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

Abstract

The invention relates to a secant-method based internal model position control method for a permanent magnet linear synchronous motor and belongs to a novel internal model control system. The novel internal model control system comprises a kernel ridge regression internal model and a secant method controller; the kernel ridge regression internal model is high-precision linear motor nonlinear model built by the kernel ridge regression process. The inverse of the kernel ridge regression internal model is acquired through iteration solving by the secant method to serve as the controller; the output of the kernel ridge regression internal model and the real position of the motor are subjected to difference operation, the difference value is fed back to the input of the secant method controller through a filter, so that the internal model control method based on the secant method is formed to realize position control for the permanent magnet linear synchronous motor. The secant-method based internal model position control method is characterized in that, the internal model of the permanent magnet linear synchronous motor is built by the kernel ridge regression process, and the inverse of the kernel ridge regression internal model is acquired through iteration solving by the secant method to serve as the controller. By the secant-method based internal model position control method, high tracking precision of the internal model position control system of the permanent magnet linear synchronous motor, high robustness and interference resistance capacity are achieved.

Description

A kind of permanent magnetic linear synchronous motor Secant Method internal mold position control method

Technical field

The present invention relates to a kind of permanent magnetic linear synchronous motor Secant Method internal mold position control method.

Background technology

In many industrial control fields, often need to control controlled device moving linearly, but because linear actuator development is still immature, have to for a long time through machinery conversion, obtain rectilinear motion by rotatablely moving of electric rotating machine.And the direct linear drives of linear electric motors has advantages of many uniquenesses without intermediate mechanical switching mechanism.The advantage of linear electric motors is a lot, very little etc. such as the loss very large and that cause of the thrust of fast response time, generation, aspect very high acceleration, positioning precision and rigidity, can realize the motion of level and smooth indifference.Permanent magnetic linear synchronous motor particularly, because its volume is very little, very light weight, and there is generating and braking function, the advantage and disadvantage that has comprised magneto and linear electric motors, therefore, has obtained very high attention in different fields.

Concerning linear motor control system, generally all adopt PID adjuster to regulate system, it simple in structure, easily realizes, and has good dynamic property.But system exists and to be subject to the impact of system parameter variations, to the adaptive capacity of load variations the shortcoming such as a little less than poor and antijamming capability, and in the tuning process of controller parameter, often since a large amount of engineering experiences repeatedly debug.Therefore, dynamic property is being required to high occasion, adopting traditional PID adjustment device will be subject to certain limitation, can not meet the requirement of related fields.

Internal model control is the control method that a kind of practicality is very strong, results from the earliest process control and has obtained application of result.Its feature is also applicable to the permanent magnetic linear synchronous motor of response fast.Its design principle is simple, and parameter tuning is directly perceived, strong robustness, and control performance is good, has therefore obtained domestic and international many scholars' concern.Yet conventional internal mode controller is difficult to realize the coupling completely of internal mold and contrary mould controller, makes its consideration of can only compromising between tracing property and robustness, be difficult to reach two excellent control.

Summary of the invention

The object of the present invention is to provide a kind of permanent magnetic linear synchronous motor internal model control method, to solve the matching problem of just contrary mould in existing internal model control system, to reach the two excellent of tracing property and robustness.

For achieving the above object, technical scheme of the present invention is: a kind of permanent magnetic linear synchronous motor Secant Method internal mold position control method, it is characterized in that: by giving permanent magnetic linear synchronous motor a nonlinear regression model (NLRM) building based on core ridge regression in parallel, utilize the displacement output valve of permanent magnetic linear synchronous motor and the displacement output valve of regression model poor, through a low pass filter, feed back to the input of internal mode controller, after doing to differ from the shift value of expectation, be input to Secant Method controller and suppress parameter variation, model mismatch and load disturbance; In the middle of core ridge regression introducing internal mode controller, utilize core ridge regression to build object model, realize high-precision model construction; By the analysis to internal model structure, the design of Secant Method controller is converted into the rooting to nonlinear function, and utilizes Secant Method to realize solving of controlled quentity controlled variable, specifically comprise the steps:

Step S1: known, the nonlinear discrete controlled system of single-input single-output is expressed as:

