CN101276207A - Multivariable non-linear system prediction function control method based on Hammerstein model - Google Patents

Abstract

The present invention provides a controlling method of a multivariate nonlinear system prediction function based on the hammerstein model, characterized in that the method includes following steps: (1) establishing the hammerstein model according to the process characteristic and the input output data; (2) solving the prediction function control rate of the multivariate linear subsystem according to the hammerstein model linear part model parameters, set values and practical process output of; (3) solving the equation V(k)=F(U(k)) to obtain optimal control law U(k) according to the hammerstein model nonlinear part model parameters and the multivariate linear multivariate nonlinear system prediction function control rate; (4) solving and implementing the optimal control law according to multivariate nonlinear system prediction function controller. The invention realizes one prediction function control of multivariate nonlinear system, realizing that the control problem of the nonlinear system is transformed to the linear system control problem and the solving problem of the nonlinear equation, improving the solving speed of the optimal control law, reducing the on-line computational complexity, ensuring the real-time requirement of the control system.

Description

Nonlinear multivariable systems Predictive function control method based on the Hammerstein model

Technical field

The present invention relates to industrial process control field, relate in particular to a kind of nonlinear multivariable systems Predictive function control method based on the Hammerstein model.

Background technology

Most of Industry Control all has constraint, and has a nonlinear characteristic, time variation and uncertainty, great majority have the object useable linear model approximation of small nonlinearity, as a kind of model mismatch, Robustness Design or on-line identification model parameter by system overcome the influence that small nonlinearity causes, and make these algorithms applicable to weakly non-linear system, and the achievement in research of using existing linear control theory obtains to control preferably effect.Though most of industrial process can carry out modeling and control by the local linearization method near the working point, have the non-linear controlled device of special construction for some, be difficult to obtain satisfied control effect with conventional linear control method.Therefore, be the focus and the difficult point of the research of control circle for the control of system with strong nonlinearity always, the PREDICTIVE CONTROL that adopts linear model departs from greatlyyer with actual, does not reach the purpose and the control effect of optimal control, must adopt nonlinear prediction to control.

Linearization technique is the conventional method of research nonlinear system.With the nonlinear system local linearization mainly is in order to continue to use existing achievement in the linear system, calculates simply, and real-time is good.For non-linear stronger system, be difficult to the dynamic and static characteristic of reflection system on a large scale with single inearized model, controlling performance even stability all are difficult to be guaranteed.Therefore during actual treatment, following three kinds of linearization techniques are arranged: a kind of method is with near the linearization each sampled point of non-linear mechanism model, then linearizing model is adopted linear predictive control algorithm, be characterized in all adopting new model, can reduce the error that linearization brings as far as possible in each sampling instant.But frequent online replacing model needing to cause the relevant matrix parameter of repeated calculation, and calculated amount strengthens, nor be beneficial to off-line the parameter of controller is optimized design; Another kind of effective method is a multi-model process.Introduce the approximate thought in by stages exactly, describe same nonlinear object with a plurality of linearizing models.The advantage of multi-model process be can off-line the most of controlled variable of calculating, difficult point then is the stationarity when how to determine the opportunity that model switches and guaranteeing that model switches; Also having a kind of is the method for feedback linearization, promptly nonlinear system is introduced the nonlinear feedback compensation rule, makes nonlinear system realize linearization to the virtual controlling input quantity, just can use linear forecast Control Algorithm.Yet there are many nonlinear system not satisfy the condition of feedback linearization, its application is restricted.

Model of mind such as fuzzy model, neural network model, also can approach many nonlinear system, thereby produced based on PREDICTIVE CONTROL side's neural network of neural network with its parallel processing, distributed storage, good robustness, adaptivity, self-study habit, the circle has broad application prospects in control.But PREDICTIVE CONTROL for neural network, the difficulty that exists is also many at present, the learning process of artificial neural network is a long quite slowly process, and PREDICTIVE CONTROL is owing to introduce multi-step prediction mechanism, calculated amount is original just very big, if introduce online learning process again, just further increased the weight of computation burden.Although the series connection of a plurality of neural networks can be obtained the prediction of output of multistep, can increase the complexity of controller like this, directly influence finding the solution of controlled quentity controlled variable.Simultaneously, onlinely if desired carry out Model Distinguish, so online network training can be consuming time more, the real-time of influence control.

