CN108964545B - A kind of synchronous motor neural network contragradience Discrete Control Method based on command filtering - Google Patents

Abstract

The synchronous motor neural network contragradience Discrete Control Method based on command filtering that the invention discloses a kind of, it is more for permasyn morot variable, coupling is strong, and the problem of being highly susceptible to external loading and the variation influence of motor relevant parameter, a kind of neural network adaptive controller is devised based on command filtering technology and Backstepping principle, nerual network technique is for approaching unknown nonlinear terms, adaptive Backstepping is used for the design of controller, and command filtering technology is for solving the problems, such as " calculating explosion ".Part of the present invention supplemented with the complete controller design lacked in conventional method increases Liapunov stability analysis；After being controlled to adjust by controller, motor running can be rapidly achieved stable state, it is more suitable for needing the control object of fast dynamic response, simulation result shows that this new controller overcomes the influence of parameter inaccuracy and ensure that ideal control effect, realizes the quickly and stably tracking to position.

Description

Synchronous motor neural network backstepping discrete control method based on command filtering

Technical Field

The invention belongs to the technical field of position tracking control of permanent magnet synchronous motors, and particularly relates to a synchronous motor neural network backstepping discrete control method based on command filtering.

Background

In recent years, with the rapid development of power electronic technology, microelectronic technology, novel motor control theory and rare earth permanent magnet materials, permanent magnet synchronous motors can be rapidly popularized and applied. Compared with the traditional electrically excited synchronous motor, the permanent magnet synchronous motor, especially the rare earth permanent magnet synchronous motor has the advantages of less loss, high efficiency and obvious electricity-saving effect.

The permanent magnet synchronous motor provides excitation by the permanent magnet, so that the structure of the motor is simpler, the processing and assembling cost is reduced, a collecting ring and an electric brush which are easy to cause problems are omitted, and the running reliability of the motor is improved; because the efficiency and the power density of the motor are improved without exciting current and exciting loss, the motor is a motor which is researched more in recent years and is applied to more and more fields, and the research on the motor is very necessary.

However, the mathematical model of the synchronous motor has the characteristics of nonlinearity, strong coupling, multivariable, and the like, and is easily affected by uncertain factors such as motor parameter variation and external load disturbance, and therefore, it is a challenging subject to realize high-performance control of the synchronous motor. Since the eighties, the development of control technologies, particularly control theory strategies, is very rapid, and some advanced control strategy methods (such as sliding mode control, variable structure control, fuzzy control, backstepping method, expert control and the like) are being tried to be introduced into a permanent magnet synchronous motor controller, so that a new way is opened up for promoting the development of high performance towards the direction of intellectualization, flexibility and full digitalization. However, most of the above-mentioned control techniques and methods are often used in the design process of a continuous model controller of a permanent magnet synchronous motor, and the research on a discrete model thereof is rarely involved.

Due to the wide application of computer control systems, and compared with continuous control methods, discrete control methods are superior in ensuring the stability and realizability of the systems, so that the theoretical research of modeling, analysis and design of discrete systems is in an increasingly important position. The big advantage of the back stepping method is that the original high-order system can be simplified by using virtual control variables, so that the final output result can be automatically obtained by an appropriate Lyapunov equation.

The self-adaptive backstepping control method decomposes a complex nonlinear system into a plurality of simple low-order subsystems, designs the controller step by introducing virtual control variables, and finally determines a control law and a self-adaptive law, thereby realizing the effective control of the system. However, continuous derivation of the virtual control function in the conventional backstepping control easily causes a "calculation explosion" problem. The problem of 'computing explosion' can be effectively solved by introducing a command filtering technology in the design process of the controller.

In addition, the ability of neural network technology to handle unknown nonlinear functions has attracted extensive attention in the control community at home and abroad and is used in the design of complex control systems with high degree of nonlinearity and uncertainty.

Disclosure of Invention

The invention aims to provide a synchronous motor neural network backstepping discrete control method based on command filtering, wherein unknown nonlinear terms of a system are approximated through a neural network technology, the command filtering technology is used for solving the problem of 'calculation explosion', and a controller is constructed by using a backstepping method, so that the tracking control of the position of a synchronous motor is realized.