Y (k+1)=P (y (k) ..., y (k-n+1), u (k), ..., u (k-m+1)), u (k) wherein, u (k-m+1) and y (k) ..., y (k-n+1) is respectively system k input and output constantly, n and m are respectively the exponent number of input and output, and n>m; Permanent magnetic linear synchronous motor position ring inputoutput data is carried out to l sampling, make x _i=[y (i) ..., y (i-n+1), u (i) ..., u (i-m+1)], y _i=y (i+1), i=1,2 ..., l, utilizes the training of core Ridge Regression Modeling Method to obtain the nonlinear model of permanent magnetic linear synchronous motor, and permanent magnetic linear synchronous motor position ring model is: G _m: y _m(k+1)=Y ^t(K _{l * l}+ λ I _{l * l}) ^-1k _{l * 1}(x)=f (X (k), u (k)); In formula, λ is regular terms parameter, and f (X (k), u (k)) is nonlinear regression function, and ym (k+1) is internal mold output displacement;

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

Step S2: sample and retain the internal mold input signal { u (k-1) that m claps, u (k-m) } and the permanent magnetic linear synchronous motor position output signal { y (k) that claps of n, y (k-n+1) } composition X (k),, when input u (k), internal mold is output as ym (k+1)=f (X (k), u (k));

Step S3: permanent magnetic linear synchronous motor actual displacement output valve y (k+1) is poor with the internal mold output displacement ym (k+1) described in step S1, obtain displacement error signal xi (k+1);

Step S4: ξ (k+1) is compensated input variable η (k+1) through low pass filter;

Step S5: the reference displacement input y* (k+1) of permanent magnetic linear synchronous motor is poor with the compensation input variable η (k+1) in step S3, obtain the reference-input signal y'(k+1 with disturbance);

Step S6:y'(k+1) controller through Secant Method gets final product controlled input variable u (k), and its concrete preparation method is: provide control rate $u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(X\left(k\right),u^i\left(k\right))-f(X\left(k\right),u^{i-1}\left(k\right))}f(X\left(k\right),u^i\left(k\right)),$ Wherein i is iterations, sample and retain the output voltage that the m of Secant Method controller claps u (k-1) ... u (k-m) } and n clap reference-input signal with disturbance y'(k) ..., y'(k-n+1) }, bring control rate into and carry out iterative computation, when | u ⁱ⁺¹(k)-u ⁱ(k) | iteration stopping during≤δ, wherein δ >0 is given arbitrarily small number, represents to stop iteration precision value;

Step S7: by u (k) and K _e* after v work difference, divided by a constant relevant to permanent magnetic linear synchronous motor structure, obtain the expectation set-point of current regulator q shaft current, wherein K _efor the constant relevant to electric machine structure, v is motor speed, and the expectation set-point of current regulator d shaft current is made as to 0, and the output of current regulator is carried out to the driving signal that SVPWM modulation has just obtained the PWM rectifier of actual linear motor stator electric end.

Compared to prior art, the present invention has following beneficial effect:

1, the present invention utilizes core Ridge Regression Modeling Method to build high accuracy permanent magnetic linear synchronous motor nonlinear model, and by the analysis of internal mould mathematic(al) structure, the design of contrary mould controller is converted into asking for nonlinear equation root, with flat-sawn iterative method, realize asking for of controlled quentity controlled variable, the method proposing has been avoided online e-learning and adjustment, and the design of Secant Method controller more makes positive inversion model can reach very high matching precision, thereby stability and the robustness of system have been guaranteed;

2, system configuration of the present invention is simple, stability is high, and control method parameter does not need online adjusting in real time;

3, the dynamic property of effectively having improved permanent magnetic linear synchronous motor, can be applicable in the middle of engineering practice.

Accompanying drawing explanation

Fig. 1 is Secant Method internal model control structure figure.

Fig. 2 is the linear electric motors nonlinear model design of graphics of core ridge regression.

Fig. 3 is the flow chart of Secant Method controller.

Fig. 4 is permanent magnetic linear synchronous motor Secant Method internal mold position control system block diagram.

Embodiment

Below in conjunction with accompanying drawing 1-4, technical scheme of the present invention is specifically described.

