CN102998974A - Multi-model generalized predictive control system and performance evaluation method thereof - Google Patents

Abstract

The invention provides a multi-model generalized predictive control system and a performance evaluation method thereof. A plurality of fixed models and two self-adaptation models are adopted to parallelly identify dynamic characteristics of a system, optimal partial models are switched at each sampling instant to serve as current models based on performance indexes, optimal controllers are designed to control, and a minimum variance standard performance evaluation method is adopted to conduct performance evaluation on the multi-model switched generalized predictive control system. Compared with the traditional single-model generalized predictive control system, the multi-model switched generalized predictive control is adopted in a system for treating procedure parameter hopping, transient state performance of the system is improved, transient state errors are removed, and stability of the system is guaranteed.

Description

Multi-model generalized predictable control system and performance estimating method thereof

Technical field

The present invention relates to a kind of industrial control system, relate in particular to monitoring and the assessment of the performance of a kind of generalized predictable control system based on the multi-model switching and control system thereof.

Background technology

Modern industrial process has mostly been realized integrated and robotization, exists a large amount of control loops in the process, and the not good validity that will reduce control loop of control loop performance causes the commercial production can not safe and stable operation.Only have the good and control system that obtain regular maintenance of those designs just can obtain economic benefit steady in a long-term, yet in large-scale industrial process, the control loop that usually can exist many dynamic perfromances to suddenly change, but corresponding service engineer is seldom.

Generalized predictive control (GPC) combines Rolling optimal strategy with adaptive approach, adopt parameter model, design comparatively flexibly, and have good control performance and robustness, therefore be widely used in the industrial process fields such as petrochemical industry, oil refining, pharmacy, electric power and wastewater treatment.Under large operating mode, because identification and the modeling of system are very complicated, be difficult to set up the overall accurate model in the actual industrial process, cause the generalized predictive control of single model to be difficult to satisfy the requirement of system.Owing to be subject to the interference of random noise, the steady-state error of system is difficult to eliminate again, and these all cause the performance of control loop not good, only can not tackle the problem at its root by adjusting parameter.Therefore be badly in need of taking new control strategy or transforming hardware device and could improve the performance of system, and need some effective methods to assess the performance in each loop.

The concept of control system Performance Evaluation is proposed in 1989 by Harris the earliest, adopts the Performance Evaluation index based on minimum variance, and with its lower limit as the single variable control system Performance Evaluation, for the Performance Evaluation of single argument control loop is laid a good foundation.Performance Evaluation for further research control system, forefathers have done a lot of work, and obtained plentiful and substantial achievement in research, mainly comprise the following aspects: based on the Performance Evaluation of the feedforward feedback control loop of minimum variance, based on the Performance Evaluation of the unstable and nonminimum phase systems of minimum variance, the Performance Evaluation of the Model Predictive Control system of belt restraining etc.But the Performance Evaluation of generalized predictable control system still is in the starting stage.

Summary of the invention

The present invention is directed to the technical matters that exists in the above-mentioned prior art: propose a kind of multi-model generalized predictable control system, this system has solved the impact that the sudden change of control system parameter brings system, improved transient performance and steady-state behaviour, and confirmed that its performance obviously is better than the single model generalized predictable control system.

The present invention also provides a kind of performance estimating method of multi-model generalized predictable control system, is used for the performance of above-mentioned multi-model generalized predictable control system is assessed.

For achieving the above object, the technical solution used in the present invention is as follows:

The multi-model generalized predictable control system, adopt the adaptive model of a plurality of fixed models, a routine and one again the adaptive model of initialize form, the dynamic perfromance of parallel identification system, wherein, fixed model is used for improving the transient performance of system, adaptive model then is used for the steady-state error of the system of eliminating, and guarantees Systems balanth, again the adaptive model of initialize can further improve system transient performance, shorten transient state time.

On multi-model switches, at first design performance index, these performance index have considered that historical error is on the impact of system, in each sampling instant, system all will switch on the submodel that makes the performance index minimum automatically, according to the submodel that obtains, design generalized predictive controller, thereby the transient performance of the system of realization and the raising of steady-state behaviour.

