CN113176731A - Dual-neural-network self-learning IPMSM active disturbance rejection control method - Google Patents

Dual-neural-network self-learning IPMSM active disturbance rejection control method Download PDF

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CN113176731A
CN113176731A CN202110417874.7A CN202110417874A CN113176731A CN 113176731 A CN113176731 A CN 113176731A CN 202110417874 A CN202110417874 A CN 202110417874A CN 113176731 A CN113176731 A CN 113176731A
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贾红云
李明阳
蔡骏
贾周
曹永娟
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses an IPMSM active disturbance rejection control method for self-learning of a double neural network. The control method gives full play to the advantages of the active disturbance rejection controller, has better position and rotating speed tracking effect, and has strong load resistance and self-adaptive capacity, so that the control method better meets the requirements in engineering practice.

Description

Dual-neural-network self-learning IPMSM active disturbance rejection control method
Technical Field
The invention relates to the field of permanent magnet synchronous motor control, in particular to an IPMSM active disturbance rejection control method for double neural network self-learning.
Background
The traditional vector control strategy of the permanent magnet synchronous motor generally adopts PID (proportion integration differentiation) control, and different combinations of the three parameters can be suitable for most servo control occasions, so that the method has wide application effect. In addition, a combination control of PID and feedforward, a cascade control of a plurality of PIDs, and the like are widely used in industrial process control. Although the PID is widely applied, the inherent defects exist, such as the contradiction between the rapidity and the overshoot of the tracking target signal, low steady-state precision, poor interference resistance and the like, and the requirement of high-performance control is difficult to achieve. In response to these problems, more control methods are applied to the field of motor servo control, such as: sliding mode control, adaptive control, model prediction control, fuzzy control, active disturbance rejection control and the like.
The Active Disturbance Rejection Control (ADRC) technology is provided from the perspective of engineering practice and application by koro jingqing researchers combining the advantages of the natural Disturbance Rejection of PID and the independence of models and the theory of state observers. Before the disturbance influence control system finally outputs, disturbance information can be actively extracted from input and output signals of a controlled object and eliminated by a control signal, so that the influence on the controlled object is reduced.
Non-linear adrc (nladrc), although powerful, has excessive control parameters and is difficult to determine the stability boundary using frequency domain analysis commonly used in engineering, limiting its application to some extent.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems that a proportional-integral (PI) regulator adopted by a built-in permanent magnet synchronous motor vector servo control system in the background technology has poor anti-interference performance, low steady-state precision, difficult achievement of ideal control effect of tracking reference signals and the like, the invention discloses a dual-neural-network self-learning IPMSM auto-anti-interference control method.
The technical scheme is as follows: the invention relates to a double-neural network self-learning IPMSM active disturbance rejection control method, which comprises the following steps:
step 1, establishing a voltage equation, an electromagnetic torque equation and a mechanical motion equation of the built-in permanent magnet synchronous motor under d axis and q axis of a synchronous rotating coordinate system;
step 2, designing a third-order tracking-differentiator to obtain a rotor position tracking signal v1First order differential signal v2And a second order differential signal v3；
Step 3, designing a three-order nonlinear extended state observer to the rotor position angle thetamObserving a first order differential signal, a second order differential signal and disturbance of a rotor position angle;
step 4, designing a nonlinear state error feedback control rate according to the step 2 and the step 3;
step 5, designing an RBF neural network to perform online parameter setting on the nonlinear extended state observer according to the step 3;
and 6, designing a BP neural network to carry out online parameter setting on the nonlinear state error feedback control rate according to the step 4.