The Hammerstein model description be the system that a class can be divided into static non linear and dynamic linear.This class model is simple in structure, the process that can be used for describing the pH N-process He have many nonlinear characteristics such as power function, dead band, switch.Based on the nonlinear multivariable systems Predictive function control method of Hammerstein model, can solve the PREDICTIVE CONTROL problem of many industrial processs.

Summary of the invention

The objective of the invention is to overcome the prior art deficiency, a kind of nonlinear multivariable systems Predictive function control method based on the Hammerstein model is provided.

Nonlinear multivariable systems Predictive function control method based on the Hammerstein model comprises the steps:

1) sets up the Hammerstein model according to process characteristic and inputoutput data;

2) find the solution the Predictive function control rate of multi-variable linear system according to the linear department pattern parameter of Hammerstein model, setting value and real process output;

3) obtain optimal control law U (k) according to Hammerstein model non-linear partial model parameter and multi-variable linear system Predictive function control rate solving equation group V (k)=F (U (k));

4) find the solution and implement optimal control law according to multivariable nonlinearity Predictive function control device.

Describedly set up Hammerstein model step according to process characteristic and inputoutput data:

Nonlinear multivariable systems Hammerstein model is:

Linear segment: $\left\{\begin{array}{c}{X}_m\left(k\right)=A_m{X}_m(k-1)+B_{m}V(k-1)\\ Y_m\left(k\right)=C_m{X}_m\left(k\right)\end{array}\right.$

Non-linear partial: V (k)=F _m(U (k))

X wherein _m(k) maintain the state variable of system for n, V (k) is the control variable of m dimensional linear subsystem, Y _m(k) for q maintains the system output variable, U (k) maintains system control variable, F for p _m() is R ⁿ→ R ^mNonlinear function, A _m∈ R ^{N * n}, B _m∈ R ^{N * m}, C _m∈ R ^{Q * n}Be the state-space model parameter.

According to control theory as can be known the state-transition matrix of linear segment model be $\mathrm{\Φ}\left(k\right)=A_m^k,$ Therefore the equation of motion of linear subsystem is:

$X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$

Described output according to the linear department pattern parameter of Hammerstein model, setting value and real process found the solution the Predictive function control rate step of multi-variable linear system:

(a), suppose the important v of V (k) with the input of intermediate variable V (k) as linear subsystem _i(k), i=1 ..., the number of the basis function of m is N all, thereby obtains:

$V(k+h)=\left[\begin{array}{c}{v}_1(k+h)\\ \·\\ \·\\ \·\\ v_m(k+h)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\·\·\·{\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{m1}\left(k\right)\·\·\·{\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]\·\left[\begin{array}{c}{f}_1\left(h\right)\\ \·\\ \·\\ \·\\ f_N\left(h\right)\end{array}\right]=\mathrm{\μ}\left(k\right)f\left(h\right)$

Wherein: μ ₁₁(k) ..., μ _MN(k) be the linear combination coefficient of each basis function, f ₁(h) ..., f _N(h) be that each basis function is at h functional value constantly.

(b) will $X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$ Bring Y into _m(k)=C _mX _m(k) can get:

$Y_m(k+h)=\left[\begin{array}{c}{r}_1\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,1)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,p)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\end{array}\right].$

Wherein:

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);$ i＝1，…，m；l＝1，…，N；s＝1，…，q，

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},$ i＝0，…，h-1.

(c) Predictive function control is a kind of closed loop control algorithm, therefore needs to introduce the feedback compensation link, gets predicated error and is: E (k+h)=Y (k)-Y _m(k), wherein:

E (k+h)=[e ₁(k+h) ..., e _q(k+h)] _TPredicated error for model;

Y (k)=[y ₁(k) ..., y _q(k)] ^TOutput for current time process object;

Y _m(k)=[y _M1(k) ..., y _Mq(k)] ^TOutput for the current time forecast model.

