is the initial mutation rate, msIs the upper limit of iteration times, and after a target individual is selected, a mutant individual is generated, and a Fractional Order Proportional Differential (FOPD) controller of the mutant individual is obtained;
step 3, step response simulation: performing a step response simulation using a Fractional Order Proportional Derivative (FOPD) controller for each individual to control the speed of the permanent magnet synchronous motor;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the variation of the overall average fitness in the last 10 iterations is less than delta or the number of iterations reaches an upper limit, the optimization will be terminated and the individual with the greatest fitness will be considered as the best individual, resulting in the final Fractional Order Proportional Derivative (FOPD) controller.
The method specifically comprises the following steps: under an ESO based control scheme, the q-axis current loop is converted to an integrator. Therefore, by feed forward compensation, tracking errors in motor speed under slowly varying disturbances can be completely eliminated. The feedback controller can then be designed to achieve good step response performance. The FOPD controller acts as a speed controller,
C(s)＝Kp(1+Kdsμ) (13)
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure BDA0002883755750000151
As a design specification, the open-loop transfer function g(s) ═ c(s) p(s) can be obtained at the crossover frequency ωcThe amplitude characteristic is shown as a formula (14), the phase angle characteristic is shown as a formula (15),
|C(jωc)P(jωc)|＝1 (14)
Figure BDA0002883755750000152
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I denotes Fractional Order Proportional Derivative (FOPD) controller at omegacThe phase of (c). From equations (14) and (15), if the derivative order μ is given, k can be calculated directlypAnd kd. To obtain good step response performance, a DE-based optimization method is used to search for the derivative order μ. In order to quantify the tracking performance of the servo system, the loss function is defined as shown in equation (16).
Figure BDA0002883755750000153
Where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller.
Fig. 3 shows the main steps of a fractional order proportional-derivative (FOPD) controller for order tuning of a permanent magnet synchronous motor speed servo system by a Differential Evolution (DE) based optimization method.
Step 1, initialization: n μ values were randomly selected to construct the population. Then according to the design specification (omega)c，
Figure BDA0002883755750000154
) A Fractional Order Proportional Derivative (FOPD) controller is calculated for each individual.
Step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure BDA0002883755750000161
wherein P is0Is the initial mutation rate, msIs the upper limit of iteration times, and after a target individual is selected, a mutant individual is generated, and a Fractional Order Proportional Differential (FOPD) controller of the mutant individual is obtained.
Step 3, step response simulation: performing a step response simulation using a Fractional Order Proportional Derivative (FOPD) controller for each individual to control the speed of the permanent magnet synchronous motor; the fitness of each individual is defined as F ═ 1/J.
Step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the variation of the overall average fitness in the last 10 iterations is less than delta or the number of iterations reaches an upper limit, the optimization will be terminated and the individual with the greatest fitness will be considered as the best individual, resulting in the final Fractional Order Proportional Derivative (FOPD) controller.
This embodiment mode also provides a speed servo system of a permanent magnet synchronous motor, including: an Extended State Observer (ESO) and fractional proportional derivative (FOPD) controller; the Extended State Observer (ESO) is used for performing feedforward compensation on a q-axis current loop of the permanent magnet synchronous motor; the Fractional Order Proportional Derivative (FOPD) controller is used for carrying out order setting on a speed servo system of the permanent magnet synchronous motor through an optimization method based on Differential Evolution (DE).
In some embodiments, a first processing unit is also included; the first processing unit is configured to perform operations including: determining that a q-axis current loop after feedforward compensation using an Extended State Observer (ESO) satisfies:
Figure BDA0002883755750000171
Figure BDA0002883755750000172
Figure BDA0002883755750000173
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is a fractional order proportional-derivative controller output signal, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer.
In some embodiments, the present permanent magnet synchronous motor speed servo system further comprises a second processing unit,
the second processing unit is used for executing: the Fractional Order Proportional Derivative (FOPD) controller satisfies:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure BDA0002883755750000174
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure BDA0002883755750000181
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I denotes Fractional Order Proportional Derivative (FOPD) controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure BDA0002883755750000182
where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
In some embodiments: the second processing unit is further configured to perform:
step 1, initialization: n μ values were randomly selected to construct the population. Then according to the design specification (omega)c，
Figure BDA0002883755750000183
) A Fractional Order Proportional Derivative (FOPD) controller is calculated for each individual.
Step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure BDA0002883755750000184
wherein, P0Is the initial mutation rate, msIs the upper limit of iteration times, and after a target individual is selected, a mutant individual is generated, and a Fractional Order Proportional Differential (FOPD) controller of the mutant individual is obtained;
step 3, step response simulation: performing a step response simulation using a Fractional Order Proportional Derivative (FOPD) controller for each individual to control the speed of the permanent magnet synchronous motor;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the variation of the overall average fitness in the last 10 iterations is less than delta or the number of iterations reaches an upper limit, the optimization will be terminated and the individual with the greatest fitness will be considered as the best individual, resulting in the final Fractional Order Proportional Derivative (FOPD) controller.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that the present invention is not limited to the details of the embodiments shown and described, but is capable of numerous equivalents and substitutions without departing from the spirit of the invention and its scope is defined by the claims appended hereto.

Claims (8)

1. A fractional order composite control method is characterized by comprising the following steps:
step 1, performing feedforward compensation on a q-axis current loop of a permanent magnet synchronous motor by using an extended state observer;
and 2, the fractional order proportional-differential controller carries out order setting on the speed servo system of the permanent magnet synchronous motor through an optimization method based on differential evolution.