Further, in step 1, the voltage equation of the motor in the synchronous rotating coordinate system is as follows:
Figure BDA0003026625360000021
wherein: i.e. idAnd iqThe direct and alternating components of the stator current, respectively; rsIs a stator resistor; p is differential operation; u. ofdAnd uqThe stator voltage direct and alternating axis components are respectively; l isdAnd LqThe direct and alternating components of the stator inductance are respectively; psifFor rotor permanent magnet flux linkage, omegaeIs the electrical angular velocity of the motor rotation;
the electromagnetic torque equation of the motor under the synchronous rotating coordinate system is as follows:
Te＝1.5pniq[ψf+id(Ld-Lq)] (2)
according to the relation between the position and the rotating speed of the rotor:
Figure BDA0003026625360000022
when adopting idWhen the vector control is 0, the mechanical motion equation of the motor under the synchronous rotating coordinate system is as follows:
Figure BDA0003026625360000023
in formulae (2) to (4): p is a radical ofnThe number of pole pairs of the motor is shown; t isLIs the load torque; b is a damping coefficient; thetamIs the rotor mechanical angle, omega, of an electric machinemIs the mechanical angular speed of the rotor of the motor.
Further, in step 2:
defining a tracking function:
fst＝-r3[v1(k)-vref(k)]-3r2v2(k)-3rv3(k) (5)
the discrete form of the third order tracking differentiator is as follows:
Figure BDA0003026625360000024
in the formula: v. of1(k +1) is a tracking signal of the original signal, v2(k +1) is a first order differential signal of the original signal, v3(k +1) is the second order differential signal of the original signal, h0A system sampling period;
v is obtained by the formula (6)1、v2And v3。
Further, the third-order nonlinear extended state observer designed in step 3 is as follows:
Figure BDA0003026625360000031
wherein:
Figure BDA0003026625360000032
in the formula: z is a radical of1，z2，z3Respectively rotor position thetam、ωmAnd an estimate of the disturbance; fal (e)kα, δ) is a continuous power function with a linear segment near the origin as an error feedback function; delta is the interval length of the linear segment, and delta belongs to (0, 1); beta is a01、β02、β03Is the observer gain; a is the power of the nonlinear segment interval and is a constant to be determined;
the ESO in the corresponding discrete form is expressed as:
Figure BDA0003026625360000033
further, the nonlinear state error feedback discrete equation in step 4 is expressed as:
Figure BDA0003026625360000034
in the formula, beta1And beta2Proportional gain and differential gain, respectively; alpha is alpha1And alpha2Is a non-linear factor, δ1Is a filter factor;
the compensated control quantity is as follows:
Figure BDA0003026625360000035
further, step 5 designs beta in the nonlinear extended state observer by the RBF neural network01、β02、β03The online setting is carried out, and the online setting is carried out,
taking x as [ u ]c(k)，y0(k)，y0(k-1)]TAs input vector of RBF neural network, where uc(k) And y0(k) Respectively the control quantity and the system output quantity of the system; the hidden layer takes 6 nodes, namely the value of q is 6; constructed error approximation function en(k) And an error objective function J0The following were used:
Figure BDA0003026625360000041
obtaining the output weight coefficient w by the steepest gradient descent methodj(k) Node base width parameter sigmaj(k) And node center cij(k) The iterative algorithm of (1) is respectively:
Figure BDA0003026625360000042
in the formula eta0For learning rate, the value range is [0, 1 ]]，α1Is a momentum factor with a value range of [0, 1%]；
Defining:
Figure BDA0003026625360000043
in the formula, a1，a2，a3Is constant and has the value range of (0, 1)](ii) a n is a positive integer greater than 1, the original network becomes optimized a1，a2，a3These three constants;
if the reference input of the controller is thetamrThe feedback input is thetamfThen, define:
erf＝θmr-θmf (16)
according to the error between the input and output of the system, a1，a2，a3The incremental coefficients are respectively:
Figure BDA0003026625360000044
a1，a2，a3the three-parameter setting formula is as follows:
Figure BDA0003026625360000051
in the formula
Figure BDA0003026625360000052
For the controlled object Jacobian information, the Jacobian matrix is as follows:
Figure BDA0003026625360000053
the control quantity correction value and the actual output value output by the RBF neural network and the correction learning algorithm are as follows:
Figure BDA0003026625360000054
further, step 6 is to design a parameter beta in the feedback control rate of the BP neural network on the nonlinear state error1And beta2Carrying out on-line setting:
constructing an objective function:
Figure BDA0003026625360000055
the correction formula of the neuron weight coefficient of the output layer obtained according to the steepest gradient descent method is as follows:
Figure BDA0003026625360000056
where eta is the learning rate, eta>0；βg(g ═ 1,2) is the weight coefficient of the hidden layer and the output layer;
in conjunction with the single neuron algorithm, the sign function l (k) is constructed such that:
Figure BDA0003026625360000057
the formula of the adjusted weighting coefficient is:
Figure BDA0003026625360000061
at the moment, the construction of the IPMSM active disturbance rejection controller self-learned by the double neural network is completed.