(d) reference locus adopts the single order exponential form, and then k+H reference locus constantly is:

$Y_r(k+h)=\left[\begin{array}{c}{y}_{r1}(k+h)\\ \·\\ \·\\ \·\\ y_{\mathrm{rq}}(k+h)\end{array}\right]=\left\{\begin{array}{c}{c}_1(k+h)-{{\mathrm{\α}}_1}^h\·[c_1\left(k\right)-y_1\left(k\right)]\\ \·\\ \·\\ \·\\ c_q(k+h)-{{\mathrm{\α}}_q}^h\·[c_q\left(k\right)-y_q\left(k\right)]\end{array}\right\}$

Wherein: h=1 ..., H; H is the total number of match point; y _R1(k+h) ..., y _Rq(k+h) be the k+h value of q reference locus constantly; c ₁(k+h) ..., c _q(k+h) be k+h q setting value constantly; The calculating of setting value adopts polynomial form as follows: $c_i(k+h)=\underset{l=0}{\overset{d_i}{\mathrm{\Σ}}}{c}_{\mathrm{il}}\left(k\right)h^l,$ d _iBe setting value polynomial expression exponent number, c _Il(k) be the setting value multinomial coefficient; y ₁(k) ..., y _q(k) be current time q process object real output value; ${\mathrm{\α}}_i=e^{-\frac{T_s}{T_{\mathrm{ri}}}},$ I=1 ..., q, T _sBe the sampling period, T _RiFor following the tracks of the i bar reference locus Expected Response time.

(e) adopt following optimization aim:

$J=\underset{j=1}{\overset{H}{\mathrm{\Σ}}}\underset{i=1}{\overset{q}{\mathrm{\Σ}}}{[{\tilde{y}}_i(k+h)-y_{\mathrm{ri}}(k+h)]}^2$

Wherein: ${\tilde{y}}_i(k+h)=y_{\mathrm{mi}}(k+h)+e_i(k+h);$

(f) by finding the solution above-mentioned optimization problem, promptly by finding the solution $\frac{\∂J}{{\∂\mathrm{\μ}}_{\mathrm{ij}}\left(k\right)}=0,$ Just can obtain matrix of coefficients:

$\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{q1}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]=-Z^{-1}\·M\·{\left[\begin{array}{c}v\left(\mathrm{1,1}\right)\\ \·\\ \·\\ \·\\ v(1,p)\\ \·\\ \·\\ \·\\ v(s,1)\\ \·\\ \·\\ \·\\ v(s,q)\end{array}\right]}_{\mathrm{Hq}\×1}$

Wherein:

$M={\left[\begin{array}{ccccccc}{T}_{11}(h_1,1)& \·\·\·& T_{11}(h_1,p)& \·\·\·& T_{11}(h_s,1)& \·\·\·& T_{11}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{1N}(h_1,1)& \·\·\·& T_{1N}(h_1,p)& \·\·\·& T_{1N}(h_s,1)& \·\·\·& T_{1N}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{m1}(h_1,1)& \·\·\·& T_{m1}\left(h_{1,}p\right)& \·\·\·& T_{m1}(h_s,1)& \·\·\·& T_{m1}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{\mathrm{mN}}(h_1,1)& \·\·\·& T_{\mathrm{mN}}(h_1,p)& \·\·\·& T_{\mathrm{mN}}(h_s,1)& \·\·\·& T_{\mathrm{mN}}(h_s,p)\end{array}\right]}_{\mathrm{mN}\×\mathrm{Sq}}$

$Z={\left[\begin{array}{ccccccc}{w}_{11}\left(\mathrm{1,1}\right)& \·\·\·& w_{1N}\left(\mathrm{1,1}\right)& \·\·\·& w_{m1}\left(\mathrm{1,1}\right)& \·\·\·& w_{\mathrm{mN}}\left(\mathrm{1,1}\right)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(1,N)& \·\·\·& w_{1N}(1,N)& \·\·\·& w_{m1}(1,N)& \·\·\·& w_{\mathrm{mN}}(1,N)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,1)& \·\·\·& w_{1N}(m,1)& \·\·\·& w_{m1}(q,1)& \·\·\·& w_{\mathrm{mN}}(q,1)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,N)& \·\·\·& w_{1N}(m,N)& \·\·\·& w_{m1}(q,N)& \·\·\·& w_{\mathrm{mN}}(q,N)\end{array}\right]}_{\mathrm{mN}\×\mathrm{mN}}$