A kind of performance estimating method of multi-model generalized predictable control system, be used for above-mentioned multi-model generalized predictable control system is carried out Performance Evaluation, to adopt the performance estimating method of minimum variance as the benchmark of estimating, determine whether system operates in optimum state, for the transformation of existing control system technical application provides foundation.

Beneficial effect: compare with the generalized predictive control of existing single model from the generalized predictable control system that switches based on multi-model of the present invention, greatly improved transient performance and the steady-state behaviour of system, and the self-regulation ability of the system during the model parameter saltus step.The performance of system obviously improves after the employing multi-model generalized predictive control.

Description of drawings

Fig. 1 (1) and Fig. 1 (2) are respectively curve of output and the controlled quentity controlled variable change curve of single model generalized predictable control system;

Fig. 2 (1) and Fig. 2 (2) are respectively curve of output and the controlled quentity controlled variable change curve of multi-model generalized predictable control system.

Embodiment

The invention will be further described below in conjunction with accompanying drawing and example.

The mathematical model of the controlled device that (1) the present invention is directed to is as follows:

A(z ^-1)y(k)=B(z ^-1)u(k-1)+C(z ^-1)ξk)/Δ(1)

In the following formula, input, output and average that u (k), y (k), ξ (k) are respectively controlled device are zero white noise sequence, Δ=1-z ^-1Be difference operator.Here get A=[a ₁, a ₂, a ₃]=[1 ,-2,1.1], B=[b ₀, b ₁]=[1,2], C=1.

(2) the multi-model collection is by 8 fixed models that parameter is known, but the adaptive model of the adaptive model of a routine and an initialize forms.For the fixed model collection, desirable α then ₁=1 ,-2}, a ₂=2 ,-1,1,2}, b ₀=1, b ₁=2 totally 8 fixed models.Model parameter and data parameters are represented with vector form, namely

${\mathrm{\θ}}_0=[a_1...a_{n_a},b_0...b_{n_b}]$

φ(k)=[-Δy(k-1)…-Δy(k-n _a)

Δu(k-d)…Δu(k-n _b-d)]

The vector representation form of formula (2) is:

Δy(k)=φ ^T(k)θ ₀+C(z ^-1)ξ(k)(3)

The vector representation that is obtained the multi-model collection by formula (3) is:

Δy _i(k)=φ _i ^T(k)θ _i(k)+C(z ^-1)ξ _i(k)

i=1,2,...m,m+1,m+2 (4)

In the following formula, θ _i(k) be a fixed value (i=1,2 ..., m=8); When i=m+1, choose conventional adaptive model; When i=m+2, choose again the adaptive model of assignment.For adaptive model, adopt following projection algorithm to carry out identification:

${\widehat{\mathrm{\θ}}}_{m+1}\left(k\right)={\widehat{\mathrm{\θ}}}_{m+1}(k-1)+\frac{\mathrm{\α}\left(t\right)\mathrm{\φ}\left(k\right)e_{m+1}\left(k\right)}{1+{\mathrm{\φ}}^T\left(k\right)\mathrm{\φ}\left(k\right)}---\left(5\right)$

$e_{m+1}\left(k\right)=y\left(k\right)-{\hat{y}}_{m+1}\left(k\right)$ (6)

$=y\left(k\right)-{\mathrm{\φ}}^T\left(k\right){\widehat{\mathrm{\θ}}}_{m+1}(k-1)$

In the formula, α (t) is a real number that changes, and its variation range is 0＜α (t)＜2.

(3) in each sampling instant, system chooses optimization model according to switching index, and it is as follows to switch index:

$J_i\left(k\right)=\frac{e_i^2\left(k\right)}{1+{\mathrm{\φ}}^T\left(k\right)\mathrm{\φ}\left(k\right)}(i=\mathrm{1,2}\·\·\·m+2)---\left(7\right)$

$e_i\left(k\right)=\left\{\begin{array}{c}y\left(k\right)-{\mathrm{\φ}}^T\left(k\right){\mathrm{\θ}}_i,i=\mathrm{1,2},\·\·\·m\\ y\left(k\right)-{\mathrm{\φ}}^T\left(k\right){\widehat{\mathrm{\θ}}}_i(k-1),i=m+1,m+2\end{array}\right.---\left(8\right)$

In the formula, e _i(k) be that i model is in k output error constantly;

For the adaptive model of assignment again, establishing s is constantly optimization model of k, then has:

1) if s ≠ m+2, then order

As assignment adaptive model M again _M+2The initial value of identification;

2) if s=m+2, then

Carry out identification according to formula (5).