Has the advantages that: compared with the prior art, the invention has the advantages that: the invention applies the nonlinear active disturbance rejection control (the advantages of wide parameter adaptability, strong robustness and the like) to the built-in permanent magnet synchronous motor servo control system, and simultaneously introduces a neural network (strong self-learning and self-adaptive capability) algorithm to set the parameters in the nonlinear active disturbance rejection control on line; the advantages of ADRC are fully exerted by automatically adjusting the key parameters in the active disturbance rejection controller in real time on line through the dual neural network, so that the ADRC meets the requirements of engineering practice.
Drawings
FIG. 1 is a block diagram of a Radial Basis (RBF) neural network of the present invention;
FIG. 2 is a block diagram of an error Back Propagation (BP) neural network of the present invention;
fig. 3 is a structural diagram of the dual neural network optimized active disturbance rejection control of the present invention.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
S1: establishing voltage mathematical models (a voltage equation, an electromagnetic torque equation and a mechanical motion equation) of three-phase currents of a stator of the built-in permanent magnet synchronous motor under d axis and q axis;
the voltage equation of the motor under the synchronous rotating coordinate system is as follows:
Figure BDA0003026625360000062
wherein: i.e. idAnd iqThe direct and alternating components of the stator current, respectively; rsIs a stator resistor; p is differential operation; u. ofdAnd uqThe stator voltage direct and alternating axis components are respectively; l isdAnd LqThe direct and alternating axes being stator inductances respectivelyA component; psifFor rotor permanent magnet flux linkage, omegaeIs the electrical angular velocity at which the motor rotates.
The electromagnetic torque equation of the motor under the synchronous rotating coordinate system is expressed as follows:
Te＝1.5pniq[ψf+id(Ld-Lq)] (2)
according to the relation between the position and the rotating speed of the rotor:
Figure BDA0003026625360000063
when adopting idWhen the vector control is 0, the mechanical motion equation of the motor under the synchronous rotating coordinate system can be expressed as follows:
Figure BDA0003026625360000071
in formulae (2) to (4): p is a radical ofnThe number of pole pairs of the motor is shown; t isLIs the load torque; b is a damping coefficient; thetamIs the rotor mechanical angle, omega, of an electric machinemIs the mechanical angular speed of the rotor of the motor.
S2: designing a third-order tracking-differentiator to obtain a rotor position tracking signal v1First order differential signal v2And a second order differential signal v3；
Defining a tracking function:
fst＝-r3[v1(k)-vref(k)]-3r2v2(k)-3rv3(k) (5)
the discrete form of the third order tracking differentiator is available as follows:
Figure BDA0003026625360000072
in the formula: v. of1(k +1) is a tracking signal of the original signal, v2(k +1) is the first order differential signal of the original signal (speed tracking), v3(k +1) is the second order differential of the original signalSignal, h0Is the system sampling period.