Wherein:

$w_{\mathrm{ij}}(t,R)=\underset{l=1}{\overset{S}{\mathrm{\Σ}}}\underset{\mathrm{\ρ}=1}{\overset{p}{\mathrm{\Σ}}}{T}_{\mathrm{tR}}(h_l,\mathrm{\ρ})\·T_{\mathrm{ij}}(h_l,\mathrm{\ρ});$

i＝1，…，m；j＝1，…，N；t＝1，…，m；R＝1，…，N

$v(i,j)=-r_j\left(h_i\right)+y_j\left(k\right)-y_{\mathrm{mj}}\left(k\right)+{{\mathrm{\α}}_j}^{h_i}\·[c_j\left(k\right)-y_j\left(k\right)]-\underset{l=1}{\overset{d_j}{\mathrm{\Σ}}}{c}_{\mathrm{jl}}\left(k\right)h_i^l.$

i＝1，…，S；j＝1，…，q

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);$ i＝1，…，m；l＝1，…，N；s＝1，…，q，

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},$ i＝0，…，h-1.

Thereby obtain matrix of coefficients μ (k).

(g) therefore obtain multi-variable linear system Predictive function control rate: V (k+h)=μ (k) f (h).

Describedly find the solution and implement the optimal control law step according to multivariable nonlinearity Predictive function control device:

(h) algorithm initialization: the correlation parameter of the parameter of given model, basis function and multivariable nonlinearity Predictive function control device;

(i) read in k process output valve Y (k) constantly, and k, k+H _j, j=1 ..., q setting value constantly;

(j) calculate k+h _j, h _j=1 ..., H _jReference locus value Y constantly _r(k+h _j);

(k) optimization is found the solution and is obtained k intermediate controlled amount V constantly _m(k);

(l) find the solution the root of Nonlinear System of Equations, obtain current controlled quentity controlled variable U (k);

(m) calculate Y _m(k+1) and carry out U (k);

(n) make k=k+1 change step (j).

The present invention carries out organic combination with the advantage of Predictive function control and Hammerstein model, to give full play to advantage separately; What propose has well brought into play the advantage of Predictive function control based on the nonlinear multivariable systems Predictive function control method of Hammerstein model, and control law is found the solution simply, and on-line calculation is little, has guaranteed the real-time requirement of control system.Realized quick control, also provide approach for the application of Nonlinear Predictive Functional Control in real process to Complex Nonlinear System.

Description of drawings

The present invention is further described below in conjunction with drawings and Examples;

Fig. 1 is multivariate Hammerstein model structure figure;

Fig. 2 is the control system structural drawing;

Fig. 3 (a) is a nonlinear multivariable systems Predictive function control analogous diagram, output 1.

Fig. 3 (b) is a nonlinear multivariable systems Predictive function control analogous diagram, output 2.

Embodiment

Nonlinear multivariable systems Predictive function control method based on the Hammerstein model comprises the steps:

1) sets up the Hammerstein model according to process characteristic and inputoutput data;

2) find the solution the Predictive function control rate of multi-variable linear system according to the linear department pattern parameter of Hammerstein model, setting value and real process output;

3) obtain optimal control law U (k) according to Hammerstein model non-linear partial model parameter and multi-variable linear system Predictive function control rate solving equation group V (k)=F (U (k));

4) find the solution and implement optimal control law according to multivariable nonlinearity Predictive function control device.

Describedly set up Hammerstein model step according to process characteristic and inputoutput data:

Nonlinear multivariable systems Hammerstein model is:

Linear segment: $\left\{\begin{array}{c}{X}_m\left(k\right)=A_m{X}_m(k-1)+B_{m}V(k-1)\\ Y_m\left(k\right)=C_m{X}_m\left(k\right)\end{array}\right.$

Non-linear partial: V (k)=F _m(U (k))

X wherein _m(k) maintain the state variable of system for n, V (k) is the control variable of m dimensional linear subsystem, Y _m(k) for q maintains the system output variable, U (k) maintains system control variable, F for p _m() is R ⁿ→ R ^mNonlinear function, A _m∈ R ^{N * n}, B _m∈ R ^{N * m}, C _m∈ R ^{Q * n}Be the state-space model parameter.