In order to achieve the purpose, the invention adopts the following technical scheme:

a synchronous motor neural network backstepping discrete control method based on command filtering comprises the following steps:

a. establishing a dynamic model of a permanent magnet synchronous motor

Under the synchronous rotation d-q coordinate, the dynamic model of the permanent magnet synchronous motor is expressed as:

wherein theta is the angular position of the rotor of the permanent magnet synchronous motor, omega is the angular speed of the rotor of the permanent magnet synchronous motor, J is the moment of inertia, and T_LFlux linkage n generated for load torque, phi for permanent magnet_pIs the number of magnetic pole pairs, i_qFor q-axis stator current, i_dIs d-axis stator current, u_qIs the q-axis stator voltage u of the permanent magnet synchronous motor_dFor d-axis stator voltage, L of permanent magnet synchronous motor_dAnd L_qIs the stator inductance R under a d-q coordinate system_sThe equivalent resistance of the stator of the permanent magnet synchronous motor and the friction coefficient B are defined as the equivalent resistance of the stator of the permanent magnet synchronous motor;

to simplify the dynamic model of a permanent magnet synchronous motor, the following variables are defined:

the discrete dynamic model of the permanent magnet synchronous motor is then represented as:

wherein x is₁(k +1) represents the rotor angular position of the (k +1) th sample;

x₂(k +1) represents the rotor angular velocity of the (k +1) th sample;

x₃(k +1) represents the k +1 thSub-sampled q-axis stator current;

x₄(k +1) represents the d-axis stator current for the (k +1) th sample; delta_tRepresents a sampling period;

b. according to the backstepping principle, a synchronous motor neural network backstepping discrete control method based on command filtering is designed, wherein the discrete dynamic model is simplified into two independent subsystems, namely a state variable x₁(k),x₂(k) And a control input u_q(k) Formed subsystem and composed of state variables x₄(k) And a control input u_d(k) A component subsystem; wherein:

the first subsystem is:

the second subsystem is: x is the number of₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Approximating a continuous function f (Z (k)) using a RBF neural networkⁿ→R；f(Z(k))＝W^TS(Z(k))；

Wherein,is an input vector, q is the neural network input dimension, R^qA real number vector set;

W＝[W₁,...,W_l]^T∈R^lis a weight vector, the number of nodes of the neural network is a positive integer, l is greater than 1, R^lA real number vector set;

Rⁿis an n-dimensional real number vector set, and R is a real number set; wherein, W₁,...,W_lIs the weight of the weight vector;

S(Z(k))＝[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lis a vector of basis functions, in which s_i(Z (k)) is used as a Gaussian function of the form:

wherein, mu_i＝[μ_i1,...,μ_iq]^TIs the center of the acceptance domain, and η_iThen the width of the gaussian function;

when the number of nodes of the neural network is large enough, the RBF neural network approaches to a compact setTo an arbitrary precision ε>0；

Define the command filter as:

wherein, ζ, ω_nIs a command filter parameter;

z_j,1(k)＝x_jc(k)，

x_jc(k) and x_jc(k +1) represents the output signal of the kth and kth +1 samples of the jth command filter;

z_j,1(k),z_j,2(k) the output signal sampled the kth time of the jth command filter;

z_j,1(k+1),z_j,2(k +1) is the output signal of the (k +1) th sample of the jth command filter;

α_j(k) the input signal sampled the kth time of the jth command filter;

if the input signal alpha_j(k) For all constants k ≧ 0, such that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+2)-2α_j(k+1)+α_j(k)|≤ρ₂If true, it can be derived for an arbitrary constant τ_j> 0, presence of omega_n> 0 and ζ ∈ (0, 1)]So that | z_j,1(k)-α_j(k)|≤τ_j，Δz_j,1(k)＝|z_j,1(k+1)-z_j,1(k) I is bounded;

where ρ is₁And ρ₂Are all normal numbers, α_j(k +1) denotes the (k +1) th sampled input signal of the j-th command filter, α_j(k +2) represents the k +2 sampled input signal of the jth command filter; at the same time z_j,1(0)＝α_j(0)， z_j,2(0) 0 is the initial value of the command filter, α_j(0) An initial input signal representing a command filter;

the system error variables are defined as follows:

wherein x is_d(k) For the desired position signal, x_1c(k)、x_2c(k) Is the output signal of the command filter;

c.1. to ensure x₁(k) Capable of effectively tracking expected position signal x_d(k) The Lyapunov control function is selected as follows:

according to the 1 st equation x in the discrete dynamic model formula (3)₁(k+1)＝x₁(k)+Δ_tx₂(k) The error variables can be found to be:

e₁(k+1)＝x₁(k+1)-x_d(k+1)＝x₁(k)+Δ_tx₂(k)-x_d(k+1)；

the difference can be found from equation (5):

