阅读说明：本技术 一种永磁直线电机有限级量化迭代学习控制方法 (Finite-stage quantization iterative learning control method for permanent magnet linear motor ) 是由 陶洪峰 黄彦德 庄志和 于 2021-08-06 设计创作，主要内容包括：本发明公开了一种永磁直线电机有限级量化迭代学习控制方法,涉及电机优化控制领域,该方法基于提升技术将重复运行的永磁直线电机转换为时间序列的输入输出矩阵模型,并将有限级对数量化器与编码解码机制相结合用以量化信号,从而减少传输数据量。针对采用编码解码方案量化信号的系统,基于优化的思想设计迭代学习控制算法,根据性能指标函数得到迭代学习优化控制算法的前馈实现。基于压缩映射方法,证明了所设计的量化迭代学习优化算法在数学期望意义下的收敛性。该方法可以解决使用网络传输信号的永磁直线电机的跟踪控制问题,实现对期望轨迹的高精度跟踪。(The invention discloses a finite-stage quantization iterative learning control method for a permanent magnet linear motor, which relates to the field of motor optimization control. Aiming at a system for quantizing signals by adopting a coding and decoding scheme, an iterative learning control algorithm is designed based on an optimization idea, and feedforward realization of the iterative learning optimization control algorithm is obtained according to a performance index function. Based on a compression mapping method, the convergence of the designed quantitative iterative learning optimization algorithm in a mathematical expected meaning is proved. The method can solve the tracking control problem of the permanent magnet linear motor using network transmission signals, and realize high-precision tracking of the expected track.)

1. A finite-stage quantization iterative learning control method for a permanent magnet linear motor is characterized by comprising the following steps:

firstly, establishing a dynamic model of a permanent magnet linear motor:

the dynamic model is represented by the following kinetic equation:

where R denotes the stator resistance, m denotes the total mass of the rotor part of the motor, psi_fIndicating stator permanent magnet excitation flux linkage, k₁＝π/τ，k₂1.5 pi/τ, τ denotes the pole pitch, u (t) denotes the mover voltage, p (t) denotes the motor position, ω (t) denotes the motor mover speed;

secondly, constructing a discrete state space equation of the permanent magnet linear motor:

selecting a sampling period T meeting the Shannon sampling theorem_sDiscretizing a continuous system model formula (1) by using an Euler method to obtain a discrete system model of the permanent magnet linear motor as follows:

defining the position and the rotor speed of the permanent magnet linear motor as state variables: x ═ p ω]^TIf the input variable is defined as the rotor voltage u and the output is defined as the motor rotation speed ω, the dynamic model of the permanent magnet linear motor shown in the formula (1) is described as follows:

wherein T and k respectively represent sampling time and batch, and the operation period of the batch process is T; within each cycle of the repetitive process, for a point in time T e 0, T]Taking N sampling points; u. of_k(t)，y_k(t) and x_k(t) input, output and state vectors at time t of the kth lot of the system, respectively; a, B and C are parameter matrixes of the discrete system in the formula (3), and CB is not equal to 0; and assuming the initial state of each batch of the system to be consistent, i.e. x_k(0)＝x₀；

Thirdly, establishing a track tracking model:

for a linear discrete system in the form of equation (3), converting a state space expression of the system into a time-series input-output matrix model:

y_k＝Gu_k+d_k (4)

wherein:

d_k＝[CA CA² CA³…CA^N]^Tx_k(0)

u_k＝[u_k(0),u_k(1),...,u_k(N-1)]^T

y_k＝[y_k(1),y_k(2),...,y_k(N)]^T

g is an input-output transfer matrix on a time series; d_kIs the influence of the initial state of the system on the output, assumingThen d_k＝0；

Step four, designing a quantization codec:

in a system using network transmission signals, the signals are quantized, and an input end quantization codec is designed as follows:

where 0 represents a zero vector having the same dimensions as the system input, u_k(t)、Andare respectively an encoder E₁Input, output and internal states of;is a decoder D₁I.e. the controller output u_k(t) an estimate of; q (-) is a finite-level logarithmic quantizer defined by equation (7):

wherein v represents the input of the finite-stage logarithmic quantizer;μ is the selected quantization density, and the quantization levels are as follows:

Z＝{±z_i|z_i＝μⁱz₀,i＝0,1,2,…,L-1}∪{0},0<μ<1,z₀>0

wherein L represents a positive quantization level, z₀>0 represents the maximum allowable level;

the output side quantization codec is designed as follows:

where 0 represents a zero vector having the same dimensions as the system output, y_k(t)、Andare respectively an encoder E₂Input, output and internal states of;is a decoder D₂I.e. the system output y_k(t) an estimate of; q (-) is a finite-level logarithmic quantizer defined by equation (7); the parameter setting of the input-end finite-stage logarithmic quantizer and the parameter setting of the output-end finite-stage logarithmic quantizer can be different;

fifthly, establishing a relational expression of signals before and after quantization:

the input v and the output q (v) of the log quantizer have quantization error Δ v whenWhen the fan shape is bounded, q (v) ═ v + η · v ═ 1+ η) v is obtained, and | η | ≦ δ; when in useQ (v) ═ 0 ═ v + d,the relation between the input v and the output q (v) of the finite-stage logarithmic quantizer is thus obtained as follows:

q(v)＝(1+η)v+d (10)

wherein eta represents a relative quantization error and satisfies that eta is less than or equal to delta; d represents a transmission error, satisfies

For k batches the signals at time t are:

q(v_k(t))＝(1+η_k(t))v_k(t)+d_k(t) (11)

wherein eta is_k(t) represents the relative quantization error of the signal at time t for k batches, d_k(t) represents the transmission error of the signal at time t of k batches;

from the input quantization codec definition and equation (11), we obtain:

according to the mathematical induction method, there areIs established so thatAnd u_k+1(t) is given by:

lifting the formula (13) into a vector form to obtainAnd u_k+1The vector relationship of (a) is:

wherein:

according to the definition of the output end quantization coding decoderAnd y_k+1The vector relationship of (a) is:

wherein:

the relative quantization error is independent of the quantizer input, so for any k batches at time t there is E v_k(t)η_k(t)]0; the relative quantization errors produced by the different quantizers are also independent of each other, i.e.i ≠ j and i, j ∈ {1,2 }; while in the same quantizer, the relative quantization error eta_k(t) in the interval [ - δ, δ]Inner uniform distribution and for arbitrary k₁，k₂And t₁，t₂Satisfies the following conditions:

wherein the content of the first and second substances,thus, the content is simplified by taking the mathematical expectationAndthe expression of (1);

the actual tracking error e exists in the system_k+1＝y_d-y_k+1And correcting errors with assistanceThe actual tracking error really reflects the tracking performance of the system, and the controller corrects the input signals of the current batch by using the auxiliary correction error; according toObtaining:

therefore, a relation between the current actual tracking error sequence and the auxiliary correction error sequence of the previous batch is established:

wherein, defineIn order to transmit the error, the transmission error is calculated, the value of beta is related to the selection of parameters of quantizers at two sides, and if the parameters selected by the quantizers at the input end and the output end are the same, the simplification is realized

Sixthly, designing a quantitative iterative learning control trajectory tracking optimization algorithm:

considering a norm optimal iterative learning control framework, the control input of each batch is obtained by optimizing a performance index function, and the general form of the performance index function is as follows:

the performance index function comprises the actual tracking error and the control oscillation, and a symmetrical positive definite weight matrix is respectively used in the optimization processQ and R denote their priorities, i.e. Q ═ Q^T>0，R＝R^T>0；

Taking the weight matrix Q-qI, R-rI, and the induction norm is defined as follows:

contains no random variable, and thus its expectation is equal to itself;

definition ofΞ＝σ²diag(γ₁₁,γ₂₂,…,γ_NN) Obtained according to equation (18):

xi and sigma²I are all symmetric positive definite matrixes; the performance index function equation (19) is substituted with equation (20) to obtain:

the finite-stage quantization iterative learning control updating law is obtained by solving an optimization problem with mixed parameters, and the specific form is as follows:

to solve the min-maximize problem of equation (22), the min-maximize problem is converted to a min-minimize problem using a lagrangian dual function; therefore, the min-max problem is restated as a convex optimization problem, so that a global optimal solution is guaranteed;

first consider the error w for transmission_k+1Because the performance indicator function (21) has only the first term and w_k+1In relation, therefore the maximization problem inside the optimization equation (22) is expressed as:

the maximization problem has strong duality; since equation (23) is a maximization problem with constraints, the lagrange multiplier λ is introduced_k+1The following lagrange function is obtained:

wherein the Lagrange multiplier λ_k+1Not less than 0, according to KKT condition, by pairing w_k+1And λ_k+1Differentiating to obtain an optimal solution, and usingAndindicating that the optimal solution yields:

to guarantee the convex optimization requirement of the performance index function, the Hessian matrix of the Lagrangian function (24) should be negative semi-definite, i.e.Thus, it is possible to provideReversible, withThe pseudo-inverse is shown as follows:

is a solution of the following equation:

as can be seen from equations (26) and (27), the optimal solutionAndall values of (a) depend on u_k+1Obtaining L (w)_k+1,λ_k+1) The dual function of (d) is:

converting the maximization problem (23) into a dual function g (lambda)_k+1) The minimization problem of (a), namely:

wherein g (lambda)_k+1) The specific expression of (A) is as follows:

combining the minimization problem outside the original optimization problem (22) with the minimization problem (29) results in a new dual function, i.e. the minimization-maximization problem of the original optimization problem (22) is transformed into the minimization-minimization problem as follows:

wherein J_dual(u_k+1,λ_k+1) Represents a new dual performance indicator function and is a convex function, and has:

since equation (32) is a convex function, there is an efficient numerical algorithm to compute the global optimal solution of equation (31); in which minimization problemsIs about_k+1The convex optimization problem of (1), thus the optimal solutionBy a dual function through the pair lambda_k+1Differentiation was obtained, yielding:

wherein the content of the first and second substances,when in useWhen is, Q_k+1Is a positive definite matrix;

for u is paired_k+1Differentiating to obtain:

due to (G)^TQ_k+1G + xi + R) is reversible, and the updating law of the finite-scale quantitative iterative learning control obtained by sorting the formula (34) is as follows:

wherein:

gain matrix Q_k+1The value of which depends on the solution of the optimization problem (31) as a function of the batch

Seventhly, analyzing the convergence of the quantitative iterative learning trajectory tracking optimization algorithm:

for the desired tracking trajectory y_dThere is an ideal input u_dSatisfy y_d＝Gu_dDefinition ofThen for the k +1 batch:

a control update law (35) is substituted for an equation (37) to obtain:

according to the relation of the input end signals, obtaining the equivalent form of the auxiliary correction error as follows:

due to the fact thatIs a reversible matrix in accordance withComprises the following steps:

the formula (39) and the formula (40) are substituted into the formula (38) to obtain:

two sides of equation (41) are expected:

obtaining I-K according to formula (36)_u-K_ζ0, orderTaking norm on both sides of formula (42) to obtain E (Δ u)_k+1) The inequality of (a) is:

||E(Δu_k+1)||≤||K_u-K_eG+K_ζ||||E(Δu_k)||+b (43)

after k iterations of the system, E (Δ u)_k+1) The inequality of (d) translates into:

if the selected weight matrix and quantization density make the constraint condition hold:

||K_u-K_eG+K_ζ||≤ρ<1 (45)

derived from the compressed mapping theoremEquation (43) is therefore simplified to:

c according to E (E)_k)＝GE(Δu_k) Obtaining:

i.e. the error norm E (E) in the expected sense_k) | | converge to a bounded value;

eighthly, realizing the track tracking of the permanent magnet linear motor by using the quantization signal of the quantization coder-decoder:

and determining a generated input vector of each iteration batch of the permanent magnet linear motor according to the finite-stage quantization iteration learning control law, obtaining an actual input vector under the action of the quantization coder-decoder, performing track tracking control on the permanent magnet linear motor by using the actual input vector, and tracking the expected output of the permanent magnet linear motor under the control action of the actual input vector.

Technical Field

The invention relates to the field of motor optimization control, in particular to a finite-stage quantization iterative learning control method for a permanent magnet linear motor.

Background

The permanent magnet linear motor is a novel motor without an intermediate transmission mechanism, and can directly convert electric energy into mechanical energy of linear motion. The device has the advantages of simple structure, large thrust volume ratio, high efficiency, accurate positioning and the like, so the device is widely applied to the fields of industrial transportation systems, office automation, military and the like.