V is obtained by calculation of (6)1-v3。
The system matrix defining the tracking function is:
Figure BDA0003026625360000073
the three eigenvalues corresponding to the matrix are calculated to be-1, -1, -1 respectively, and the stability of Hurwitz is satisfied.
S3: designing a three-order nonlinear extended state observer to the rotor position angle thetamAnd observing a first order differential signal, a second order differential signal and disturbance of a rotor position angle, wherein a third order nonlinear expansion state observer is designed as follows:
Figure BDA0003026625360000074
wherein:
Figure BDA0003026625360000075
in the formula: z is a radical of1，z2，z3Respectively rotor position thetam、ωmAnd an estimate of the disturbance; fal (e)kα, δ) is a continuous power function with a linear segment near the origin, here as an error feedback function; delta is the interval length of the linear segment, and delta belongs to (0, 1); beta is a01、β02、β03Is the observer gain; a is the power of the nonlinear segment interval and is a constant to be determined. The third order nonlinear extended state observer corresponding to the discrete form is expressed as:
Figure BDA0003026625360000081
s4: and designing a nonlinear state error feedback control rate according to the S2 and the S3.
The error signal and the error differential signal of the transition process can be generated based on the tracking-differentiator, and an error integral signal can be generated, and the three signals can form a nonlinear control combination. The error integration signal is not used here because the disturbances of the system can be estimated and compensated. The non-linear state error feedback discrete equation can be expressed as:
Figure BDA0003026625360000082
in the formula, beta1And beta2Proportional gain and differential gain, respectively; alpha is alpha1And alpha2Is a non-linear factor, δ1Is a filter factor.
The compensated control quantity is:
Figure BDA0003026625360000083
s5: according to S3, designing an RBF neural network to perform online parameter setting on the nonlinear extended state observer;
designing beta in nonlinear extended state observer by RBF neural network01、β02、β03And carrying out on-line setting.
The basic structure of the RBF neural network is shown in figure 1.
The design is as follows:
taking x as [ u ]c(k)，y0(k)，y0(k-1)]TAs input vector of RBF neural network, where uc(k) And y0(k) Respectively the control quantity and the system output quantity of the system; the hidden layer takes 6 nodes, namely the value of q is 6; constructed error approximation function en(k) And an error objective function J0The following were used:
Figure BDA0003026625360000084
using steepest gradient descentMethod, the output weight coefficient w can be obtainedj(k) Node base width parameter sigmaj(k) And node center cij(k) The iterative algorithm of (1) is respectively:
Figure BDA0003026625360000091
in the formula eta0For learning rate, the value range is [0, 1 ]]，α1Is a momentum factor with a value range of [0, 1%]。
In order to accelerate the self-learning speed of the RBF neural network and to set initial parameters more conveniently, the following definitions are defined:
Figure BDA0003026625360000092
in the formula, a1，a2，a3Is constant and has the value range of (0, 1)](ii) a n is a positive integer greater than 1. The original network becomes optimized a1，a2，a3These three constants.
If the reference input of the controller is thetamrThe feedback input is thetamfThen, define:
erf＝θmr-θmf (16)
according to the error between the system input and output, then a1，a2，a3The three parameter increment coefficients are:
Figure BDA0003026625360000093
a1，a2，a3the three-parameter setting formula is as follows:
Figure BDA0003026625360000094
in the formula
Figure BDA0003026625360000095
For the controlled object Jacobian information, the Jacobian matrix is as follows:
Figure BDA0003026625360000096
the control quantity correction value and the actual output value output by the RBF neural network and the correction learning algorithm are as follows:
Figure BDA0003026625360000097
s6: according to S4, designing a BP neural network to perform online parameter setting on the nonlinear state error feedback control rate;
designing parameter beta in nonlinear state error feedback control rate of BP neural network1And beta2And carrying out on-line setting. The design is as follows:
the basic structure of the BP neural network is shown in fig. 2.
