CN103684170A - Secant-method based internal model position control method for permanent magnet linear synchronous motor - Google Patents

Abstract

The invention relates to a method for controlling the position of an internal model of a permanent magnet synchronous linear motor with a chord cut method, and is a new type of internal model control system. Including the kernel ridge regression internal model and the controller of the chord intercept method; the kernel ridge regression internal model is a high-precision linear motor nonlinear model constructed based on the kernel ridge regression method; the chord intercept method controller is iterated through the chord intercept method Solving the inverse of the internal model of kernel ridge regression is used as the controller, and the output of the internal model of kernel ridge regression is different from the actual position of the motor, and then fed back to the input of the controller of the chord-intercept method through the filter to form the internal model control method of the chord-intercept method. Position control for permanent magnet synchronous linear motors. The present invention has the following two characteristics: first, the internal model of the permanent magnet synchronous linear motor is constructed using the kernel ridge regression method; second, the inverse of the kernel ridge regression internal model is iteratively obtained as a controller by using the chord intercept method; The invention realizes the high tracking accuracy of the internal model position control system of the permanent magnet synchronous linear motor, and has strong robustness and anti-interference ability at the same time.

Description

A Chord Intersection Internal Model Position Control Method for Permanent Magnet Synchronous Linear Motor

technical field

The invention relates to a method for controlling the position of an internal mold of a permanent magnet synchronous linear motor with a chord cut method.

Background technique

In many industrial control fields, it is often necessary to control the controlled object to make a linear motion. However, due to the immature development of the linear drive, it has been necessary to obtain the linear motion through the mechanical conversion of the rotary motion of the rotating motor for a long time. The linear motor can be directly driven linearly without the need for an intermediate mechanical conversion mechanism and has many unique advantages. Linear motors have many advantages, such as fast response, very large thrust and very small loss, etc. In terms of high acceleration, positioning accuracy and rigidity, smooth and error-free motion can be achieved. Especially the permanent magnet synchronous linear motor, because of its small size, light weight, and power generation and braking functions, contains the advantages and characteristics of permanent magnet motors and linear motors, so it has been highly recognized in different fields. Pay attention to.

For linear motor control systems, PID regulators are generally used to regulate the system. Its structure is simple, easy to implement, and has good dynamic performance. However, the system has shortcomings such as being easily affected by system parameter changes, poor adaptability to load changes, and weak anti-interference ability. In the process of controller parameter setting, it is often repeated debugging based on a large amount of engineering experience. Therefore, in the case of high dynamic performance requirements, the use of traditional PID regulators will be subject to certain limitations and cannot meet the requirements of related aspects.

Internal model control is a very practical control method, which was first produced in process control and has been applied in results. Its characteristics are also suitable for fast-response permanent magnet synchronous linear motors. It has simple design principle, intuitive parameter setting, strong robustness and good control performance, so it has attracted the attention of many scholars at home and abroad. However, it is difficult for the conventional internal model controller to achieve a complete match between the internal model and the inverse model controller, so that it can only be considered as a compromise between tracking and robustness, and it is difficult to achieve dual optimal control.

Contents of the invention

The object of the present invention is to provide an internal model control method of a permanent magnet synchronous linear motor to solve the matching problem of positive and negative modes in the existing internal model control system, so as to achieve the dual excellence of tracking and robustness.

In order to achieve the above object, the technical solution of the present invention is: a permanent magnet synchronous linear motor chord method internal model position control method, characterized in that: by paralleling the permanent magnet synchronous linear motor with a nonlinear regression based on nuclear ridge regression model, the difference between the displacement output value of the permanent magnet synchronous linear motor and the displacement output value of the regression model is used, and it is fed back to the input terminal of the internal model controller through a low-pass filter, and then input to the string intercept after making a difference with the expected displacement value The method controller is used to suppress parameter changes, model mismatch and load disturbance; the kernel ridge regression is introduced into the internal model controller, and the kernel ridge regression is used to construct the object model to achieve high-precision model construction; through the analysis of the internal model structure, The design of the chord-intercept method controller is transformed into finding the root of the nonlinear function, and the solution of the control quantity is realized by using the chord-intercept method, which specifically includes the following steps:

