CN105159082A - IPSO-extended-implicit-generalized-prediction-based servo system position control method - Google Patents

Abstract

The invention, which belongs to the servo system control field, relates to an IPSO-extended-implicit-generalized-prediction-based servo system position control method. The method comprises: position data of a servo system at all time are collected; according to the collected data, an implicit generalized prediction model of the servo system at current time is identified by using a least square method of an aided model; non-linear part identification of the system model is carried out by using a particle swarm algorithm according to the collected data as well as a prediction output value of the identified implicit generalized prediction model; on the basis of the current servo system position, position control of the servo system is carried out; and thus the servo system moves according to a predetermined track; and the step (1) is carried out again at next time. According to the invention, the control method belongs to the field of the automatic control technology; and requirements during the actual industrial process can be met.

Description

The control method of the servo-drive system position that a kind of expansion Implicit Generalized based on IPSO is predicted

Technical field

The invention belongs to servo system control field, is the control method of the servo-drive system position that a kind of expansion Implicit Generalized based on IPSO is predicted.

Background technology

Servo-drive system has purposes widely in many aspects, as numerically-controlled machine, and robot.The accurate control of servo-drive system is not only related to the quality of product, ensures production effect especially.Therefore the control studying servo-drive system has very strong realistic meaning.

Since the people such as Richalct have put forward long-range prediction control concept, people carry out for the research of PREDICTIVE CONTROL always, on Richalct basis, the people such as clarke has put forward generalized predictive control self-tuner, this algorithm is based on carima model, have employed the optimality criterion of long duration, in conjunction with identification and self-correcting mechanism, there is stronger robustness and the feature such as model needs is low, and there is the scope of application widely.

Also have many about Generalized Predictive Algorithm in searching document and patent.As the high water tank control method (publication number: CN104076831A) optimized based on generalized predictive control, be characterized in gathering the height of each moment high water tank and entering the data of penstock aperture, according to the data gathered, the pid parameter that current time enters penstock is calculated based on the identification of Generalized Prediction system optimizing control, according to the PID controller parameter of current time as penstock, control into penstock aperture, and then control high water tank.This algorithm still adopts traditional generalized predictive control, utilizes least square method to carry out identification, and have ignored mission nonlinear on model construction.

Summary of the invention

The control method of the servo-drive system position that the object of the present invention is to provide a kind of expansion Implicit Generalized based on IPSO in automatic control technology field to predict.

The object of the present invention is achieved like this:

Based on the control method of the servo-drive system position that the expansion Implicit Generalized of IPSO is predicted, the method for stating comprises:

(1) data of the position of the servo-drive system in each moment are gathered;

(2) according to the Implicit Generalized forecast model of the data separate submodel least squares identification current time servo-drive system gathered;

(3) particle cluster algorithm is utilized to carry out the identification of the non-linear partial of system model according to the prediction output valve of the data gathered and identification Implicit Generalized forecast model out

(4) according to the position of current servo-drive system, the position control of servo-drive system is carried out; Make it to move according to projected path;

(5) entering the next moment returns step (1);

The Implicit Generalized forecast model of the described data separate submodel least squares identification current time servo-drive system according to gathering specifically comprises the steps:

Can obtain n precursor arranged side by side according to diophantus predictive equation is

$\left\{\begin{array}{c}y(k+1)=g_0\mathrm{\Δ}u\left(k\right)+f(k+1)+d_{nl}(k+1)\\ y(k+2)=g_1\mathrm{\Δ}u\left(k\right)+g_0\mathrm{\Δ}u(k+1)+f(k+2)+d_{nl}(k+2)\\ ...\\ y(k+n)=g_{n-1}\mathrm{\Δ}u\left(k\right)+...+g_0\mathrm{\Δ}u(k+n-1)+f(k+n)+d_{nl}(k+n)\end{array}\right.$

Y (k), u (k), d _nl(k), f (k) represents output, the input of system respectively, the non-linear partial of system and open-loop prediction vector;

y(k+n)＝g _n-1Δu(k)+…+g ₀Δu(k+n-1)+f(k+n)+d _nl(k+n)