x is to be₂(k) Viewed as a control input, x, to the first subsystem_d(k +1) is the expected position signal of the (k +1) th sampling, and an error variable e is set₂(k)＝x₂(k)-x_1c(k) Constructing a virtual control functionThen the following results are obtained:

c.2. according to the 2 nd equation in the discrete dynamical model formula (3):

x₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_Lthe error variable can be obtained:

e₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)；

selecting a Lyapunov function:then to V₂(k) Calculating the difference to obtain:

load torque T in actual operation of permanent magnet synchronous motor_LThere is an upper limit d, therefore | T_LD is less than or equal to | and d is a normal number;

constructing a virtual control function:

setting error variable e₃(k)＝x₃(k)-x_2c(k) Then Δ V₂(k) Expressed as:

derived from the young inequality:

therefore, substituting equation (11) into equation (10) yields:

c.3. from equation 3 of the discrete dynamical model equation (3):

x₃(k+1)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k) the error variable can be obtained:

selecting Lyapunov functionsTo V₃(k) Calculating the difference to obtain:

wherein f is₃(k)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)；

As can be seen from the RBF neural network approximation principle, the method can be used for any small positive number epsilon₃There is always a neural network systemSo that

Wherein delta₃Expressing approximation error and satisfying inequality | delta₃|≤ε₃，||W₃Is the vector W₃Thereby:

wherein S is₃(Z₃(k) Is a vector of basis functions, Z₃(k)＝[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T；

Selecting u from control inputs_q(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₃，λ₃Is a normal number, and is,is eta₃The estimated value of (1), define | | W₃||＝η₃And η₃> 0, define variable η₃Has an estimation error ofSubstituting equations (7), (12), and (15) into equation (14) yields:

c.4. recording the system error variable e₄(k)＝x₄(k) Selecting Lyapunov functionP is a normal number; the 4 th expression of the discrete dynamical model formula (3):

x₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k) the error variable can be obtained:

e₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

v is obtained₄(k) The difference of (a) can be obtained:

wherein f is₄(k)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k) As can be seen from the RBF neural network approximation principle, for arbitrarily small positive numbers ε₄There is always a neural network systemSo thatWherein, delta₄Expressing approximation error and satisfying inequality | delta₄|≤ε₄Wherein, | | W₄Is the vector W₄Thereby:

wherein S is₄(Z₄(k) Is a vector of basis functions, Z₄(k)＝[x₂(k),x₃(k),x₄(k)]^T；

Selecting u from control inputs_d(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₄，λ₄Is a normal number, and is,is eta₄The estimated value of (1), define | | W₄||＝η₄And η₄> 0, define variable η₄Has an estimation error ofSubstituting equation (19) into equation (18) yields:

d. performing stability analysis on the built neural network back-stepping controller of the permanent magnet synchronous motor

Selecting a Lyapunov function as follows:

differentiating V (k) to obtain:

according to the above formulaAndformula available when performing the (k +1) th sampling of the estimation errorAnd law of adaptationm is 3,4, and has:

is composed of Young' S inequality and | | | S_m(Z_m(k))||²＜l_m，m＝3,4，l_mThe number of nodes representing the neural network system can be obtained:

definition ofM is an arbitrary positive number because | x_jc(k)-α_j(k)|≤τ_jJ is 1,2, and is obtained by substituting equation (21) with equation (22) to equation (26) according to equation (20):

wherein l₃，l₄Respectively representing neural network systemsAndthe number of nodes of (a);

wherein,

τ₁,τ₂are all constants greater than zero;

selecting suitable parameters P and sampling period delta_tTo make it satisfyIf the selection parameter is satisfiedIf m is 3,4, thenAndif yes, obtaining delta V (k) less than or equal to 0;

it is further known that for arbitrarily small positive numbers sigma,this is true.

The invention has the following advantages:

(1) the invention is directed to a discrete time system having greater stability and realizability than the control method of a continuous time system.

(2) The invention utilizes the neural network adaptive backstepping method to approach the nonlinear term of the output voltage, constructs the neural network adaptive backstepping controller of the synchronous motor, effectively solves the nonlinear control problem in the system, and has the advantages of simple and easy structure, convenient realization, reasonable design and stronger load disturbance resistance.

(3) The invention adopts the command filtering technology, thereby effectively avoiding the problem of 'computing explosion' in the traditional back-stepping method; meanwhile, the controller constructed by the neural network self-adaptive backstepping method technology can make the tracking error converge in a sufficiently small neighborhood of the origin point, so as to achieve more accurate control precision;

the neural network self-adaptive back-stepping algorithm can be realized by software programming, the setting of the parameters of the motor can be omitted, the permanent magnet synchronous motor is easy to be directly controlled, the cost is reduced, and the method is safe and reliable and has wide application prospect.