(4) based on the above-mentioned optimization model of choosing, the design generalized predictive controller.

It is as follows at first to choose performance index:

$\min J=E\left\{\underset{j=N_1}{\overset{n_2}{\mathrm{\Σ}}}\right[y(k+j)-y_r{(k+j)}^2+$ (9)

$\underset{j=N_1}{\overset{N_u}{\mathrm{\Σ}}}\mathrm{\λ}\left(j\right){\left[\mathrm{\Δu}(k+j-1)\right]}^2\}$

In the formula, Δ u (k+j)=0 (j=N _u... N ₂), be illustrated in N _uControlled quentity controlled variable will no longer change after step.y _rBe object output expectation value; N ₁Minimum prediction time domain, N ₂Be maximum predicted time domain, N _uBe the control time domain; λ (j) is the control weighting sequence.For shortcut calculation, suppose in the following discussion N ₁=1, N ₂=N, λ (j) is constant λ.

The expectation value of controlled device output can be obtained by following formula:

y _r(k+j)=βy _r(k+j-1)+(1-β)ω (10)

Here j ∈ 1,2 ... N}; β is the softening factor, and 0＜β＜1; ω is the output setting value.Introduce the Diophantine equation, as follows:

1=E _j(z ^-1)A(z ^-1)Δ+z ^-jF _j(z ^-1) (11)

E _j(z ^-1)B(z ^-1)=G _j(z ^-1)+z ^-jH _j(z ^-1) (12)

J=1 in the following formula ..., N, and

E _j(z ^-1)=e ₀+e ₁z ^-1+…+e _j-1z ^-(j-1)

$F_j\left(z^{-1}\right)=f_0+f_1{z}^{-1}\·\·\·f_{n_a}{z}^{{-n}_a}$

G _j(z ^-1)=g ₀+g ₁z ^-1+…g _j-1z _-(j-1)

$H_j\left(z^{-1}\right)=h_0+h_1{z}^{-1}+\·\·\·h_{n_b-1}{z}^{-(n_b-1)}$

Obtaining j by formula (1), (11) and (12) was output as after the step

y(k+j)=G _j(z ^-1)Δu(k+j-1)+F _j(z ^-1)y(k)+E _j(z ^-1)ξ(k+j)(13)

For so that performance index in the formula (9) are minimum, adopt the gradient method optimizing to find the solution, obtain optimum solution and be:

Δu(k)=(G ^TG+λI) ^-1G ^T[y _r(k)-HΔu(k-1)-Fy(k)] (14)

Here

y _r(k)=[y _r(k+1)...y _r(k+N)]

F(z ^-1)=[F ₁(z ^-1)，…，F _N(z ^-1)] ^T

H(z ^-1)=[H ₁(z ^-1)，…，H _N(z ^-1)] ^T

$G=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="HDA00002481564900011.png,HDA00002481564900012.png"\; state="\{\{state\}\}">g</figure-callout>}}_0& & & 0\\ g_1& {\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="HDA00002481564900011.png,HDA00002481564900012.png"\; state="\{\{state\}\}">g</figure-callout>}}_0& & \\ \&CenterDot;& & & \\ \&CenterDot;& & & \\ \&CenterDot;& & & \\ g_{N_u-1}& g_{N_u-1}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="HDA00002481564900011.png,HDA00002481564900012.png"\; state="\{\{state\}\}">g</figure-callout>}}_0\\ \&CenterDot;& & & \\ \&CenterDot;& & & \\ \&CenterDot;& & & \\ g_{N-1}& g_{N-2}& \&CenterDot;\&CenterDot;\&CenterDot;& g_{{N-N}_u}\end{array}\right]$

Can get thus controlled quentity controlled variable is:

u(k)=u(k-1)+p ^T[y _r(k)-HΔu(k-1)-Fy(k)](15)

P in the formula ^TMatrix (G ^TG+ λ I) ^-1G ^TThe first row.