Make X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], θ (k)=[g _n-1, g _n-1..., g ₀, f (k+n)] ^t,

y(k+n)＝X(k)θ(k)+d _nl(k+n)

Prediction of output value is

Y (k+n/k)=X (k) θ (k)+d _nlor y (k/k-n)=X (k-n) θ (k)+d (k+n) _nl(k)

The stepping type of submodel least square method is

$\widehat{\mathrm{\θ}}\left(k\right)=\widehat{\mathrm{\θ}}(k-1)+K\left(k\right)\[y\left(k\right)-X(k-1)\widehat{\mathrm{\θ}}(k-1)\]$

$K\left(k\right)=P(k-1){\hat{X}}^T(k-n){\[{\mathrm{\λ}}_1+{\hat{X}}^T(k-n)P(k-1){\hat{X}}^T(k-n)\]}^{-1}$

$P\left(k\right)=\[I-K\left(k\right)\hat{X}(k-n)\]P(k-1)/{\mathrm{\λ}}_1$

In formula, λ ₁for forgetting factor, 0 < λ ₁< 1,

The estimated value of gained θ (k) g ₀, g ₁..., g _n-1with f (k+n), k moment n walks estimated value and calculates:

$\hat{y}(k+n/k)=\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)+d_{nl}(k+n)$

In formula, X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], Δ u (k), Δ u (k+1) ..., Δ u (k+n-1) obtains according to error correction:

$\left(\begin{array}{c}{y}_0(k+1)\\ y_0(k+2)\\ .\\ .\\ .\\ y_0(k+p-1)\\ y_0(k+p)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+p-1/k)\\ \hat{y}(k+p/)\end{array}\right)+\left(\begin{array}{c}{h}_2\\ h_3\\ .\\ .\\ .\\ h_{p-1}\\ h_p\end{array}\right)e(k+1)$

In formula, p is model time domain length (p>=n), h ₂, h ₃..., h _pfor error correction coefficient;

$e\left(k+1\right)=y\left(k+1\right)-\hat{y}\left(k+1/k\right)$ For predicated error, h ₂=h ₃=...=h _p=1;

By f and Y ₀equivalence, the predicted vector f obtaining subsequent time is

$f=\left(\begin{array}{c}f(k+1)\\ f(k+2)\\ .\\ .\\ .\\ f(k+n)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+n+1/k)\end{array}\right)+\left(\begin{array}{c}1\\ 1\\ .\\ .\\ .\\ 1\end{array}\right)e(k+1).$

The described step utilizing particle cluster algorithm to carry out the identification of the non-linear partial of system model according to the data of collection and the prediction output valve of identification Implicit Generalized forecast model is out:

Non-linear relevant with input quantity, i.e. d _nl=au (k) ^b, adaptive value function is

$j=\hat{y}(k+n/k)-\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)-d_{nl}\left(k\right),$

X _i=(x _i1, x _i2..., x _iD) be i-th particle D tie up position vector, because unknown number only has a and b, so the dimension of the position of particle is 2, i.e. D=2, according to the parameter θ (k) that submodel least squares identification obtains, then calculates X _icurrent adaptive value function, in each iteration, the speed of particle renewal self and position;

$v_{ij}^{n+1}={\mathrm{wv}}_{ij}^n+c_1{r}_1(p_{ij}-x_{ij}^n)+c_2{r}_2(p_{gj}-x_{ij}^n)$

$x_{ij}^{n+1}=x_{ij}^n+v_{ij}^{n+1}$

Wherein: i=1,2 ..., N; J=1,2 ..., D; N is particle number, and n is iterations, and w is inertia weight; r ₁and r ₂for being evenly distributed on (0, the random number l); C ₁and C ₂for Studying factors, be usually taken as 2, i-th particle, n-th position iteration in jth dimension, p _ijthat i-th particle searches optimum position, p up to now in jth dimension _gjbeing that particle searches overall optimum position up to now in jth dimension, is the speed that i-th particle is tieed up in jth in n-th iteration;