(4) The invention does not need to modify the parameters of the controller according to the difference of the permanent magnet synchronous motor, can realize the stable control of the synchronous motors with all models and powers in principle, reduces the measurement of the parameters of the synchronous motor in the control process, and is beneficial to realizing the quick response of the rotation speed adjustment of the rotor of the permanent magnet synchronous motor.

Drawings

FIG. 1 is a schematic diagram of a composite controlled object composed of a neural network back-stepping controller, a coordinate transformation and an SVPWM inverter of a permanent magnet synchronous motor according to the present invention;

FIG. 2 is a simulation diagram of the tracking of the rotor angular position and the rotor angular position set value after the control of a neural network back-stepping controller of a permanent magnet synchronous motor based on command filtering in the invention;

FIG. 3 is a simulation diagram of the tracking error of the rotor angular position and the set value of the rotor angular position after the control of the neural network back-stepping controller of the permanent magnet synchronous motor based on command filtering according to the present invention;

FIG. 4 is a simulation diagram of the voltage of the d-axis stator of the permanent magnet synchronous motor after being controlled by the neural network back-stepping controller of the permanent magnet synchronous motor based on command filtering according to the present invention;

FIG. 5 is a simulation diagram of the q-axis stator voltage of the PMSM after being controlled by the neural network back-stepping controller based on command filtering in the present invention.

Detailed Description

The invention is described in further detail below with reference to the following figures and detailed description:

referring to fig. 1, the components used in the method for controlling the neural network backstepping discrete control of the synchronous motor based on command filtering include a neural network backstepping discrete controller 1 of the permanent magnet synchronous motor, a coordinate transformation unit 2, an SVPWM inverter 3, a rotation speed detection unit 4 and a current detection unit 5. The rotating speed detection unit 4 and the current detection unit 5 are mainly used for detecting the current value and the rotating speed related variable of the permanent magnet synchronous motor, the actually measured current and the actually measured rotating speed variable are used as input, voltage control is carried out through the neural network backstepping discrete controller 1 of the permanent magnet synchronous motor, and finally the voltage is converted into the rotating speed of the three-phase electric control synchronous motor.

In FIG. 1,. omega._γ(k) Is referred to rotor angular velocity, U_α(k),U_β(k) The voltage is obtained after transformation of an alpha and beta coordinate system, and U, V and W are three-phase alternating-current voltages.

A synchronous motor neural network backstepping discrete control method based on command filtering comprises the following steps:

a. establishing a dynamic model of a permanent magnet synchronous motor

Under the synchronous rotation d-q coordinate, the dynamic model of the permanent magnet synchronous motor is expressed as:

wherein theta is the angular position of the rotor of the permanent magnet synchronous motor, omega is the angular speed of the rotor of the permanent magnet synchronous motor, J is the moment of inertia, and T_LFlux linkage n generated for load torque, phi for permanent magnet_pIs the number of magnetic pole pairs, i_qFor q-axis stator current, i_dIs d-axis stator current, u_qIs the q-axis stator voltage u of the permanent magnet synchronous motor_dFor d-axis stator voltage, L of permanent magnet synchronous motor_dAnd L_qIs the stator inductance R under a d-q coordinate system_sThe equivalent resistance of the stator of the permanent magnet synchronous motor and B is the friction coefficient.

To simplify the dynamic model of a permanent magnet synchronous motor, the following variables are defined:

the discrete dynamic model of the permanent magnet synchronous motor is then represented as:

wherein x is₁(k +1) denotes the rotor angular position of the (k +1) th sample.

x₂(k +1) denotes the rotor angular velocity of the (k +1) th sample.

x₃(k +1) denotes the q-axis stator current of the (k +1) th sampling.

x₄(k +1) represents the d-axis stator current for the (k +1) th sample; delta_tRepresenting the sampling period.

b. According to the backstepping principle, a synchronous motor neural network backstepping discrete control method based on command filtering is designed, wherein the discrete dynamic model is simplified into two independent subsystems, namely a state variable x₁(k),x₂(k) And a control input u_q(k) Formed subsystem and composed of state variables x₄(k) And a control input u_d(k) And (4) forming a subsystem. Wherein:

the first subsystem is:

the second subsystem is: x is the number of₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)。

Approximating a continuous function f (Z (k)) using a RBF neural networkⁿ→R；f(Z(k))＝W^TS(Z(k))。

Wherein,is an input vector, q is the neural network input dimension, R^qIs a set of real vectors.