As shown in Figure 1, a kind of permanent magnetic linear synchronous motor Secant Method internal mold position control method of the present invention, it is characterized in that: by giving permanent magnetic linear synchronous motor a nonlinear regression model (NLRM) building based on core ridge regression in parallel, utilize the displacement output valve of permanent magnetic linear synchronous motor and the displacement output valve of regression model poor, through a low pass filter, feed back to the input of internal mode controller, after doing to differ from the shift value of expectation, be input to Secant Method controller and suppress parameter variation, model mismatch and load disturbance; In the middle of core ridge regression introducing internal mode controller, utilize core ridge regression to build object model, realize high-precision model construction; By the analysis to internal model structure, the design of Secant Method controller is converted into the rooting to nonlinear function, and utilizes Secant Method to realize solving of controlled quentity controlled variable, specifically comprise the steps:

Step S1: known, the nonlinear discrete controlled system of single-input single-output is expressed as:

Y (k+1)=P (y (k) ..., y (k-n+1), u (k), ..., u (k-m+1)), u (k) wherein, u (k-m+1) and y (k) ..., y (k-n+1) is respectively system k input and output constantly, n and m are respectively the exponent number of input and output, and n>m; Permanent magnetic linear synchronous motor position ring inputoutput data is carried out to l sampling, make x _i=[y (i) ..., y (i-n+1), u (i) ..., u (i-m+1)], y _i=y (i+1), i=1,2 ..., l, utilizes the training of core Ridge Regression Modeling Method to obtain the nonlinear model of permanent magnetic linear synchronous motor, and permanent magnetic linear synchronous motor position ring model is: G _m: y _m(k+1)=Y ^t(K _{l * l}+ λ I _{l * l}) ^-1k _{l * 1}(x)=f (X (k), u (k)); In formula, λ is regular terms parameter, and f (X (k), u (k)) is nonlinear regression function, and ym (k+1) is internal mold output displacement;

, σ is core width, X (k)=y (k) ..., y (k-n+1), u (k-1) ..., u (k-n+1) }, by adjusting λ and σ, realize the training (as shown in Figure 2) to regression model;

Step S2: sample and retain the internal mold input signal that m claps u (k-1) ..., u (k-m) } and the permanent magnetic linear synchronous motor position output signal { y (k) that claps of n, y (k-n+1) } form X (k),, when input u (k), internal mold is output as y _m(k+1)=f (X (k), u (k));

Step S3: by the internal mold output displacement y described in permanent magnetic linear synchronous motor actual displacement output valve y (k+1) and step S1 _m(k+1) poor, obtain displacement error signal xi (k+1);

Step S4: ξ (k+1) is compensated input variable η (k+1) through low pass filter;

Step S5: the reference displacement input y* (k+1) of permanent magnetic linear synchronous motor is poor with the compensation input variable η (k+1) in step S3, obtain the reference-input signal y'(k+1 with disturbance);

Step S6: as shown in Figure 3, y'(k+1) controller through Secant Method gets final product controlled input variable u (k),

Its concrete preparation method is: provide control rate

$u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(X\left(k\right),u^i\left(k\right))-f(X\left(k\right),u^{i-1}\left(k\right))}f(X\left(k\right),u^i\left(k\right)),$ Wherein i is iterations,

Sample and retain the output voltage that the m of Secant Method controller claps u (k-1) ..., u (k-m) } and n clap reference-input signal with disturbance y'(k) ..., y'(k-n+1) }, bring control rate into and carry out iterative computation, when | u ⁱ⁺¹(k)-u ⁱ(k) | iteration stopping during≤δ, wherein δ >0 is given arbitrarily small number, represents to stop iteration precision value;

Step S7: by u (k) and K _e* after v work difference, divided by a constant relevant to permanent magnetic linear synchronous motor structure, obtain the expectation set-point of current regulator q shaft current, wherein K _efor the constant relevant to electric machine structure, v is motor speed, and the expectation set-point of current regulator d shaft current is made as to 0, and the output of current regulator is carried out to the driving signal that SVPWM modulation has just obtained the PWM rectifier of actual linear motor stator electric end.

As shown in Figure 4, adopt ripe vector control technology to design, first with current sensor, detect the stator three-phase current i of permanent magnetic linear synchronous motor _a, i _b, i _c, and stator three-phase current is converted through clarke, obtain the current i under two-phase rest frame _αand i _β, through park, converting the current i under two-phase rest frame _αand i _βbe transformed into the current i under two-phase rotating coordinate system _dand i _q, i _dand i _qbe the feedback current of electric current loop, the given value of current of expecting for permanent magnetic linear synchronous motor is i _q ^*=T _e ^*/ (1.5p ψ), p is number of pole-pairs, ψ is rotor-exciting magnetic linkage, T _e ^*for the electromagnetic torque of motor is given, in order to improve the power factor of generator, reduce torque pulsation, establish d shaft current and be given as i _d ^*shown in=0, figure, be q shaft current control block diagram, d shaft current control block diagram and tune machine parameter are the same with q axle; The transfer function of q shaft current ring control object is 1/ (Ls+R), wherein L is stator inductance, and R is stator winding resistance, considers that electric current loop needs follow-up control faster, adopt pi regulator to carry out tuning Regulator parameter by typical type 1 system, the transfer function of pi regulator is G _i(s)=k ₁(τ ₁s+1)/s, k in formula ₁=R/ (3T _sk _pWM), τ ₁=L/R, K _pWMfor little gains such as PWM rectifier Qiao roads, K when adopting SVPWM modulation _pWM=1.