According to control theory as can be known the state-transition matrix of linear segment model be $\mathrm{\Φ}\left(k\right)=A_m^k,$ Therefore the equation of motion of linear subsystem is:

$X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$

Application is carried out PREDICTIVE CONTROL based on the nonlinear multivariable systems Predictive function control method of Hammerstein model to the binary distillation column object of separation of methanol and water, and object is following 2 inputs, 2 output nonlinear system:

$\left[\begin{array}{c}{y}_1\left(z\right)\\ y_2\left(z\right)\end{array}\right]=\left[\begin{array}{cc}{G}_{11}\left(z\right)& G_{12}\left(z\right)\\ G_{21}\left(z\right)& G_{22}\left(z\right)\end{array}\right]\left[\begin{array}{c}{v}_1\left(z\right)\\ v_2\left(z\right)\end{array}\right]$

$\left\{\begin{array}{c}{v}_1=10u_1-2.36u_1{u}_2\\ v_2=10u_2-18.23u_1{u}_2\end{array}\right.$

Wherein:

$G_{11}\left(z\right)=\frac{{-0.0157z}^{-1}}{1-0.9552z^{-1}}$

$G_{12}\left(z\right)=\frac{{-0.0047z}^{-1}}{1-0.02754z^{-1}}$

$G_{21}\left(z\right)=\frac{{-0.0201z}^{-1}}{1-0.9060z^{-1}}$

$G_{22}\left(z\right)=\frac{{-0.0302z}^{-1}}{1-0.8991z^{-1}}$

The state space description that can obtain multivariate Hammerstein model is as follows:

$\left\{\begin{array}{c}{X}_m\left(k\right)=A_m{X}_m(k-1)+B_{m}V(k-1)\\ Y_m\left(k\right)=C_m{X}_m\left(k\right)\end{array}\right.$

Wherein: $A_m=\left[\begin{array}{cc}0.9952& 0.02754\\ 0.9060& 0.8991\end{array}\right],$ $B_m=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right],$ $C_m=\left[\begin{array}{cc}-0.0157& -0.0047\\ -0.0201& -0.0302\end{array}\right]$

Described output according to the linear department pattern parameter of Hammerstein model, setting value and real process found the solution the Predictive function control rate step of multi-variable linear system:

(a), suppose the important v of V (k) with the input of intermediate variable V (k) as linear subsystem _i(k), i=1 ..., the number of the basis function of m is N all, thereby obtains:

$V(k+h)=\left[\begin{array}{c}{v}_1(k+h)\\ \·\\ \·\\ \·\\ v_m(k+h)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\·\·\·{\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{m1}\left(k\right)\·\·\·{\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]\·\left[\begin{array}{c}{f}_1\left(h\right)\\ \·\\ \·\\ \·\\ f_N\left(h\right)\end{array}\right]=\mathrm{\μ}\left(k\right)f\left(h\right)$

Wherein: μ ₁₁(k) ..., μ _MN(k) be the linear combination coefficient of each basis function, f ₁(h) ..., f _N(h) be that each basis function is at h functional value constantly.

(b) will $X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$ Bring Y into _m(k)=C _mX _m(k) can get:

$Y_m(k+h)=\left[\begin{array}{c}{r}_1\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,1)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,p)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\end{array}\right].$

Wherein:

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);$ i＝1，…，m；l＝1，…，N；s＝1，…，q，

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},$ i＝0，…，h-1.

(c) Predictive function control is a kind of closed loop control algorithm, therefore needs to introduce the feedback compensation link, gets predicated error and is: E (k+h)=Y (k)-Y _m(k), wherein:

E (k+h)=[e ₁(k+h) ..., e _q(k+h)] ^TPredicated error for model;

Y (k)=[y ₁(k) ..., y _q(k)] ^TOutput for current time process object;

Y _m(k)=[y _M1(k) ..., y _Mq(k)] ^TOutput for the current time forecast model.