W＝[W₁,...,W_l]^T∈R^lIs a weight vector, the number of nodes of the neural network is a positive integer, l is greater than 1, R^lIs a set of real vectors.

RⁿIs an n-dimensional real number vector set, and R is a real number set; wherein, W₁,...,W_lIs the weight of the weight vector W.

S(Z(k))＝[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lIs a vector of basis functions, in which s_i(Z (k)) is used as a Gaussian function of the form:

wherein, mu_i＝[μ_i1,...,μ_iq]^TIs the center of the acceptance domain, and η_iThe width of the gaussian function.

When the number of nodes of the neural network is large enough, the RBF neural network approaches to a compact setTo an arbitrary precision ε>0。

Define the command filter as:

wherein, ζ, ω_nAre command filter parameters.

z_j,1(k)＝x_jc(k)，j＝1,2。

x_jc(k) And x_jc(k +1) denotes the output signal of the kth and (k +1) th samples of the jth command filter.

z_j,1(k),z_j,2(k) Is the output signal of the kth sample of the jth command filter.

z_j,1(k+1),z_j,2(k +1) is the output signal of the (k +1) th sample of the jth command filter.

α_j(k) Is the input signal sampled the kth time of the jth command filter.

If the input signal alpha_j(k) For all constants k ≧ 0, such that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+2)-2α_j(k+1)+α_j(k)|≤ρ₂If true, it can be derived for an arbitrary constant τ_j> 0, presence of omega_n> 0 and ζ ∈ (0, 1)]So that | z_j,1(k)-α_j(k)|≤τ_j，Δz_j,1(k)＝|z_j,1(k+1)-z_j,1(k) L is bounded.

Where ρ is₁And ρ₂Are all normal numbers, α_j(k +1) denotes the (k +1) th sampled input signal of the j-th command filter, α_j(k +2) represents the k +2 sampled input signal of the jth command filter; at the same time z_j,1(0)＝α_j(0)， z_j,2(0) 0 is the initial value of the command filter, α_j(0) Representing the initial input signal of the command filter.

The system error variables are defined as follows:

wherein x is_d(k) For the desired position signal, x_1c(k)、x_2c(k) Is the output signal of the command filter.

c.1. To ensure x₁(k) Capable of effectively tracking expected position signal x_d(k) The Lyapunov control function is selected as follows:

according to the 1 st equation x in the discrete dynamic model formula (3)₁(k+1)＝x₁(k)+Δ_tx₂(k) The error variables can be found to be:

e₁(k+1)＝x₁(k+1)-x_d(k+1)＝x₁(k)+Δ_tx₂(k)-x_d(k+1)。

the difference can be found from equation (5):

x is to be₂(k) Viewed as a control input, x, to the first subsystem_d(k +1) is the expected position signal of the (k +1) th sampling, and an error variable e is set₂(k)＝x₂(k)-x_1c(k) Constructing a virtual control functionThen the following results are obtained:

c.2. according to the 2 nd equation in the discrete dynamical model formula (3):

x₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_Lthe error variable can be obtained:

e₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)。

selecting a Lyapunov function:then to V₂(k) Calculating the difference to obtain:

load torque T in actual operation of permanent magnet synchronous motor_LThere is an upper limit d, therefore | T_LD is not more than | and d is a normal number.

Constructing a virtual control function:

setting error variable e₃(k)＝x₃(k)-x_2c(k) Then Δ V₂(k) Expressed as:

derived from the young inequality:

therefore, substituting equation (11) into equation (10) yields:

c.3. from equation 3 of the discrete dynamical model equation (3):

x₃(k+1)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k) the error variable can be obtained:

selecting Lyapunov functionsTo V₃(k) Calculating the difference to obtain:

wherein f is₃(k)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)。

As can be seen from the RBF neural network approximation principle, the method can be used for any small positive number epsilon₃There is always a neural network systemSo that

Wherein delta₃Expressing approximation error and satisfying inequality | delta₃|≤ε₃，||W₃Is the vector W₃Thereby:

wherein S is₃(Z₃(k) Is a vector of basis functions, Z₃(k)＝[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T。