Step S1: It is known that the nonlinear discrete controlled system with single input and single output is expressed as:

y(k+1)=P(y(k),...,y(k-n+1),u(k),...,u(k-m+1)), where u(k ),...,u(k-m+1) and y(k),...,y(k-n+1) are the input and output of the system at the kth moment respectively, and n and m are the order of the input and output respectively , and n>m; sample the input and output data of the permanent magnet synchronous linear motor position loop l times, let x _i =[y(i),…,y(i-n+1),u(i),…, u(i-m+1)], y _i =y(i+1), i=1,2,…,l, use the kernel ridge regression method to train the nonlinear model of the permanent magnet synchronous linear motor, that is, the permanent magnet The position loop model of synchronous linear motor is: G _m :y _m (k+1)=Y ^T (K _l×l +λI _l×l ) ^-1 K _l×1 (x)=f(X(k),u (k)); In the formula, λ is a regular term parameter, f(X(k), u(k)) is a nonlinear regression function, and ym(k+1) is an internal model output displacement;

, σ is the kernel width, X(k)={y(k),…,y(k-n+1),u(k-1),…,u(k-n+1)}, by adjusting λ and σ to realize the training of the regression model;

Step S2: Sampling and retaining the internal model input signal {u(k-1),...,u(k-m)} of m beats and the position output signal of permanent magnet synchronous linear motor {y(k),...,y( k-n+1)} form X(k), then when u(k) is input, the internal model output is ym(k+1)=f(X(k),u(k));

Step S3: Make a difference between the actual displacement output value y(k+1) of the permanent magnet synchronous linear motor and the internal model output displacement ym(k+1) described in step S1, to obtain the displacement error signal ξ(k+1);

Step S4: ξ(k+1) obtains the compensation input quantity η(k+1) through a low-pass filter;

Step S5: Make a difference between the reference displacement input y*(k+1) of the permanent magnet synchronous linear motor and the compensation input amount η(k+1) in step S3, and obtain the reference input signal y'(k+1) with disturbance 1);

Step S6: y'(k+1) can get the control input quantity u(k) through the controller of chord method, and the specific method of obtaining it is: give the control rate $u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(x\left(k\right),u^i\left(k\right))-f(x\left(k\right),u^{i-1}\left(k\right))}f(x\left(k\right),u^i\left(k\right)),$ where i is the number of iterations, sample and retain the m-beat output voltage {u(k-1),...,u(km)} of the chordal-intercept controller and n-beat reference input signal {y'(k ),…,y'(k-n+1)}, bring in the control rate for iterative calculation, when |u ⁱ⁺¹ (k)-u ⁱ (k)|≤δ, the iteration stops, where δ>0 is Given any small number, it means to stop the iteration precision value;

Step S7: After taking the difference between u(k) and K _e *v, divide it by a constant related to the structure of the permanent magnet synchronous linear motor to obtain the expected given value of the q-axis current of the current regulator, where K _e is related to the structure of the motor The constant, v is the motor speed, set the expected given value of the d-axis current of the current regulator to 0, and perform SVPWM modulation on the output of the current regulator to obtain the actual driving signal of the PWM rectifier at the stator end of the linear motor.

Compared with the prior art, the present invention has the following beneficial effects:

1. The present invention uses the Kernel Ridge regression method to build a high-precision permanent magnet synchronous linear motor nonlinear model, and through the analysis of the mathematical structure of the internal model, the design of the inverse model controller is converted into the calculation of the root of the nonlinear equation. The chord-intercept iteration method is used to obtain the control quantity. The proposed method avoids online network learning and adjustment, and the design of the chord-intercept method controller makes the forward and reverse models achieve high matching accuracy, thus ensuring System stability and robustness;

2. The system of the present invention has simple structure and high stability, and the parameters of the control method do not need to be adjusted online in real time;

3. The dynamic performance of the permanent magnet synchronous linear motor is effectively improved, which can be applied in engineering practice.

Description of drawings

Figure 1 is a structural diagram of the internal model control of the chord-section method.

Fig. 2 is the construction diagram of the linear motor nonlinear model of Kernel Ridge regression.

Figure 3 is a flowchart of the chord-intercept controller.

Figure 4 is a block diagram of the internal model position control system of the permanent magnet synchronous linear motor with the chord cut method.

Detailed ways

The technical solution of the present invention will be specifically described below in conjunction with accompanying drawings 1-4.