(d) reference locus adopts the single order exponential form, and then k+H reference locus constantly is:

$Y_r(k+h)=\left[\begin{array}{c}{y}_{r1}(k+h)\\ \·\\ \·\\ \·\\ y_{\mathrm{rq}}(k+h)\end{array}\right]=\left\{\begin{array}{c}{c}_1(k+h)-{{\mathrm{\α}}_1}^h\·[c_1\left(k\right)-y_1\left(k\right)]\\ \·\\ \·\\ \·\\ c_q(k+h)-{{\mathrm{\α}}_q}^h\·[c_q\left(k\right)-y_q\left(k\right)]\end{array}\right\}$

Wherein: h=1 ..., H; H is the total number of match point; y _R1(k+h) ..., y _Rq(k+h) be the k+h value of q reference locus constantly; c ₁(k+h) ..., c _q(k+h) be k+h q setting value constantly; The calculating of setting value adopts polynomial form as follows: $c_i(k+h)=\underset{l=0}{\overset{d_i}{\mathrm{\Σ}}}{c}_{\mathrm{il}}\left(k\right)h^l,$ d _iBe setting value polynomial expression exponent number, c _Il(k) be the setting value multinomial coefficient; y ₁(k) ..., y _q(k) be current time q process object real output value; ${\mathrm{\α}}_i=e^{-\frac{T_s}{T_{\mathrm{ri}}}},$ I=1 ..., q, T _sBe the sampling period, T _RiFor following the tracks of the i bar reference locus Expected Response time.

(e) adopt following optimization aim:

$J=\underset{j=1}{\overset{H}{\mathrm{\Σ}}}\underset{i=1}{\overset{q}{\mathrm{\Σ}}}{[{\tilde{y}}_i(k+h)-y_{\mathrm{ri}}(k+h)]}^2$

Wherein: ${\tilde{y}}_i(k+h)=y_{\mathrm{mi}}(k+h)+e_i(k+h);$

(f) by finding the solution above-mentioned optimization problem, promptly by finding the solution $\frac{\∂J}{{\∂\mathrm{\μ}}_{\mathrm{ij}}\left(k\right)}=0,$ Just can obtain matrix of coefficients:

$\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{q1}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]=-Z^{-1}\·M\·{\left[\begin{array}{c}v\left(\mathrm{1,1}\right)\\ \·\\ \·\\ \·\\ v(1,p)\\ \·\\ \·\\ \·\\ v(s,1)\\ \·\\ \·\\ \·\\ v(s,q)\end{array}\right]}_{\mathrm{Hq}\×1}$

Wherein:

$M={\left[\begin{array}{ccccccc}{T}_{11}(h_1,1)& \·\·\·& T_{11}(h_1,p)& \·\·\·& T_{11}(h_s,1)& \·\·\·& T_{11}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{1N}(h_1,1)& \·\·\·& T_{1N}(h_1,p)& \·\·\·& T_{1N}(h_s,1)& \·\·\·& T_{1N}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{m1}(h_1,1)& \·\·\·& T_{m1}\left(h_{1,}p\right)& \·\·\·& T_{m1}(h_s,1)& \·\·\·& T_{m1}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{\mathrm{mN}}(h_1,1)& \·\·\·& T_{\mathrm{mN}}(h_1,p)& \·\·\·& T_{\mathrm{mN}}(h_s,1)& \·\·\·& T_{\mathrm{mN}}(h_s,p)\end{array}\right]}_{\mathrm{mN}\×\mathrm{Sq}}$