Selecting u from control inputs_q(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₃，λ₃Is a normal number, and is,is eta₃The estimated value of (1), define | | W₃||＝η₃And η₃> 0, define variable η₃Has an estimation error ofSubstituting equations (7), (12) and (15) into publicThe formula (14) gives:

c.4. recording the system error variable e₄(k)＝x₄(k) Selecting Lyapunov functionP is a normal number; the 4 th expression of the discrete dynamical model formula (3):

x₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k) the error variable can be obtained:

e₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

v is obtained₄(k) The difference of (a) can be obtained:

wherein f is₄(k)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k) As can be seen from the RBF neural network approximation principle, for arbitrarily small positive numbers ε₄There is always a neural network systemSo thatWherein, delta₄Expressing approximation error and satisfying inequality | delta₄|≤ε₄Wherein, | | W₄Is the vector W₄Thereby:

wherein S is₄(Z₄(k) Is a vector of basis functions, Z₄(k)＝[x₂(k),x₃(k),x₄(k)]^T。

Selecting u from control inputs_d(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₄，λ₄Is a normal number, and is,is eta₄The estimated value of (1), define | | W₄||＝η₄And η₄> 0, define variable η₄Has an estimation error ofSubstituting equation (19) into equation (18) yields:

d. performing stability analysis on the built neural network back-stepping controller of the permanent magnet synchronous motor

Selecting a Lyapunov function as follows:

differentiating V (k) to obtain:

according to the above formulaAndformula available when performing the (k +1) th sampling of the estimation errorAnd law of adaptationAnd m is 3 and 4. And has the following components:

is composed of Young' S inequality and | | | S_m(Z_m(k))||²＜l_m，m＝3,4，l_mThe number of nodes representing the neural network system can be obtained:

definition ofM is an arbitrary positive number because | x_jc(k)-α_j(k)|≤τ_jJ is 1,2, and is obtained by substituting equation (21) with equation (22) to equation (26) according to equation (20):

wherein l₃，l₄Respectively representing neural network systemsAndthe number of nodes.

Wherein,

τ₁,τ₂are all constants greater than zero.

Selecting suitable parameters P and sampling period delta_tTo make it satisfyIf the selection parameter is satisfiedIf m is 3,4, thenAndif true, Δ V (k) is less than or equal to 0.

It is further known that for arbitrarily small positive numbers sigma,this is true.

From the above analysis, the control law u can be obtained_q(k),u_d(k) The tracking error of the system can be converged to a sufficient neighborhood of the origin, and other signals are guaranteed to be bounded.

e. And simulating the established neural network backstepping discrete controller of the permanent magnet synchronous motor in a virtual environment, and verifying the feasibility of the provided neural network backstepping control method of the permanent magnet synchronous motor. The neural network backstepping discrete controller of the permanent magnet synchronous motor is designed by a discrete control method and is used for controlling the input quantity of a discrete dynamic system,

the permanent magnet synchronous motor system and related load parameters are:

J＝0.0003978kg·m²；B＝0.001158N·m/(rad/s)；

R_s＝0.68Ω；L_d＝0.00285H；L_q＝0.00315H；n_p＝3；Φ＝0.1245H；

selecting the control law parameters as follows:

λ₃＝0.87,λ₄＝0.0021,γ₃＝0.98,γ₄＝0.25,ζ＝2.0,ω_n＝200；

the selected neural network membership function is as follows:

wherein, mu₁……μ₉Respectively, as output values of hidden layer neurons, and z (k) represents input vectors of the neural network.

The desired position signal and the sampling period are respectively:

x_d(k)＝2cos(0.5πkΔ_t)；Δ_t＝0.0025s。

the corresponding simulation results are shown in fig. 2, 3,4 and 5. The simulation results of fig. 2 and 3 show that the method of the invention has ideal tracking effect and fast response speed, and the simulation results of fig. 4 and 5 show that the neural network backstepping discrete controller of the permanent magnet synchronous motor corresponding to the method of the invention has ideal effect, small fluctuation and fast response speed.

Aiming at the problems that a permanent magnet synchronous motor has a plurality of variables and strong coupling and is easily influenced by external loads and the change of relevant parameters of the motor, the method designs a neural network self-adaptive controller based on a command filtering technology and a back-stepping method principle, wherein the neural network technology is used for approaching unknown nonlinear terms, the self-adaptive back-stepping method is used for designing the controller, and the command filtering technology is used for solving the problem of 'calculation explosion'. In addition, the invention supplements the part of the complete controller design which is lacked in the traditional method, and increases the stability analysis of Lyapunov; after the controller is used for controlling and adjusting, the operation of the motor can quickly reach a stable state, and the motor is more suitable for a control object needing quick dynamic response.