$v_{ij}^n=\left\{\begin{array}{cc}{v}_{\max d}& v_{ij}^n>v_{\max d}\\ v_{ij}^n& -v_{\max d}\&le;v_{ij}^n\&le;v_{\max d}\\ -v_{\max d}& v_{ij}^n<-v_{\max d}\end{array}\right.$

Carry out self optimum position of more new particle and overall optimum position:

$P_{ij}^{n+1}=\left\{\begin{array}{cc}{P}_{ij}^n& J\left(x_{ij}^n\right)\&GreaterEqual;J\left(p_{ij}^n\right)\\ x_{ij}^n& J\left(x_{ij}^n\right)<J\left(p_{ij}^n\right)\end{array}\right.$

In formula, J () is adaptive value function,

p _gj＝minJ(p _ij)i＝1,2...N

Inertia weight w upgrades:

In formula,

Therefore the speed iteration of each particle:

In formula, C ₁c ₂for constant, rand () is random number, when the predetermined threshold is reached or when reaching iterative steps, exits calculating, exports optimal location, and then carries out rolling optimization.

Beneficial effect of the present invention is: the control method of the servo-drive system position that a kind of expansion Implicit Generalized based on IPSO in automatic control technology field disclosed by the invention is predicted, can meet the needs of actual industrial process.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is curve of output and the planning curve of predicting Self-correc ting control based on the Implicit Generalized improving population (IPSO).

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further:

Step of the present invention

(1) data of the position of the servo-drive system in each moment are gathered;

(2) according to the Implicit Generalized forecast model of the data separate submodel least squares identification current time servo-drive system gathered;

(3) particle cluster algorithm is utilized to carry out the identification of the non-linear partial of system model according to the prediction output valve of the data gathered and identification Implicit Generalized forecast model out

(4) according to the position of current servo-drive system, the position control of servo-drive system is carried out; Make it to move according to projected path;

Entering the next moment returns step (1);

Implicit Generalized forecast model according to the data separate submodel least squares identification current time servo-drive system gathered specifically comprises the steps:

Root can obtain n precursor arranged side by side according to diophantus predictive equation

$\left\{\begin{array}{c}y(k+1)=g_0\mathrm{\&Delta;}u\left(k\right)+f(k+1)+d_{nl}(k+1)\\ y(k+2)=g_1\mathrm{\&Delta;}u\left(k\right)+g_0\mathrm{\&Delta;}u(k+1)+f(k+2)+d_{nl}(k+2)\\ ...\\ y(k+n)=g_{n-1}\mathrm{\&Delta;}u\left(k\right)+...+g_0\mathrm{\&Delta;}u(k+n-1)+f(k+n)+d_{nl}(k+n)\end{array}\right.---\left(19\right)$

Y (k), u (k), d _nlk (), f (k) represents output, the input of system respectively, the non-linear partial of system and open-loop prediction vector.

An equation last by formula (19) obtains:

y(k+n)＝g _n-1Δu(k)+…+g ₀Δu(k+n-1)+f(k+n)+d _nl(k+n)(20)

Make X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], θ (k)=[g _n-1, g _n-1..., g ₀, f (k+n)] ^t, then formula (20) can be written as

y(k+n)＝X(k)θ(k)+d _nl(k+n)(21)

Prediction of output value is

Y (k+n/k)=X (k) θ (k)+d _nlor y (k/k-n)=X (k-n) θ (k)+d (k+n) _nl(k) (22)

The stepping type of submodel least square method is

$\widehat{\mathrm{\&theta;}}\left(k\right)=\widehat{\mathrm{\&theta;}}(k-1)+K\left(k\right)\&lsqb;y\left(k\right)-X(k-1)\widehat{\mathrm{\&theta;}}(k-1)\&rsqb;---\left(23\right)$

$K\left(k\right)=P(k-1){\hat{X}}^T(k-n){\&lsqb;{\mathrm{\&lambda;}}_1+{\hat{X}}^T(k-n)P(k-1){\hat{X}}^T(k-n)\&rsqb;}^{-1}---\left(24\right)$

$P\left(k\right)=\&lsqb;I-K\left(k\right)\hat{X}(k-n)\&rsqb;P(k-1)/{\mathrm{\&lambda;}}_1---\left(25\right)$

In formula, λ ₁for forgetting factor, 0 < λ ₁< 1.