$Z={\left[\begin{array}{ccccccc}{w}_{11}\left(\mathrm{1,1}\right)& \·\·\·& w_{1N}\left(\mathrm{1,1}\right)& \·\·\·& w_{m1}\left(\mathrm{1,1}\right)& \·\·\·& w_{\mathrm{mN}}\left(\mathrm{1,1}\right)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(1,N)& \·\·\·& w_{1N}(1,N)& \·\·\·& w_{m1}(1,N)& \·\·\·& w_{\mathrm{mN}}(1,N)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,1)& \·\·\·& w_{1N}(m,1)& \·\·\·& w_{m1}(q,1)& \·\·\·& w_{\mathrm{mN}}(q,1)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,N)& \·\·\·& w_{1N}(m,N)& \·\·\·& w_{m1}(q,N)& \·\·\·& w_{\mathrm{mN}}(q,N)\end{array}\right]}_{\mathrm{mN}\×\mathrm{mN}}$

Wherein:

$w_{\mathrm{ij}}(t,R)=\underset{l=1}{\overset{S}{\mathrm{\Σ}}}\underset{\mathrm{\ρ}=1}{\overset{p}{\mathrm{\Σ}}}{T}_{\mathrm{tR}}(h_l,\mathrm{\ρ})\·T_{\mathrm{ij}}(h_l,\mathrm{\ρ});$

i＝1，…，m；j＝1，…，N；t＝1，…，m；R＝1，…，N

$v(i,j)=-r_j\left(h_i\right)+y_j\left(k\right)-y_{\mathrm{mj}}\left(k\right)+{{\mathrm{\α}}_j}^{h_i}\·[c_j\left(k\right)-y_j\left(k\right)]-\underset{l=1}{\overset{d_j}{\mathrm{\Σ}}}{c}_{\mathrm{jl}}\left(k\right)h_i^l.$

i＝1，…，S；j＝1，…，q

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);$ i＝1，…，m；l＝1，…，N；s＝1，…，q，

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},$ i＝0，…，h-1.

Thereby obtain matrix of coefficients μ (k).

(g) therefore obtain multi-variable linear system Predictive function control rate: V (k+h)=μ (k) f (h).

Describedly find the solution and implement the optimal control law step according to multivariable nonlinearity Predictive function control device:

(h) algorithm initialization: the correlation parameter of the parameter of given model, basis function and multivariable nonlinearity Predictive function control device;

(i) read in k process output valve Y (k) constantly, and k, k+H _j, j=1 ..., q setting value constantly;

(j) calculate k+h _j, h _j=1 ..., H _jReference locus value Y constantly _r(k+h _j);

(k) optimization is found the solution and is obtained k intermediate controlled amount V constantly _m(k);

(l) find the solution the root of Nonlinear System of Equations, obtain current controlled quentity controlled variable U (k);

(m) calculate Y _m(k+1) and carry out U (k);

(n) make k=k+1 change step (j).

Simulation result is as follows: when t=200min, and y ₁Setting value by c ₁=95% is changed to c ₁=96%; During t=400min, y ₂Setting value by c ₂=0.5% changes to c ₂=0.4%; During t=600min, y ₁Setting value by c ₁=96% is changed to c ₁=95%; During t=800min, y ₂Setting value by c ₂=0.4% changes to c ₂=0.5%.Get and optimize time domain H ₁=10, H ₂=20; The response time T of reference locus _R1=T _R2=0.01min; Sampling time T _s=1min;

Carry out Computer Simulation under same condition, can see, nonlinear multivariable systems Predictive function control response speed is fast, and surplus difference is zero and setting value dynamic tracking effect is all controlled effective than traditional PID.

Claims (4)

1, a kind of nonlinear multivariable systems Predictive function control method based on the Hammerstein model is characterized in that comprising the steps:

1) sets up the Hammerstein model according to process characteristic and inputoutput data;

2) find the solution the Predictive function control rate of multivariate linear subsystem according to the linear department pattern parameter of Hammerstein model, setting value and real process output;

3) obtain optimal control law U (k) according to Hammerstein model non-linear partial model parameter and multi-variable linear system Predictive function control rate solving equation group V (k)=F (U (k));

4) find the solution and implement optimal control law according to multivariable nonlinearity Predictive function control device.