It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A synchronous motor neural network backstepping discrete control method based on command filtering is characterized in that,

the method comprises the following steps:

a. establishing a dynamic model of a permanent magnet synchronous motor

Under the synchronous rotation d-q coordinate, the dynamic model of the permanent magnet synchronous motor is expressed as:

wherein theta is the angular position of the rotor of the permanent magnet synchronous motor, omega is the angular speed of the rotor of the permanent magnet synchronous motor, J is the moment of inertia, and T_LFlux linkage n generated for load torque, phi for permanent magnet_pIs the number of magnetic pole pairs, i_qFor q-axis stator current, i_dIs d-axis stator current, u_qIs the q-axis stator voltage u of the permanent magnet synchronous motor_dFor d-axis stator voltage, L of permanent magnet synchronous motor_dAnd L_qIs the stator inductance R under a d-q coordinate system_sThe equivalent resistance of the stator of the permanent magnet synchronous motor and the friction coefficient B are defined as the equivalent resistance of the stator of the permanent magnet synchronous motor;

to simplify the dynamic model of a permanent magnet synchronous motor, the following variables are defined:

the discrete dynamic model of the permanent magnet synchronous motor is then represented as:

wherein x is₁(k +1) represents the rotor angular position of the (k +1) th sample;

x₂(k +1) represents the rotor angular velocity of the (k +1) th sample;

x₃(k +1) represents the q-axis stator current of the (k +1) th sampling;

x₄(k +1) represents the d-axis stator current for the (k +1) th sample; delta_tRepresents a sampling period;

b. according to the backstepping principle, a synchronous motor neural network backstepping discrete control method based on command filtering is designed, wherein the discrete dynamic model is simplified into two independent subsystems, namely a state variable x₁(k),x₂(k) And a control input u_q(k) Formed subsystem and composed of state variables x₄(k) And a control input u_d(k) A component subsystem; wherein:

the first subsystem is:

the second subsystem is: x is the number of₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

Approximating a continuous function f (Z (k)) using a RBF neural networkⁿ→R；f(Z(k))＝W^TS(Z(k))；

Wherein,is an input vector, q is the neural network input dimension, R^qA real number vector set;

W＝[W₁,...,W_l]^T∈R^lis a weight vector, the number of nodes of the neural network is a positive integer, l is greater than 1, R^lA real number vector set;

Rⁿis an n-dimensional real number vector set, and R is a real number set; wherein, W₁,...,W_lIs the weight of the weight vector W;

S(Z(k))＝[s₁(Z(k)),...,s_l(Z(k))]^T∈R^lis a vector of basis functions, in which s_i(Z (k)) is used as a Gaussian function of the form:

wherein, mu_i＝[μ_i1,...,μ_iq]^TIs the center of the acceptance domain, and η_iThen the width of the gaussian function;

when the number of nodes of the neural network is large enough, the RBF neural network approaches to a compact setTo an arbitrary precision ε>0；

Define the command filter as:

wherein, ζ, ω_nIs a command filter parameter;

z_j,1(k)＝x_jc(k)，j＝1,2；

x_jc(k) and x_jc(k +1) represents the output signal of the kth and kth +1 samples of the jth command filter;

z_j,1(k),z_j,2(k) the output signal sampled the kth time of the jth command filter;

z_j,1(k+1),z_j,2(k +1) is the output signal of the (k +1) th sample of the jth command filter;

α_j(k) the input signal sampled the kth time of the jth command filter;

if the input signal alpha_j(k) For all constants k ≧ 0, such that | α_j(k+1)-α_j(k)|≤ρ₁And | α_j(k+2)-2α_j(k+1)+α_j(k)|≤ρ₂If true, it can be derived for an arbitrary constant τ_j> 0, presence of omega_n> 0 and ζ ∈ (0, 1)]So that | z_j,1(k)-α_j(k)|≤τ_j，Δz_j,1(k)＝|z_j,1(k+1)-z_j,1(k) I is bounded;

where ρ is₁And ρ₂Are all normal numbers, α_j(k +1) denotes the j-th order filterInput signal sampled at the k +1 st time, alpha_j(k +2) represents the k +2 sampled input signal of the jth command filter; at the same time z_j,1(0)＝α_j(0)，z_j,2(0) 0 is the initial value of the command filter, α_j(0) An initial input signal representing a command filter;

the system error variables are defined as follows:

wherein x is_d(k) For the desired position signal, x_1c(k)、x_2c(k) Is the output signal of the command filter;

c.1. to ensure x₁(k) Capable of effectively tracking expected position signal x_d(k) The Lyapunov control function is selected as follows:

according to the 1 st equation x in the discrete dynamic model formula (3)₁(k+1)＝x₁(k)+Δ_tx₂(k) The error variables can be found to be:

e₁(k+1)＝x₁(k+1)-x_d(k+1)＝x₁(k)+Δ_tx₂(k)-x_d(k+1)；

the difference can be found from equation (5):