Be more than preferred embodiment of the present invention, all changes of doing according to technical solution of the present invention, when the function producing does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (1)

1. a permanent magnetic linear synchronous motor Secant Method internal mold position control method, it is characterized in that: by giving permanent magnetic linear synchronous motor a nonlinear regression model (NLRM) building based on core ridge regression in parallel, utilize the displacement output valve of permanent magnetic linear synchronous motor and the displacement output valve of regression model poor, through a low pass filter, feed back to the input of internal mode controller, after doing to differ from the shift value of expectation, be input to Secant Method controller and suppress parameter variation, model mismatch and load disturbance; In the middle of core ridge regression introducing internal mode controller, utilize core ridge regression to build object model, realize high-precision model construction; By the analysis to internal model structure, the design of Secant Method controller is converted into the rooting to nonlinear function, and utilizes Secant Method to realize solving of controlled quentity controlled variable, specifically comprise the steps:

Step S1: known, the nonlinear discrete controlled system of single-input single-output is expressed as:

Y (k+1)=P (y (k) ..., y (k-n+1), u (k), ..., u (k-m+1)), u (k) wherein, u (k-m+1) and y (k) ..., y (k-n+1) is respectively system k input and output constantly, n and m are respectively the exponent number of input and output, and n>m; Permanent magnetic linear synchronous motor position ring inputoutput data is carried out to l sampling, make x _i=[y (i) ..., y (i-n+1), u (i) ... u (i-m+1)], yi=y (i+1), i=1,2,, l, utilizes the training of core Ridge Regression Modeling Method to obtain the nonlinear model of permanent magnetic linear synchronous motor, and permanent magnetic linear synchronous motor position ring model is: G _m: y _m(k+1)=Y ^t(K _{l * l}+ λ I _{l * l}) ^-1k _{l * 1}(x)=f (X (k), u (k)); In formula, λ is regular terms parameter, and f (X (k), u (k)) is nonlinear regression function, and ym (k+1) is internal mold output displacement;

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

Step S2: sample and retain the internal mold input signal { u (k-1) that m claps, u (k-m) } and the permanent magnetic linear synchronous motor position output signal { y (k) that claps of n, y (k-n+1) } composition X (k),, when input u (k), internal mold is output as ym (k+1)=f (X (k), u (k));

Step S3: permanent magnetic linear synchronous motor actual displacement output valve y (k+1) is poor with the internal mold output displacement ym (k+1) described in step S1, obtain displacement error signal xi (k+1);

Step S4: ξ (k+1) is compensated input variable η (k+1) through low pass filter;

Step S5: the reference displacement input y* (k+1) of permanent magnetic linear synchronous motor is poor with the compensation input variable η (k+1) in step S3, obtain the reference-input signal y'(k+1 with disturbance);

Step S6:y'(k+1) controller through Secant Method gets final product controlled input variable u (k), and its concrete preparation method is: provide control rate $u^{i+1}\left(k\right)=u^i\left(k\right)-\frac{u^i\left(k\right)-u^{i-1}\left(k\right)}{f(X\left(k\right),u^i\left(k\right))-f(X\left(k\right),u^{i-1}\left(k\right))}f(X\left(k\right),u^i\left(k\right)),$ Wherein i is iterations, sample and retain the output voltage that the m of Secant Method controller claps u (k-1) ... u (k-m) } and n clap reference-input signal with disturbance y'(k) ..., y'(k-n+1) }, bring control rate into and carry out iterative computation, when | u ⁱ⁺¹(k)-u ⁱ(k) | iteration stopping during≤δ, wherein δ >0 is given arbitrarily small number, represents to stop iteration precision value;

Step S7: by u (k) and K _e* after v work difference, divided by a constant relevant to permanent magnetic linear synchronous motor structure, obtain the expectation set-point of current regulator q shaft current, wherein K _efor the constant relevant to electric machine structure, v is motor speed, and the expectation set-point of current regulator d shaft current is made as to 0, and the output of current regulator is carried out to the driving signal that SVPWM modulation has just obtained the PWM rectifier of actual linear motor stator electric end.

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