Utilize the estimated value of formula (23) (24) (25) gained θ (k) g ₀, g ₁..., g _n-1with f (k+n).K moment n walks estimated value and can be calculated by formula (26):

$\hat{y}(k+n/k)=\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)+d_{nl}(k+n)---\left(26\right)$

In formula, X (k)=[Δ u (k), Δ u (k+1) ... Δ u (k+n-1), 1], Δ u (k), Δ u (k+1) ..., the controlling increment of Δ u (k+n-1) in respective point replaces.Obtain according to error correction:

$\left(\begin{array}{c}{y}_0(k+1)\\ y_0(k+2)\\ .\\ .\\ .\\ y_0(k+p-1)\\ y_0(k+p)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2)\\ \hat{y}(k+3)\\ .\\ .\\ .\\ \hat{y}(k+p-1)\\ \hat{y}(k+p)\end{array}\right)+\left(\begin{array}{c}{h}_2\\ h_3\\ .\\ .\\ .\\ h_{p-1}\\ h_p\end{array}\right)e(k+1)---\left(27\right)$

In formula, p is model time domain length (p>=n), h ₂, h ₃..., h _pfor error correction coefficient; for predicated error, get h here ₂=h ₃=...=h _p=1.

By f and Y ₀equivalence, the predicted vector f utilizing formula (28) can obtain subsequent time is

$f=\left(\begin{array}{c}f(k+1)\\ f(k+2)\\ .\\ .\\ .\\ f(k+n)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+n+1/k)\end{array}\right)+\left(\begin{array}{c}1\\ 1\\ .\\ .\\ .\\ 1\end{array}\right)e(k+1)$

According to the step that the data of collection and the prediction output valve of identification Implicit Generalized forecast model out utilize particle cluster algorithm to carry out the identification of the non-linear partial of system model be:

Suppose non-linear relevant with input quantity, i.e. d _nl=au (k) ^b.Adaptive value function is x _i=(x _i1, x _i2..., x _iD) be i-th particle D tie up position vector.Because unknown number only has a and b, so the dimension of the position of particle is 2, i.e. D=2.According to the parameter θ (k) that submodel least squares identification obtains, then calculate X _icurrent adaptive value function.In each iteration, particle utilizes formula (29) and formula (30) to upgrade self speed and position.

$v_{ij}^{n+1}={\mathrm{wv}}_{ij}^n+c_1{r}_1(p_{ij}-x_{ij}^n)+c_2{r}_2(p_{gj}-x_{ij}^n)---\left(29\right)$

$x_{ij}^{n+1}=x_{ij}^n+v_{ij}^{n+1}---\left(30\right)$

Wherein: i=1,2 ..., N; J=1,2 ..., D; N is particle number, and n is iterations, and w is inertia weight; r ₁and r ₂for being evenly distributed on (0, the random number l); C ₁and C ₂for Studying factors, be usually taken as 2. i-th particle, n-th position iteration in jth dimension, p _ijthat i-th particle searches optimum position, p up to now in jth dimension _gjbeing that particle searches overall optimum position up to now in jth dimension, is the speed that i-th particle is tieed up in jth in n-th iteration.The artificial maximum flying speed arranged is utilized all to limit the speed of particulate in formula (31).