The objective function is constructed as:
Figure BDA0003026625360000101
the correction formula of the neuron weight coefficient of the output layer obtained according to the steepest gradient descent method is as follows:
Figure BDA0003026625360000102
where eta is the learning rate, eta>0；βgAnd (g is 1,2) is a weight coefficient of the hidden layer and the output layer.
In conjunction with the single neuron algorithm, the sign function l (k) is constructed such that:
Figure BDA0003026625360000103
the formula of the adjusted weighting coefficient is:
Figure BDA0003026625360000104
FIG. 3 is a structural diagram of parameters in dual neural network optimization NLADRC, which includes RBFNN optimization NLESO beta01、β02、β03Parametric, BPFNN optimized beta1、β2And (4) parameters. In the figure, the parameter regulating vector a is ═ a1,a2,a3]TGain vector K ═ 10n,102n,103n]。

Claims (7)

1. A dual neural network self-learning IPMSM active disturbance rejection control method is characterized by comprising the following steps:
step 1, establishing a voltage equation, an electromagnetic torque equation and a mechanical motion equation of the built-in permanent magnet synchronous motor under d axis and q axis of a synchronous rotating coordinate system;
step 2, designing a third-order tracking-differentiator to obtain a rotor position tracking signal v1First order differential signal v2And a second order differential signal v3；
Step 3, designing a three-order nonlinear extended state observer to the rotor position angle thetamObserving a first order differential signal, a second order differential signal and disturbance of a rotor position angle;
step 4, designing a nonlinear state error feedback control rate according to the step 2 and the step 3;
step 5, designing an RBF neural network to perform online parameter setting on the nonlinear extended state observer according to the step 3;
and 6, designing a BP neural network to carry out online parameter setting on the nonlinear state error feedback control rate according to the step 4.
2. The dual neural network self-learning IPMSM auto-disturbance rejection control method of claim 1, further comprising: in the step 1, a voltage equation of the motor in a synchronous rotating coordinate system is as follows:
Figure FDA0003026625350000011
wherein: i.e. idAnd iqThe direct and alternating components of the stator current, respectively; rsIs a stator resistor; p is differential operation; u. ofdAnd uqThe stator voltage direct and alternating axis components are respectively; l isdAnd LqThe direct and alternating components of the stator inductance are respectively; psifFor rotor permanent magnet flux linkage, omegaeIs the electrical angular velocity of the motor rotation;
the electromagnetic torque equation of the motor under the synchronous rotating coordinate system is as follows:
Te＝1.5pniq[ψf+id(Ld-Lq)] (2)
according to the relation between the position and the rotating speed of the rotor:
Figure FDA0003026625350000012
when adopting idWhen the vector control is 0, the mechanical motion equation of the motor under the synchronous rotating coordinate system is as follows:
Figure FDA0003026625350000013
in formulae (2) to (4): p is a radical ofnThe number of pole pairs of the motor is shown; t isLIs the load torque; b is a damping coefficient; thetamIs the rotor mechanical angle, omega, of an electric machinemIs the mechanical angular speed of the rotor of the motor.