2. The fractional order compound control method of claim 1, wherein in step 1, the feedforward compensation of the q-axis current loop of the permanent magnet synchronous motor by using the extended state observer comprises the following steps: the extended state observer satisfies:
Figure FDA0002883755740000011
Figure FDA0002883755740000012
Figure FDA0002883755740000013
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is fractional order proportional-derivative controlOutput signal of the device, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer.
3. The fractional order compound control method of claim 2, wherein: the fractional order proportional-differential controller for order setting by an optimization method based on differential evolution comprises the following steps: the fractional order proportional-derivative controller satisfies the following conditions:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure FDA0002883755740000021
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure FDA0002883755740000022
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I represents fractional order proportional-derivative controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure FDA0002883755740000023
wherein epsilon (t) is the reference speed and the actual speed of the permanent magnet synchronous motorDeviation between degrees, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
4. A fractional order compound control method as claimed in claim 3, characterized in that: the fractional order proportional-differential controller for carrying out order setting on the permanent magnet synchronous motor speed servo system by an optimization method based on differential evolution comprises the following steps:
step 1, initialization: randomly selecting N mu values to construct an ensemble, and then according to design specifications
Figure FDA0002883755740000024
Calculating a fractional order proportional-differential controller for each individual;
step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure FDA0002883755740000031
wherein, P0Is the initial mutation rate, msThe upper limit of the iteration times is adopted, and after a target individual is selected, a mutant individual is generated, so that a fractional order proportional-differential controller of the mutant individual is obtained;
step 3, step response simulation: controlling the speed of the permanent magnet synchronous motor by using the fractional order proportional-derivative controller of each individual, and executing step response simulation;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the change of the overall average fitness in the last 10 iterations is less than delta or the iteration number reaches the upper limit, the optimization is terminated, the individual with the maximum fitness is regarded as the optimal individual, and the final fractional order proportional-derivative controller is obtained.
5. A speed servo system of a permanent magnet synchronous motor is characterized in that: the method comprises the following steps: the system comprises an extended state observer and a fractional order proportional-derivative controller; the extended state observer is used for performing feedforward compensation on a q-axis current loop of the permanent magnet synchronous motor; the fractional order proportional-differential controller is used for carrying out order setting on a speed servo system of the permanent magnet synchronous motor through an optimization method based on differential evolution.
6. The permanent magnet synchronous motor speed servo system according to claim 5, wherein: the system also comprises a first processing unit; the first processing unit is configured to perform operations including: determining feedforward compensation using an extended state observer, comprising: the extended state observer satisfies:
Figure FDA0002883755740000041
Figure FDA0002883755740000042
Figure FDA0002883755740000043
wherein, b0Is the q-axis electron current loop parameter, iqIs the q-axis stator current, iqrIs a given value of q-axis electron current, u0Is a fractional order proportional-derivative controller output signal, beta1＝2ω0，β2＝ω0 2Wherein, ω is0Representing the bandwidth of the extended state observer.
7. The permanent magnet synchronous motor speed servo system of claim 6, wherein: further comprising a second processing unit for performing: the fractional order proportional-derivative controller satisfies the following conditions:
C(s)＝Kp(1+Kdsμ)；
wherein, KpAnd KdProportional and differential gains, respectively, μ being the derivative order from 0 to 2, taking into account the crossover frequency ωcAnd phase angle margin
Figure FDA0002883755740000044
As a design specification, the open-loop transfer function is at the crossover frequency ωcThe amplitude characteristic and the phase angle characteristic of (d) satisfy the following equation:
|C(jωc)P(jωc)|＝1，
Figure FDA0002883755740000045
wherein Arg | P (j ωc) L represents the phase of the permanent magnet synchronous motor at each stage, and Arg | C (j ω) represents the phase of the permanent magnet synchronous motorc) I denotes Fractional Order Proportional Derivative (FOPD) controller at omegacThe phase of (d);
in order to obtain good step response performance, an optimization method based on differential evolution is adopted to search a derivative order mu, and in order to quantify the tracking performance of a permanent magnet synchronous motor speed servo system, a loss function is defined as follows:
Figure FDA0002883755740000051
where ε (t) is the deviation between the reference speed and the actual speed of the permanent magnet synchronous motor, u0(t) is the output of the speed controller, k1And k2Is a weight value constant.
8. The permanent magnet synchronous motor speed servo system of claim 7, wherein: the second processing unit is further configured to perform: step 1, initialization: randomly selecting N mu values to construct an ensemble, and then according to a design ruleModel (A) of
Figure FDA0002883755740000052
Calculating a fractional order proportional-differential controller for each individual;
step 2, mutation: randomly selecting several individuals as target objects according to the mutation rate, applying the adaptive mutation rate and the mutation rate P in the mth iterationmIs defined as:
Pm＝P0·2γ,
Figure FDA0002883755740000053
wherein, P0Is the initial mutation rate, msThe upper limit of the iteration times is adopted, and after a target individual is selected, a mutant individual is generated, so that a fractional order proportional-differential controller of the mutant individual is obtained;
step 3, step response simulation: controlling the speed of the permanent magnet synchronous motor by using the fractional order proportional-derivative controller of each individual, and executing step response simulation;
step 4, selection: selection was made between mutant and target individuals, with an adaptable individual selected into the population, giving a threshold δ to check for termination conditions: if the change of the overall average fitness in the last 10 iterations is less than delta or the iteration number reaches the upper limit, the optimization is terminated, the individual with the maximum fitness is regarded as the optimal individual, and the final fractional order proportional-derivative controller is obtained.
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