For a permanent magnet linear motor executing a repetitive task, iterative learning control is a control strategy capable of effectively improving the track tracking precision. With the development of computer and communication technology, it is possible to adopt a network control system scheme in the control of the permanent magnet linear motor, wherein the permanent magnet linear motor and the iterative learning controller are located at different stations and communicate with each other through a wireless network, but limited by limited communication bandwidth and reliability, the data transmission amount needs to be reduced, and a quantized signal is taken as a common technical means for solving the problem, so that the network control system has great advantages in practical application, can meet the requirement of system tracking performance, and can reduce the transmission burden. Therefore, for the permanent magnet linear motor adopting network communication, the design problem of the iterative learning controller under the background of quantized data occurs.

On a nominal system, many iterative learning control algorithms achieve accurate tracking performance and ideal convergence performance, and achieve good performance in practical application. However, when quantization errors exist in transmission signals, the control effect of the conventional iterative learning control algorithm is not ideal, and since only a limited-level quantizer can be used in practical application, not an infinite-level quantizer under ideal conditions, the design of the controller is more demanding.

Disclosure of Invention

The invention provides a finite-stage quantization iterative learning control method for a permanent magnet linear motor aiming at the problems and the technical requirements, a quantization coder-decoder is designed by combining a logarithmic quantizer and a coding and decoding mechanism, the accurate signal transmission is realized in an iterative mode, a norm optimization algorithm framework is adopted to design a quantization iterative learning control algorithm, and the robust bounded convergence condition of the system is obtained according to a compression mapping method.

The technical scheme of the invention is as follows:

a finite-stage quantization iterative learning control method for a permanent magnet linear motor comprises the following steps:

firstly, establishing a dynamic model of a permanent magnet linear motor:

the dynamic model is represented by the following kinetic equation:

where R denotes the stator resistance, m denotes the total mass of the rotor part of the motor, psi_fIndicating stator permanent magnet excitation flux linkage, k₁＝π/τ，k₂1.5 pi/τ, τ denotes the pole pitch, u (t) denotes the mover voltage, p (t) denotes the motor position, ω (t) denotes the motor mover speed;

secondly, constructing a discrete state space equation of the permanent magnet linear motor:

selecting a sampling period T meeting the Shannon sampling theorem_sThe continuous system model formula (1) is discretized by using an Euler method, and a discrete system model of the permanent magnet linear motor is obtained as follows:

defining the position and the rotor speed of the permanent magnet linear motor as state variables: x ═ p ω]^TIf the input variable is defined as the rotor voltage u and the output is defined as the motor rotation speed ω, the dynamic model of the permanent magnet linear motor shown in the formula (1) is described as follows:

wherein T and k respectively represent sampling time and batch, and the operation period of the batch process is T; within each cycle of the repetitive process, for a point in time T e 0, T]Taking N sampling points; u. of_k(t)，y_k(t) and x_k(t) input, output and state vectors at time t of the kth lot of the system, respectively; a, B and C are parameter matrixes of the discrete system in the formula (3), and CB is not equal to 0; and assume the initial state of each batch of the systemCoincidence, i.e. x_k(0)＝x₀；

Thirdly, establishing a track tracking model:

for a linear discrete system in the form of equation (3), converting a state space expression of the system into a time-series input-output matrix model:

y_k＝Gu_k+d_k (4)

wherein:

d_k＝[CA CA² CA³ … CA^N]^Tx_k(0)

u_k＝[u_k(0),u_k(1),...,u_k(N-1)]^T

y_k＝[y_k(1),y_k(2),...,y_k(N)]^T

g is an input-output transfer matrix on a time series; d_kIs the effect of the initial state of the system on the output, assuming x_k(0)＝0,Then d_k＝0；

Step four, designing a quantization codec:

in a system using network transmission signals, because the network bandwidth is limited, the goal of accurately tracking the track needs to be realized under the condition of reducing the amount of transmitted information, so the signals can be quantized, and an input end quantization codec is designed as follows:

where 0 represents a zero vector having the same dimensions as the system input, u_k(t)、Andare respectively an encoder E₁Input, output and internal states of;is a decoder D₁I.e. the controller output u_k(t) an estimate of; q (-) is a finite-level logarithmic quantizer defined by equation (7):

where v represents the input to the finite-stage logarithmic quantizer;μ is the selected quantization density, and the quantization levels are as follows:

Z＝{±z_i|z_i＝μⁱz₀,i＝0,1,2,…,L-1}∪{0},0<μ<1,z₀>0

wherein L represents a positive quantization level, z₀>0 represents the maximum allowable level, and z can be selected to be large enough in practical application₀So thatAvoiding quantizer saturation to simplify controller design;

the output side quantization codec is designed as follows:

where 0 represents a zero vector having the same dimensions as the system output, y_k(t)、Andare respectively an encoder E₂Input, output and internal states of;is a decoder D₂I.e. the system output y_k(t) an estimate of; q (-) is a finite stage logarithmic quantizer defined by equation (7), and the parameter setting of the input finite stage logarithmic quantizer and the parameter setting of the output finite stage logarithmic quantizer may be different;

fifthly, establishing a relational expression of signals before and after quantization:

the input v and the output q (v) of the finite-stage logarithmic quantizer have a quantization error delta v, and the relation between the input v and the output q (v) needs to be given for the convenience of the design of a controller; when in useWhen the fan shape is bounded, q (v) ═ v + η · v ═ 1+ η) v is obtained, and | η | ≦ δ; when in useIs obtained at one timeThe relation between the input v and the output q (v) of the finite-stage logarithmic quantizer is thus obtained as follows:

q(v)＝(1+η)v+d (10)

wherein eta represents a relative quantization error and satisfies that eta is less than or equal to delta; d represents a transmission error, satisfies

For k batches the signals at time t are:

q(v_k(t))＝(1+η_k(t))v_k(t)+d_k(t) (11)

wherein eta is_k(t) represents the relative quantization error of the signal at time t for k batches, d_k(t) represents the transmission error of the signal at time t of k batches;

from the input quantization codec definition and equation (11), we obtain:

according to the mathematical induction method, there areIs established so thatAnd u_k+1(t) is given by:

lifting the formula (13) into a vector form to obtainAnd u_k+1The vector relationship of (a) is:

wherein:

by quantizing the codec definition at the outputAnd y_k+1The vector relationship of (a) is:

wherein:

the relative quantization error is independent of the quantizer input, so there is E v for any k batches at time t_k(t)η_k(t)]0; the relative quantization errors produced by the different quantizers are also independent of each other, i.e.i ≠ j and i, j ∈ {1,2 }; while in the same quantizer, the relative quantization error eta_k(t) in the interval [ - δ, δ]Inner uniform distribution and for arbitrary k₁，k₂And t₁，t₂Satisfies the following conditions:

wherein the content of the first and second substances,thus, the content is simplified by taking the mathematical expectationAndthe expression of (1);

the actual tracking error e exists in the system_k+1＝y_d-y_k+1And correcting errors with assistanceThe actual tracking error really reflects the tracking performance of the system, and the controller corrects the input signals of the current batch by using the auxiliary correction error; according toObtaining:

therefore, a relation between the current actual tracking error sequence and the auxiliary correction error sequence of the previous batch is established:

wherein, defineIn order to transmit the error, the transmission error is calculated,the value of beta is related to the selection of parameters of quantizers at two sides, and if the parameters selected by the quantizers at the input end and the output end are the same, the simplification is realized

Sixthly, designing a quantitative iterative learning control trajectory tracking optimization algorithm:

considering a norm optimal iterative learning control framework, the control input of each batch is obtained by optimizing a performance index function, and the general form of the performance index function is as follows:

the performance index function comprises actual tracking error and control oscillation, and the priority of the performance index function is represented by symmetrical positive definite weight matrixes Q and R in the optimization process, namely Q is Q^T>0，R＝R^T>0；

Taking the weight matrix Q-qI, R-rI, and the induction norm is defined as follows:

contains no random variable, and thus its expectation is equal to itself;

definition ofΞ＝σ²diag(γ₁₁,γ₂₂,…,γ_NN) Obtained according to equation (18):

xi and sigma²I are all symmetric positive definite matrixes; the performance index function equation (19) is substituted with equation (20) to obtain:

the finite-stage quantization iterative learning control updating law is obtained by solving an optimization problem with mixed parameters, and the specific form is as follows:

to solve the min-maximize problem of equation (22), the min-maximize problem is converted to a min-minimize problem using the lagrangian dual function; therefore, the min-max problem is reformulated as a convex optimization problem, thereby ensuring a globally optimal solution;

first considerWith respect to transmission error w_k+1Because the performance indicator function (21) has only the first term and w_k+1In relation, therefore the maximization problem inside the optimization equation (22) is expressed as:

the maximization problem has strong duality; since equation (23) is a maximization problem with constraints, the lagrange multiplier λ is introduced_k+1The following lagrange function is obtained:

wherein the Lagrange multiplier λ_k+1Not less than 0, according to KKT condition, by pairing w_k+1And λ_k+1Differentiating to obtain an optimal solution, and usingAndindicating that the optimal solution yields:

to guarantee the convex optimization requirement of the performance index function, the Hessian matrix of the Lagrangian function (24) should be negative semi-definite, i.e.Thus, it is possible to provideReversible, withThe pseudo-inverse is shown as follows:

is a solution of the following equation:

as can be seen from equations (26) and (27), the optimal solutionAndall values of (a) depend on u_k+1Obtaining L (w)_k+1,λ_k+1) The dual function of (d) is:

converting the maximization problem (23) into a dual function g (lambda)_k+1) The minimization problem of (a), namely:

wherein g (lambda)_k+1) The specific expression of (A) is as follows:

combining the minimization problem outside the original optimization problem (22) with the minimization problem (29) results in a new dual function, i.e. the minimization-maximization problem of the original optimization problem (22) is transformed into the minimization-minimization problem as follows:

wherein J_dual(u_k+1,λ_k+1) Represents a new dual performance indicator function and is a convex function, and has:

since equation (32) is a convex function, there is an efficient numerical algorithm to compute the global optimal solution of equation (31); in which minimization problemsIs about_k+1The convex optimization problem of (1), thus the optimal solutionBy a dual function through the pair lambda_k+1Differentiation was obtained, yielding:

wherein the content of the first and second substances,when in useWhen is, Q_k+1Is a positive definite matrix;

for u is paired_k+1Differentiating to obtain:

due to (G)^TQ_k+1G + xi + R) is reversible, and the finite-level quantization iterative learning control updating law obtained after the formula (34) is sorted is as follows:

wherein:

gain matrix Q_k+1The value of which depends on the solution of the optimization problem (31) as a function of the batch

Seventhly, analyzing the convergence of the quantitative iterative learning trajectory tracking optimization algorithm:

for the desired tracking trajectory y_dThere is an ideal input u_dSatisfy y_d＝Gu_dDefinition ofThen for the k +1 batch:

a control update law (35) is substituted for an equation (37) to obtain:

according to the relation of the input end signals, the equivalent form of the auxiliary correction error is obtained as follows:

due to the fact thatIs a reversible matrix in accordance withComprises the following steps:

the formula (39) and the formula (40) are substituted into the formula (38) to obtain:

two sides of equation (41) are expected:

obtaining I-K according to formula (36)_u-K_ζ0, orderTaking norm on both sides of formula (42) to obtain E (Δ u)_k+1) The inequality of (a) is:

||E(Δu_k+1)||≤||K_u-K_eG+K_ζ||||E(Δu_k)||+b (43)

after k iterations of the system, E (Δ u)_k+1) The inequality of (d) translates into:

if the selected weight matrix and quantization density make the constraint condition hold:

||K_u-K_eG+K_ζ||≤ρ<1 (45)

derived from the compressed mapping theoremEquation (43) is therefore simplified to:

c according to E (E)_k)＝GE(Δu_k) Obtaining:

i.e. the error norm E (E) in the expected sense_k) | | converge to a bounded value;

and eighthly, realizing the track tracking of the permanent magnet linear motor by using the quantization signals of the quantization coder-decoder:

and determining a generated input vector of each iteration batch of the permanent magnet linear motor according to a finite-stage quantization iteration learning control law, obtaining an actual input vector under the action of a quantization coder-decoder, performing track tracking control on the permanent magnet linear motor by using the actual input vector, and tracking the expected output of the permanent magnet linear motor under the control action of the actual input vector.

The beneficial technical effects of the invention are as follows:

the application discloses a linear system with repetitive motion characteristics, such as a permanent magnet linear motor, wherein the permanent magnet linear motor is used as a controlled object, a quantization coder-decoder is designed aiming at the condition that the bandwidth of a network transmission signal is limited, and a logarithmic quantizer is combined with a signal coding mechanism, so that the influence of a quantization error on the tracking performance is gradually reduced in the iteration process, and the transmission signal precision is improved. The method is based on a norm optimization iterative learning framework, a quantitative iterative learning control algorithm is designed, and the convergence of system tracking errors in a mathematical expectation meaning is guaranteed.