$v_{ij}^n=\left\{\begin{array}{cc}{v}_{\max d}& v_{ij}^n>v_{\max d}\\ v_{ij}^n& -v_{\max d}\&le;v_{ij}^n\&le;v_{\max d}\\ -v_{\max d}& v_{ij}^n<-v_{\max d}\end{array}\right.---\left(31\right)$

Self optimum position of more new particle and overall optimum position is carried out by formula (32):

$P_{ij}^{n+1}=\left\{\begin{array}{cc}{P}_{ij}^n& J\left(x_{ij}^n\right)\&GreaterEqual;J\left(p_{ij}^n\right)\\ x_{ij}^n& J\left(x_{ij}^n\right)<J\left(p_{ij}^n\right)\end{array}\right.---\left(32\right)$

In formula, J () is adaptive value function.

p _gj＝minJ(p _ij)i＝1,2...N(33)

Inertia weight w upgrades such as formula shown in (15):

In formula,

Therefore the speed iteration of each particle is such as formula shown in (16):

In formula, C ₁c ₂for constant, rand () is random number.When the predetermined threshold is reached or when reaching iterative steps, exit calculating, export optimal location, and then carry out rolling optimization.

Step of the present invention

Gather the data of the position of the servo-drive system in each moment;

According to the Implicit Generalized forecast model of the data separate submodel least squares identification current time servo-drive system gathered;

Prediction output valve according to the data gathered and identification Implicit Generalized forecast model out utilizes particle cluster algorithm to carry out the identification of the non-linear partial of system model

According to the position of current servo-drive system, carry out the position control of servo-drive system; Make it to move according to projected path;

Entering the next moment returns step (1);

Implicit Generalized forecast model according to the data separate submodel least squares identification current time servo-drive system gathered specifically comprises the steps:

Root can obtain n precursor arranged side by side according to diophantus predictive equation

$\left\{\begin{array}{c}y(k+1)=g_0\mathrm{\&Delta;}u\left(k\right)+f(k+1)+d_{nl}(k+1)\\ y(k+2)=g_1\mathrm{\&Delta;}u\left(k\right)+g_0\mathrm{\&Delta;}u(k+1)+f(k+2)+d_{nl}(k+2)\\ ...\\ y(k+n)=g_{n-1}\mathrm{\&Delta;}u\left(k\right)+...+g_0\mathrm{\&Delta;}u(k+n-1)+f(k+n)+d_{nl}(k+n)\end{array}\right.---\left(37\right)$

Y (k), u (k), d _nlk (), f (k) represents output, the input of system respectively, the non-linear partial of system and open-loop prediction vector.

An equation last by formula (18) obtains:

y(k+n)＝g _n-1Δu(k)+…+g ₀Δu(k+n-1)+f(k+n)+d _nl(k+n)(38)

Make X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], θ (k)=[g _n-1, g _n-1..., g ₀, f (k+n)] ^t, then formula (19) can be written as

y(k+n)＝X(k)θ(k)+d _nl(k+n)(39)

Prediction of output value is

Y (k+n/k)=X (k) θ (k)+d _nlor y (k/k-n)=X (k-n) θ (k)+d (k+n) _nl(k) (40)

The stepping type of submodel least square method is

$\widehat{\mathrm{\&theta;}}\left(k\right)=\widehat{\mathrm{\&theta;}}(k-1)+K\left(k\right)\&lsqb;y\left(k\right)-X(k-1)\widehat{\mathrm{\&theta;}}(k-1)\&rsqb;---\left(41\right)$

$K\left(k\right)=P(k-1){\hat{X}}^T(k-n){\&lsqb;{\mathrm{\&lambda;}}_1+{\hat{X}}^T(k-n)P(k-1){\hat{X}}^T(k-n)\&rsqb;}^{-1}---\left(42\right)$

$P\left(k\right)=\&lsqb;I-K\left(k\right)\hat{X}(k-n)\&rsqb;P(k-1)/{\mathrm{\&lambda;}}_1---\left(43\right)$

In formula, λ ₁for forgetting factor, 0 < λ ₁< 1.