(5) in order to estimate the current performance of above-mentioned multi-model generalized predictable control system, existing with the benchmark of system performance under the minimum variance criterion as evaluation, then disturbance is write to the closed loop transfer function, that system exports:

$y\left(k\right)=\frac{N}{1+z^{-1}\tilde{T}Q}\mathrm{\&xi;}\left(k\right)---\left(16\right)$

In the formula,

For there not being the process transfer function matrix of time lag, Q is the transport function of controller, and disturbance transfer function is N.

Adopting Diophantine to divide to N solves:

M in the formula ₀Be constant coefficient, R is reasonable canonical transport function, so

$y\left(k\right)=\frac{1-z^{-1}R}{1+z^{-1}\tilde{T}Q}\mathrm{\&xi;}\left(k\right)$

$=(1+\frac{R-I\tilde{T}Q}{1+z^{-1}\tilde{T}Q})\mathrm{\&xi;}\left(k\right)$

$=\mathrm{I\&xi;}\left(k\right)+\mathrm{L\&xi;}(k-1)---\left(18\right)$

Here,

L is a canonical transport function.Because I ξ (k), L ξ (k-1) are separate:

Var{y(k)}=Var{Iξ(k)}+Var{Lξ(k-1)} (19)

Var{y (k) is then arranged } 〉=Var{I ξ (k) }, the following formula equal sign is set up when L=0, can get

Can try to achieve minimal variance controller is:

$Q=\frac{R}{\tilde{T}I}---\left(20\right)$

The minimum variance of system is:

${\mathrm{\&sigma;}}_{\mathrm{MV}}^2=E{\left(y^{T}y\right)}_{\min }=\mathrm{Var}\left\{\mathrm{I\&xi;}\left(k\right)\right\}---\left(21\right)$

The controller performance index is:

$\mathrm{\&eta;}\left(d\right)=\frac{{\mathrm{\&sigma;}}_{\mathrm{MV}}^2}{{\mathrm{\&sigma;}}_y^2}---\left(22\right)$

Here

Variance for reality output.0≤η (d)≤1 is obviously arranged.

As can be seen from Figure 1, the control step number of system is taken as 400, changes in 100 step default values, becomes 30 by original 0; Saltus step all occurs in the parameter of system when 200 steps and 300 step.Compared to Figure 1, the controlled quentity controlled variable of Fig. 2 changes more level and smooth, can not fluctuate frequently with the saltus step of parameter, and its transient performance significantly is better than Fig. 1.After parameter was undergone mutation, Fig. 2 had better regulating power, made the output held stationary of system.When setting value changed, the transient error of multi-model generalized predictive control was less than the single model generalized predictive control, and did not have overshoot.Adopt the accurate side of Performance Evaluation of minimum variance, single model generalized predictable control system and multi-model generalized predictable control system are carried out Performance Evaluation, the comparing result that draws is as shown in the table.Result from table can find out that behind the generalized predictable control system of employing based on the multi-model switching, the variance of control system obviously reduces, and performance obviously improves, and to improving industrial benefit certain directive significance is arranged.

Claims (3)

1. multi-model generalized predictable control system, it is characterized in that, the multi-model collection that described system mainly is comprised of the adaptive model of a plurality of fixed models, a routine and one the again adaptive model of initialize, wherein, described fixed model is in order to improve the transient performance of system, described adaptive model is then in order to the steady-state error of eliminating system and guarantee Systems balanth, the adaptive model of described again initialize in order to the transient performance of further raising system, shorten transient state time.

2. multi-model generalized predictable control system according to claim 1, it is characterized in that, the raising of described system transient modelling performance and steady-state behaviour is by designing performance index, these performance index have considered that historical error is on the impact of system, then in each sampling instant, system all will switch on the submodel that makes the performance index minimum, according to the submodel that obtains automatically, design generalized predictive controller, thereby the transient performance of the system of realization and the raising of steady-state behaviour.

3. the performance estimating method of a multi-model generalized predictable control system, it is characterized in that, be used for claim 1 or 2 described multi-model generalized predictable control systems are carried out Performance Evaluation, described performance estimating method is to adopt under the minimum variance criterion system performance as the benchmark of estimating, pass through system transter, design can make systematic variance reach minimum minimal variance controller, and then controlled system performance index

Wherein The minimum variance that can reach for control system,

Variance for reality output.

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