Drawings

Fig. 1 is a model block diagram of a permanent magnet linear motor provided in the present application.

Fig. 2 is a graph of an actual output curve of the permanent magnet linear motor provided by the present application.

Fig. 3 is a graph of 2-norm convergence of the actual tracking error of the system provided by the present application.

Fig. 4 is a graph of the generated input voltage calculated by the controller provided herein.

Fig. 5 is a graph of an actual input voltage of the permanent magnet linear motor provided by the present application.

FIG. 6 is a weight matrix Q provided herein_k+1The graph is varied.

Detailed Description

The following further describes the embodiments of the present invention with reference to the drawings.

Referring to fig. 1, referring to fig. 1 in conjunction with fig. 1 to fig. 6, a model block diagram of a permanent magnet linear motor disclosed in the present application is shown. Controller output of kth lot is u_kVia an encoder E₁After encoding, transmitted over a network by a decoder D₁Receiving and decoding to obtain the actual control vectorThe actual output y of the k-th batch of the system can be obtained by acting on the permanent magnet linear motor_kWith a set desired value y stored in a desired track memory_dComparing to obtain the actual tracking error e_k. Comparing the actual tracking error precision with the set precision value, if the error precision does not reach the set precision, outputting the actual y_kVia encoder E₂After encoding, transmitted over a network by a decoder D₂Receiving and decoding to obtain estimated output valueWhich is compared with the set expected value stored in the expected track memory to obtain the auxiliary correction errorWill assist in correcting errorsCurrent controller input u_kAnd an encoder E₁Internal state quantity ofController output u passed to the optimized iterative learning controller to generate the next batch_k+1And the iteration is stopped when the error between the actual output and the expected value of the system reaches the precision requirement in the circulating operation, and the input of the controller at the moment is the optimal control input.

For the actual physical model (also called dynamic model) of the permanent magnet linear motor shown in the formula (1), variable parameters are respectively set as:

R＝8.6Ω,m＝1.635kg,ψ_f＝0.35Wb,τ＝0.031m

the system simulation time is set to be T-2 s, and the sampling time is set to be T_s0.01s, the parameter matrices of the discrete state space expression of the system are respectively:

in the present embodiment, the expected trajectory of the permanent magnet linear motor is set as follows:

in units of rad/s while making the initial state satisfy x_k(0) 0. With network transmission signals, a limited-level quantization codec is designed due to limited bandwidth, in which the parameter of the logarithmic quantizer is set to be 0.7.

The weight matrix Q is selected to be 100I, and R is selected to be 0.1I, which satisfies the formula (45). Quantifying K in the iterative learning control law when the weight matrix Q, R is determined with the quantization density μ_u,K_e,K_ζAs determined accordingly. The above-mentioned quantization iteration learning controller of this application is realized based on STM32F103RCT6 chip, and the input of chip is motor control voltage u to gather through voltage sensor and obtain. The input signal enters an STM32F103RCT6 chip through a conditioning circuit to be stored and calculated, an iterative learning updating law is constructed, and the signal obtained after the CPU calculation is used for generating an input signal u_k+1Via an encoder E₁After being coded, passNetwork transmission by a decoder D₁Receiving and decoding to obtain actual control signalAnd the actual control signal acts on the permanent magnet linear motor, and the output track is continuously corrected until the expected track is tracked. When the dynamic model (1) of the permanent magnet linear motor operates, please refer to fig. 2, which shows a track tracking effect diagram of the permanent magnet linear motor applying the quantization iterative learning control law (35), and after a certain batch k, the output of the system can accurately track to the expected track. Fig. 3 shows that the quantitative iterative learning control algorithm can still achieve bounded convergence after a certain iterative batch, which also verifies the rationality and effectiveness of the algorithm.

Fig. 4 and 5 are graphs of the generated input signal calculated by the controller and the actual input signal of the system, respectively. Comparing fig. 4 and fig. 5, it can be seen that, as the number of iterations increases, the actual input signal gradually becomes smooth from the initial step shape, and after a plurality of iterations, the actual input signal and the generated input signal curve are substantially consistent, which indicates that the quantization codec designed in the present application can achieve accurate transmission of signals in an iterative manner. FIG. 6 shows the weight matrix Q as the iteration progresses_k+1And gradually increases.

What has been described above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiment. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.