x is to be₂(k) Viewed as a control input, x, to the first subsystem_d(k +1) is the expected position signal of the (k +1) th sampling, and an error variable e is set₂(k)＝x₂(k)-x_1c(k) Constructing a virtual control functionThen the following results are obtained:

c.2. according to the 2 nd equation in the discrete dynamical model formula (3):

x₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_Lthe error variable can be obtained:

e₂(k+1)＝a₁Δ_tx₃(k)+(1-a₃Δ_t)x₂(k)+a₂Δ_tx₃(k)x₄(k)-a₄Δ_tT_L-x_1c(k+1)；

selecting a Lyapunov function:then to V₂(k) Calculating the difference to obtain:

load torque T in actual operation of permanent magnet synchronous motor_LThere is an upper limit d, therefore | T_LD is less than or equal to | and d is a normal number;

constructing a virtual control function:

setting error variable e₃(k)＝x₃(k)-x_2c(k) Then Δ V₂(k) Expressed as:

derived from the young inequality:

therefore, substituting equation (11) into equation (10) yields:

c.3. from equation 3 of the discrete dynamical model equation (3):

x₃(k+1)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)+b₄Δ_tu_q(k) the error variable can be obtained:

selecting Lyapunov functionsTo V₃(k) Calculating the difference to obtain:

wherein f is₃(k)＝(1-b₁Δ_t)x₃(k)-b₂Δ_tx₂(k)+b₃Δ_tx₂(k)x₄(k)-x_2c(k+1)；

As can be seen from the RBF neural network approximation principle, the method can be used for any small positive number epsilon₃There is always a neural network systemSo that

Wherein delta₃Expressing approximation error and satisfying inequality | delta₃|≤ε₃，||W₃Is the vector W₃Thereby:

wherein S is₃(Z₃(k) Is a vector of basis functions, Z₃(k)＝[x₂(k),x₃(k),x₄(k),x_2c(k+1)]^T；

Selecting u from control inputs_q(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₃，λ₃Is a normal number, and is,is eta₃The estimated value of (1), define | | W₃||＝η₃And η₃> 0, define variable η₃Has an estimation error ofSubstituting equations (7), (12), and (15) into equation (14) yields:

c.4. recording the system error variable e₄(k)＝x₄(k) Selecting Lyapunov functionP is a normal number; from discrete dynamic model formulae(3) The 4 th expression of (1):

x₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k) the error variable can be obtained:

e₄(k+1)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k)+c₃Δ_tu_d(k)；

v is obtained₄(k) The difference of (a) can be obtained:

wherein f is₄(k)＝(1-c₁Δ_t)x₄(k)+c₂Δ_tx₂(k)x₃(k) As can be seen from the RBF neural network approximation principle, for arbitrarily small positive numbers ε₄There is always a neural network systemSo thatWherein, delta₄Expressing approximation error and satisfying inequality | delta₄|≤ε₄Wherein, | | W₄Is the vector W₄Thereby:

wherein S is₄(Z₄(k) Is a vector of basis functions, Z₄(k)＝[x₂(k),x₃(k),x₄(k)]^T；

Selecting u from control inputs_d(k) For actual control law and adaptive lawComprises the following steps:

wherein, γ₄，λ₄Is a normal number, and is,is eta₄The estimated value of (1), define | | W₄||＝η₄And η₄> 0, define variable η₄Has an estimation error ofSubstituting equation (19) into equation (18) yields:

d. performing stability analysis on the built neural network back-stepping controller of the permanent magnet synchronous motor

Selecting a Lyapunov function as follows:

differentiating V (k) to obtain:

according to the above formulaAndformula available when performing the (k +1) th sampling of the estimation errorAnd law of adaptationAnd has the following components:

is composed of Young' S inequality and | | | S_m(Z_m(k))||²＜l_m，m＝3,4，l_mThe number of nodes representing the neural network system can be obtained:

definition ofM is an arbitrary positive number because | x_jc(k)-α_j(k)|≤τ_jJ is 1,2, and is obtained by substituting equation (21) with equation (22) to equation (26) according to equation (20):

wherein l₃，l₄Respectively representing neural network systemsAndthe number of nodes of (a);

wherein,

τ₁,τ₂are all constants greater than zero;

selecting suitable parameters P and sampling period delta_tTo make it satisfyIf the selection parameter is satisfiedThen as long asAndif yes, obtaining delta V (k) less than or equal to 0;

it is further known that for arbitrarily small positive numbers sigma,this is true.