3. The dual neural network self-learning IPMSM auto-disturbance rejection control method according to claim 2, characterized in that in step 2:
defining a tracking function:
fst＝-r3[v1(k)-vref(k)]-3r2v2(k)-3rv3(k) (5)
the discrete form of the third order tracking differentiator is as follows:
Figure FDA0003026625350000021
in the formula: v. of1(k +1) is a tracking signal of the original signal, v2(k +1) is a first order differential signal of the original signal, v3(k +1) is the second order differential signal of the original signal, h0A system sampling period;
v is obtained by the formula (6)1、v2And v3。
4. The dual neural network self-learning IPMSM auto-disturbance rejection control method according to claim 3, characterized in that: the third-order nonlinear extended state observer designed in step 3 is as follows:
Figure FDA0003026625350000022
wherein:
Figure FDA0003026625350000023
in the formula: z is a radical of1，z2，z3Respectively rotor position thetam、ωmAnd an estimate of the disturbance; fal (e)kα, δ) is a continuous power function with a linear segment near the origin as an error feedback function; delta is the interval length of the linear segment, and delta belongs to (0, 1); beta is a01、β02、β03Is the observer gain; a is the power of the nonlinear segment interval and is a constant to be determined;
the ESO in the corresponding discrete form is expressed as:
Figure FDA0003026625350000024
5. the dual neural network self-learning IPMSM auto-disturbance rejection control method according to claim 4, characterized in that: the nonlinear state error feedback discrete equation in step 4 is expressed as:
Figure FDA0003026625350000031
in the formula, beta1And beta2Proportional gain and differential gain, respectively; alpha is alpha1And alpha2Is a non-linear factor, δ1Is a filter factor;
the compensated control quantity is as follows:
Figure FDA0003026625350000032
6. the dual neural network self-learning IPMSM auto-disturbance rejection control method according to claim 4, characterized in that: step 5, designing beta of RBF neural network in nonlinear extended state observer01、β02、β03The online setting is carried out, and the online setting is carried out,
taking x as [ u ]c(k)，y0(k)，y0(k-1)]TAs input vector of RBF neural network, where uc(k) And y0(k) Respectively the control quantity and the system output quantity of the system; the hidden layer takes 6 nodes, namely the value of q is 6; constructed error approximation function en(k) And an error objective function J0The following were used:
Figure FDA0003026625350000033
obtaining the output weight coefficient w by the steepest gradient descent methodj(k) Node base width parameter sigmaj(k) Andnode center cij(k) The iterative algorithm of (1) is respectively:
Figure FDA0003026625350000034
in the formula eta0For learning rate, the value range is [0, 1 ]]，α1Is a momentum factor with a value range of [0, 1%]；
Defining:
Figure FDA0003026625350000035
in the formula, a1，a2，a3Is constant and has the value range of (0, 1)](ii) a n is a positive integer greater than 1, the original network becomes optimized a1，a2，a3These three constants;
if the reference input of the controller is thetamrThe feedback input is thetamfThen, define:
erf＝θmr-θmf (16)
according to the error between the input and output of the system, a1，a2，a3The incremental coefficients are respectively:
Figure FDA0003026625350000041
a1，a2，a3the three-parameter setting formula is as follows:
Figure FDA0003026625350000042
in the formula
Figure FDA0003026625350000043
For the controlled object Jacobian information, the Jacobian matrix is as follows:
Figure FDA0003026625350000044
the control quantity correction value and the actual output value output by the RBF neural network and the correction learning algorithm are as follows:
Figure FDA0003026625350000045
7. the dual neural network self-learning IPMSM auto-disturbance rejection control method according to claim 5, characterized in that: step 6, designing a parameter beta in the feedback control rate of the BP neural network to the nonlinear state error1And beta2Carrying out on-line setting:
constructing an objective function:
Figure FDA0003026625350000046
the correction formula of the neuron weight coefficient of the output layer obtained according to the steepest gradient descent method is as follows:
Figure FDA0003026625350000051
where eta is the learning rate, eta>0；βg(g ═ 1,2) is the weight coefficient of the hidden layer and the output layer;
in conjunction with the single neuron algorithm, the sign function l (k) is constructed such that:
Figure FDA0003026625350000052
the formula of the adjusted weighting coefficient is:
Figure FDA0003026625350000053
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CN109143863A (en) * 2018-09-13 2019-01-04 武汉科技大学 The quick self study of nonlinear system improves ADRC control method
CN110429881A (en) * 2019-07-26 2019-11-08 江苏大学 A kind of Auto-disturbance-rejection Control of permanent magnet synchronous motor
CN110989597A (en) * 2019-12-05 2020-04-10 南京理工大学 Adaptive path tracking method of integrated fuzzy neural network

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