As shown in accompanying drawing 1, a kind of permanent magnet synchronous linear motor chord method internal model position control method of the present invention is characterized in that: by paralleling a permanent magnet synchronous linear motor with a nonlinear regression model based on nuclear ridge regression, Use the difference between the displacement output value of the permanent magnet synchronous linear motor and the displacement output value of the regression model, and feed back to the input terminal of the internal model controller through a low-pass filter, and then input the difference with the expected displacement value to the string intercept method control controller to suppress parameter changes, model mismatch and load disturbance; introduce kernel ridge regression into the internal model controller, use kernel ridge regression to build the object model, and realize high-precision model construction; through the analysis of the internal model structure, The design of the intercept method controller is transformed into finding the root of the nonlinear function, and using the chord intercept method to realize the solution of the control variable, which specifically includes the following steps:

Step S1: It is known that the nonlinear discrete controlled system with single input and single output is expressed as:

y(k+1)=P(y(k),...,y(k-n+1),u(k),...,u(k-m+1)), where u(k ),...,u(k-m+1) and y(k),...,y(k-n+1) are the input and output of the system at the kth moment respectively, and n and m are the order of the input and output respectively , and n>m; sample the input and output data of the permanent magnet synchronous linear motor position loop l times, let x _i =[y(i),…,y(i-n+1),u(i),…, u(i-m+1)], y _i =y(i+1), i=1,2,…,l, use the kernel ridge regression method to train the nonlinear model of the permanent magnet synchronous linear motor, that is, the permanent magnet The position loop model of synchronous linear motor is: G _m :y _m (k+1)=Y ^T (K _l×l +λI _l×l ) ^-1 K _l×1 (x)=f(X(k),u (k)); In the formula, λ is a regular term parameter, f(X(k), u(k)) is a nonlinear regression function, and ym(k+1) is an internal model output displacement;

, σ is the kernel width, X(k)={y(k),…,y(k-n+1),u(k-1),…,u(k-n+1)}, by adjusting λ and σ to achieve the training of the regression model (as shown in Figure 2);

Step S2: Sampling and retaining the internal model input signal {u(k-1),...,u(km)} of m beats and the position output signal of permanent magnet synchronous linear motor {y(k),...,y( k-n+1)} form X(k), then when u(k) is input, the internal model output is y _m (k+1)=f(X(k),u(k));

Step S3: Make a difference between the actual displacement output value y(k+1) of the permanent magnet synchronous linear motor and the internal model output displacement y _m (k+1) described in step S1, to obtain a displacement error signal ξ(k+1);

Step S4: ξ(k+1) obtains the compensation input quantity η(k+1) through a low-pass filter;

Step S5: Make a difference between the reference displacement input y*(k+1) of the permanent magnet synchronous linear motor and the compensation input amount η(k+1) in step S3, and obtain the reference input signal y'(k+1) with disturbance 1);

Step S6: As shown in Figure 3, y'(k+1) can obtain the control input u(k) through the controller of the chord method,

The specific way to obtain it is: give the control rate

$u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(x\left(k\right),u^i\left(k\right))-f(x\left(k\right),u^{i-1}\left(k\right))}f(x\left(k\right),u^i\left(k\right)),$ where i is the number of iterations,

Sample and retain the m-beat output voltage {u(k-1),…,u(km)} of the chordal-intercept controller and the n-beat reference input signal {y'(k),…,y' with perturbation (k-n+1)}, bring in the control rate for iterative calculation, when |u ⁱ⁺¹ (k)-u ⁱ (k)|≤δ, the iteration stops, where δ>0 is a given arbitrary small number , indicating the stop iteration precision value;

Step S7: After taking the difference between u(k) and K _e *v, divide it by a constant related to the structure of the permanent magnet synchronous linear motor to obtain the expected given value of the q-axis current of the current regulator, where K _e is related to the structure of the motor The constant, v is the motor speed, set the expected given value of the d-axis current of the current regulator to 0, and perform SVPWM modulation on the output of the current regulator to obtain the actual driving signal of the PWM rectifier at the stator end of the linear motor.

As shown in Figure 4, the mature vector control technology is used for design. Firstly, the stator three-phase currents _ia , _ib and _ic of the permanent magnet synchronous linear motor are detected by the current sensor, and the three-phase stator currents are transformed by Clarke. Get the current i _α and i _β in the two-phase stationary coordinate system, and transform the current i _α and i _β in the two-phase stationary coordinate system into the current i _d and i _q in the two-phase rotating coordinate system after park transformation, i _d and i _q are the feedback current of the current loop. For the permanent magnet synchronous linear motor, the desired current is given as i _q ^* =T _e ^* /(1.5pψ), p is the number of pole pairs, ψ is the rotor excitation flux linkage, T _e ^* is the electromagnetic torque setting of the motor. In order to improve the power factor of the generator and reduce the torque ripple, set the d-axis current setting as i _d ^* =0. The figure shows the q-axis current control block diagram, d The axis current control block diagram and machine parameters are the same as the q-axis; the transfer function of the q-axis current loop control object is 1/(Ls+R), where L is the stator inductance and R is the stator winding resistance. Considering that the current loop needs to be faster The tracking ability of the PI regulator is used to set the regulator parameters according to a typical type 1 system. The transfer function of the PI regulator is G _i (s)=k ₁ (τ ₁ s+1)/s, where k ₁ =R /(3T _s K _PWM ), τ ₁ =L/R, K _PWM is a small gain such as the bridge circuit of the PWM rectifier, and K _PWM =1 when SVPWM modulation is used.