Utilize the estimated value of formula (41) (42) (43) gained θ (k) g ₀, g ₁..., g _n-1with f (k+n).K moment n walks estimated value and can be calculated by formula (44):

$\hat{y}(k+n/k)=\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)+d_{nl}(k+n)---\left(44\right)$

In formula, X (k)=[Δ u (k), Δ u (k+1) ... Δ u (k+n-1), 1], Δ u (k), Δ u (k+1) ..., the controlling increment of Δ u (k+n-1) in respective point replaces.Obtain according to error correction:

$\left(\begin{array}{c}{y}_0(k+1)\\ y_0(k+2)\\ .\\ .\\ .\\ y_0(k+p-1)\\ y_0(k+p)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2)\\ \hat{y}(k+3)\\ .\\ .\\ .\\ \hat{y}(k+p-1)\\ \hat{y}(k+p)\end{array}\right)+\left(\begin{array}{c}{h}_2\\ h_3\\ .\\ .\\ .\\ h_{p-1}\\ h_p\end{array}\right)e(k+1)---\left(45\right)$

In formula, p is model time domain length (p>=n), h ₂, h ₃..., h _pfor error correction coefficient; for predicated error, get h here ₂=h ₃=...=h _p=1.

By f and Y ₀equivalence, the predicted vector f utilizing formula (46) can obtain subsequent time is

$f=\left(\begin{array}{c}f(k+1)\\ f(k+2)\\ .\\ .\\ .\\ f(k+n)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+n+1/k)\end{array}\right)+\left(\begin{array}{c}1\\ 1\\ .\\ .\\ .\\ 1\end{array}\right)e(k+1)---\left(45\right)$

According to the step that the data of collection and the prediction output valve of identification Implicit Generalized forecast model out utilize particle cluster algorithm to carry out the identification of the non-linear partial of system model be:

Suppose non-linear relevant with input quantity, i.e. d _nl=au (k) ^b.Adaptive value function is x _i=(x _i1, x _i2..., x _iD) be i-th particle D tie up position vector.Because unknown number only has a and b, so the dimension of the position of particle is 2, i.e. D=2.According to the parameter θ (k) that submodel least squares identification obtains, then calculate X _icurrent adaptive value function.In each iteration, particle utilizes formula (47) and formula (48) to upgrade self speed and position.

$v_{ij}^{n+1}={\mathrm{wv}}_{ij}^n+c_1{r}_1(p_{ij}-x_{ij}^n)+c_2{r}_2(p_{gj}-x_{ij}^n)---\left(47\right)$

$x_{ij}^{n+1}=x_{ij}^n+v_{ij}^{n+1}---\left(48\right)$

Wherein: i=1,2 ..., N; J=1,2 ..., D; N is particle number, and n is iterations, and w is inertia weight; r ₁and r ₂for being evenly distributed on (0, the random number l); C ₁and C ₂for Studying factors, be usually taken as 2.

i-th particle, n-th position iteration in jth dimension, p _ijthat i-th particle searches optimum position, p up to now in jth dimension _gjbeing that particle searches overall optimum position up to now in jth dimension, is the speed that i-th particle is tieed up in jth in n-th iteration.The artificial maximum flying speed arranged is utilized all to limit the speed of particulate in formula (49).

$v_{ij}^n=\left\{\begin{array}{cc}{v}_{\max d}& v_{ij}^n>v_{\max d}\\ v_{ij}^n& -v_{\max d}\&le;v_{ij}^n\&le;v_{\max d}\\ -v_{\max d}& v_{ij}^n<-v_{\max d}\end{array}\right.---\left(49\right)$

Self optimum position of more new particle and overall optimum position is carried out by formula (50):

$P_{ij}^{n+1}=\left\{\begin{array}{cc}{P}_{ij}^n& J\left(x_{ij}^n\right)\&GreaterEqual;J\left(p_{ij}^n\right)\\ x_{ij}^n& J\left(x_{ij}^n\right)<J\left(p_{ij}^n\right)\end{array}\right.---\left(50\right)$

In formula, J () is adaptive value function.

p _gj＝minJ(p _ij)i＝1,2...N(51)

Inertia weight w upgrades such as formula shown in (15):

In formula,

Therefore the speed iteration of each particle is such as formula shown in (53):

In formula, C ₁c ₂for constant, rand () is random number.When the predetermined threshold is reached or when reaching iterative steps, exit calculating, export optimal location, and then carry out rolling optimization.

The position control step of the servo-drive system in step (4) is as follows:

The output of expansion is such as formula shown in (55):

$\hat{Y}=G\mathrm{\&Delta;}U+f+d_{nl}---\left(55\right)$

In formula, Δ U=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1)] ^t, d _nlbe the non-linear effects amount of system, it produces extra interference by system, adds amount of nonlinearity, so based on expanding the adaptive value function of nonlinear model Generalized Prediction model cootrol method such as formula (56)

J＝(Y+d _nl-W) ^T(Y+d _nl-W)+λΔU ^YΔU(56)

The Position input variable of t servo-drive system

u(t)＝u(t-1)+G ^TG+λI(W-f-d _nl)(57)

Claims (3)

1. a control method for the servo-drive system position of predicting based on the expansion Implicit Generalized of IPSO, it is characterized in that, described method comprises:

(1) data of the position of the servo-drive system in each moment are gathered;

(2) according to the Implicit Generalized forecast model of the data separate submodel least squares identification current time servo-drive system gathered;

(3) particle cluster algorithm is utilized to carry out the identification of the non-linear partial of system model according to the prediction output valve of the data gathered and identification Implicit Generalized forecast model out

(4) according to the position of current servo-drive system, the position control of servo-drive system is carried out; Make it to move according to projected path;

(5) entering the next moment returns step (1).

2. the control method of servo-drive system position predicted of a kind of expansion Implicit Generalized based on IPSO according to claim 1, is characterized in that: the Implicit Generalized forecast model of the described data separate submodel least squares identification current time servo-drive system according to gathering specifically comprises the steps:

Can obtain n precursor arranged side by side according to diophantus predictive equation is

$\left\{\begin{array}{c}y(k+1)=g_0\mathrm{\&Delta;}u\left(k\right)+f(k+1)+d_{nl}(k+1)\\ y(k+2)=g_1\mathrm{\&Delta;}u\left(k\right)+g_0\mathrm{\&Delta;}u(k+1)+f(k+2)+d_{nl}(k+2)\\ ...\\ y(k+n)=g_{n-1}\mathrm{\&Delta;}u\left(k\right)+...+g_0\mathrm{\&Delta;}u(k+n-1)+f(k+n)+d_{nl}(k+n)\end{array}\right.$

Y (k), u (k), d _nl(k), f (k) represents output, the input of system respectively, the non-linear partial of system and open-loop prediction vector;

y(k+n)＝g _n-1Δu(k)+…+g ₀Δu(k+n-1)+f(k+n)+d _nl(k+n)

Make X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], θ (k)=[g _n-1, g _n-1..., g ₀, f (k+n)] ^t,

y(k+n)＝X(k)θ(k)+d _nl(k+n)

Prediction of output value is

Y (k+n/k)=X (k) θ (k)+d _nlor y (k/k-n)=X (k-n) θ (k)+d (k+n) _nl(k)

The stepping type of submodel least square method is

$\widehat{\mathrm{\&theta;}}\left(k\right)=\widehat{\mathrm{\&theta;}}(k-1)+K\left(k\right)\&lsqb;y\left(k\right)-X(k-1)\widehat{\mathrm{\&theta;}}(k-1)\&rsqb;$

$K\left(k\right)=P(k-1){\hat{X}}^T(k-n){\&lsqb;{\mathrm{\&lambda;}}_1+{\hat{X}}^T(k-n)P(k-1){\hat{X}}^T(k-n)\&rsqb;}^{-1}$

$P\left(k\right)=\&lsqb;I-K\left(k\right)\hat{X}(k-n)\&rsqb;P(k-1)/{\mathrm{\&lambda;}}_1$

In formula, λ ₁for forgetting factor, 0 < λ ₁< 1,

The estimated value of gained θ (k) g ₀, g ₁..., g _n-1with f (k+n), k moment n walks estimated value and calculates:

$\hat{y}(k+n/k)=\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)+d_{nl}(k+n)$

In formula, X (k)=[Δ u (k), Δ u (k+1) ..., Δ u (k+n-1), 1], Δ u (k), Δ u (k+1) ..., Δ u (k+n-1) obtains according to error correction:

$\left(\begin{array}{c}{y}_0(k+1)\\ y_0(k+2)\\ .\\ .\\ .\\ y_0(k+p-1)\\ y_0(k+p)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+p-1/k)\\ \hat{y}(k+p/)\end{array}\right)+\left(\begin{array}{c}{h}_2\\ h_3\\ .\\ .\\ .\\ h_{p-1}\\ h_p\end{array}\right)e(k+1)$

In formula, p is model time domain length (p>=n), h ₂, h ₃..., h _pfor error correction coefficient;

for predicated error, h ₂=h ₃=...=h _p=1;

By f and Y ₀equivalence, the predicted vector f obtaining subsequent time is

$f=\left(\begin{array}{c}f(k+1)\\ f(k+2)\\ .\\ .\\ .\\ f(k+n)\end{array}\right)=\left(\begin{array}{c}\hat{y}(k+2/k)\\ \hat{y}(k+3/k)\\ .\\ .\\ .\\ \hat{y}(k+n+1/k)\end{array}\right)+\left(\begin{array}{c}1\\ 1\\ .\\ .\\ .\\ 1\end{array}\right)e(k+1).$

3. the control method of servo-drive system position predicted of a kind of expansion Implicit Generalized based on IPSO according to claim 1, is characterized in that: the step that the prediction output valve of described data according to gathering and identification Implicit Generalized forecast model out utilizes particle cluster algorithm to carry out the identification of the non-linear partial of system model is:

Non-linear relevant with input quantity, i.e. d _nl=au (k) ^b, adaptive value function is

$j=\hat{y}(k+n/k)-\hat{X}\left(k\right)\widehat{\mathrm{\&theta;}}\left(k\right)-d_{nl}\left(k\right),$

X _i=(x _i1, x _i2..., x _iD) be i-th particle D tie up position vector, because unknown number only has a and b, so the dimension of the position of particle is 2, i.e. D=2, according to the parameter θ (k) that submodel least squares identification obtains, then calculates X _icurrent adaptive value function, in each iteration, the speed of particle renewal self and position;

$v_{ij}^{n+1}={\mathrm{wv}}_{ij}^n+c_1{r}_1(p_{ij}-x_{ij}^n)+c_2{r}_2(p_{gj}-x_{ij}^n)$

$x_{ij}^{n+1}=x_{ij}^n+v_{ij}^{n+1}$

Wherein: i=1,2 ..., N; J=1,2 ..., D; N is particle number, and n is iterations, and w is inertia weight; r ₁and r ₂for being evenly distributed on (0, the random number l); C ₁and C ₂for Studying factors, be usually taken as 2, i-th particle, n-th position iteration in jth dimension, p _ijthat i-th particle searches optimum position, p up to now in jth dimension _gjbeing that particle searches overall optimum position up to now in jth dimension, is the speed that i-th particle is tieed up in jth in n-th iteration;

$v_{ij}^n=\left\{\begin{array}{cc}{v}_{\max d}& v_{ij}^n>v_{\max d}\\ v_{ij}^n& -v_{\max d}\&le;v_{ij}^n\&le;v_{\max d}\\ -v_{\max d}& v_{ij}^n<-v_{\max d}\end{array}\right.$

Carry out self optimum position of more new particle and overall optimum position:

$P_{ij}^{n+1}=\left\{\begin{array}{cc}{P}_{ij}^n& J\left(x_{ij}^n\right)\&GreaterEqual;J\left(p_{ij}^n\right)\\ x_{ij}^n& J\left(x_{ij}^n\right)<J\left(p_{ij}^n\right)\end{array}\right.$

In formula, J () is adaptive value function,

p _gj＝minJ(p _ij)i＝1,2...N

Inertia weight w upgrades:

In formula,

Therefore the speed iteration of each particle:

In formula, C ₁c ₂for constant, rand () is random number, when the predetermined threshold is reached or when reaching iterative steps, exits calculating, exports optimal location, and then carries out rolling optimization.