The above are the preferred embodiments of the present invention, and all changes made according to the technical solution of the present invention, when the functional effect produced does not exceed the scope of the technical solution of the present invention, all belong to the protection scope of the present invention.

Claims (1)

1. A permanent magnet synchronous linear motor chord method internal model position control method is characterized in that: by connecting a permanent magnet synchronous linear motor in parallel with a non-linear regression model based on nuclear ridge regression construction, the displacement of the permanent magnet synchronous linear motor is utilized The difference between the output value and the displacement output value of the regression model is fed back to the input end of the internal model controller through a low-pass filter. and load disturbance; introduce Kernel Ridge Regression into the internal model controller, use Kernel Ridge Regression to construct the object model, and realize high-precision model construction; through the analysis of the internal model structure, the design of the chord intercept method controller is transformed into To find the root of the nonlinear function, and use the chord intercept method to realize the solution of the control quantity, the specific steps are as follows: Step S1: It is known that the nonlinear discrete controlled system with single input and single output is expressed as: y(k+1)=P(y(k),...,y(k-n+1),u(k),...,u(k-m+1)), where u(k ),...,u(k-m+1) and y(k),...,y(k-n+1) are the input and output of the system at the kth moment respectively, and n and m are the order of the input and output respectively , and n>m; sample the input and output data of the permanent magnet synchronous linear motor position loop l times, let x _i =[y(i),…,y(i-n+1),u(i),…, u(i-m+1)], yi=y(i+1), i=1,2,…,l, use kernel ridge regression method to train the nonlinear model of permanent magnet synchronous linear motor, that is, permanent magnet synchronous The linear motor position loop model is: G _m :y _m (k+1)=Y ^T (K _l×l +λI _l×l ) ^-1 K _l×1 (x)=f(X(k),u( k)); In the formula, λ is the regular term parameter, f(X(k), u(k)) is the nonlinear regression function, and ym(k+1) is the output displacement of the internal model;

, σ is the kernel width, X(k)={y(k),…,y(k-n+1),u(k-1),…,u(k-n+1)}, by adjusting λ and σ to realize the training of the regression model; Step S2: Sampling and retaining the internal model input signal {u(k-1),...,u(k-m)} of m beats and the position output signal of permanent magnet synchronous linear motor {y(k),...,y( k-n+1)} form X(k), then when u(k) is input, the internal model output is ym(k+1)=f(X(k),u(k)); Step S3: Make a difference between the actual displacement output value y(k+1) of the permanent magnet synchronous linear motor and the internal model output displacement ym(k+1) described in step S1, to obtain the displacement error signal ξ(k+1); Step S4: ξ(k+1) obtains the compensation input quantity η(k+1) through a low-pass filter; Step S5: Make a difference between the reference displacement input y*(k+1) of the permanent magnet synchronous linear motor and the compensation input amount η(k+1) in step S3, and obtain the reference input signal y'(k+1) with disturbance 1); Step S6: y'(k+1) can get the control input quantity u(k) through the controller of chord method, and the specific method of obtaining it is: give the control rate $u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(x\left(k\right),u^i\left(k\right))-f(x\left(k\right),u^{i-1}\left(k\right))}f(x\left(k\right),u^i\left(k\right)),$ where i is the number of iterations, sample and retain the m-beat output voltage {u(k-1),...,u(km)} of the chordal-intercept controller and n-beat reference input signal {y'(k ),…,y'(k-n+1)}, bring in the control rate for iterative calculation, when |u ⁱ⁺¹ (k)-u ⁱ (k)|≤δ, the iteration stops, where δ>0 is Given any small number, it means to stop the iteration precision value; Step S7: After taking the difference between u(k) and K _e *v, divide it by a constant related to the structure of the permanent magnet synchronous linear motor to obtain the expected given value of the q-axis current of the current regulator, where K _e is related to the structure of the motor The constant, v is the motor speed, set the expected given value of the d-axis current of the current regulator to 0, and perform SVPWM modulation on the output of the current regulator to obtain the actual driving signal of the PWM rectifier at the stator end of the linear motor.

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