2, a kind of nonlinear multivariable systems Predictive function control method based on the Hammerstein model according to claim 1 is characterized in that describedly setting up Hammerstein model step according to process characteristic and inputoutput data:

Nonlinear multivariable systems Hammerstein model is:

Linear segment: $\left\{\begin{array}{c}{X}_m\left(k\right)=A_m{X}_m(k-1)+B_{m}V(k-1)\\ Y_m\left(k\right)=C_m{X}_m\left(k\right)\end{array}\right.$

Non-linear partial: V (k)=F _m(U (k))

X wherein _m(k) maintain the state variable of system for n, V (k) is the control variable of m dimensional linear subsystem, Y _m(k) for q maintains the system output variable, U (k) maintains system control variable, F for p _m() is R ⁿ→ R ^mNonlinear function, A _m∈ R ^{N * n}, B _m∈ R ^{N * m}, C _m∈ R ^{Q * n}Be the state-space model parameter.

According to control theory as can be known the state-transition matrix of linear segment model be $\mathrm{\Φ}\left(k\right)=A_m^k,$ Therefore the equation of motion of linear subsystem is:

$X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$

3, a kind of nonlinear multivariable systems Predictive function control method based on the Hammerstein model according to claim 1 is characterized in that describedly finding the solution the Predictive function control rate step of multi-variable linear system according to the linear department pattern parameter of Hammerstein model, setting value and real process output:

(a), suppose the important v of V (k) with the input of intermediate variable V (k) as linear subsystem _i(k), i=1 ..., the number of the basis function of m is N all, thereby obtains:

$V(k+h)=\left[\begin{array}{c}{v}_1(k+h)\\ \·\\ \·\\ \·\\ v_m(k+h)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\·\·\·{\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{m1}\left(k\right)\·\·\·{\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]\·\left[\begin{array}{c}{f}_1\left(h\right)\\ \·\\ \·\\ \·\\ f_N\left(h\right)\end{array}\right]=\mathrm{\μ}\left(k\right)f\left(h\right)$

Wherein: μ ₁₁(k) ..., μ _MN(k) be the linear combination coefficient of each basis function, f ₁(h) ..., f _N(h) be that each basis function is at h functional value constantly.

(b) will $X_m(k+h)=\mathrm{\Φ}\left(h\right)X_m\left(k\right)+\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}\mathrm{\Φ}(h-t-1)B_{m}V(k+t)$ Bring Y into _m(k)=C _mX _m(k) can get:

$Y_m(k+h)=\left[\begin{array}{c}{r}_1\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,1)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{il}}(h,p)\·{\mathrm{\μ}}_{\mathrm{il}}\left(k\right)\end{array}\right],$

Wherein:

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);i=1,\·\·\·,m;l=1,\·\·\·,N;s=1,\·\·\·,q,$

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},i=0,\·\·\·,h-1.$

(c) Predictive function control is a kind of closed loop control algorithm, therefore needs to introduce the feedback compensation link, gets predicated error and is: E (k+h)=Y (k)-Y _m(k), wherein:

E (k+h)=[e ₁(k+h) ..., e _q(k+h)] ^TPredicated error for model;

Y (k)=[y ₁(k) ..., y _q(k)] ^TOutput for current time process object;

Y _m(k)=[y _M1(k) ..., y _Mq(k)] ^TOutput for the current time forecast model.

(d) reference locus adopts the single order exponential form, and then k+H reference locus constantly is:

$Y_r(k+h)=\left[\begin{array}{c}{y}_{r1}(k+h)\\ \·\\ \·\\ \·\\ y_{\mathrm{rq}}(k+h)\end{array}\right]=\left\{\begin{array}{c}{c}_1(k+h)-{{\mathrm{\α}}_1}^h\·[c_1\left(k\right)-y_1\left(k\right)]\\ \·\\ \·\\ \·\\ c_q(k+h)-{{\mathrm{\α}}_q}^h\·[c_q\left(k\right)-y_q\left(k\right)]\end{array}\right\}$

Wherein: h=1 ..., H; H is the total number of match point; y _R1(k+h) ..., y _Rq(k+h) be the k+h value of q reference locus constantly; c ₁(k+h) ..., c _q(k+h) be k+h q setting value constantly; The calculating of setting value adopts polynomial form as follows: $c_i(k+h)=\underset{l=0}{\overset{d_i}{\mathrm{\Σ}}}{c}_{\mathrm{il}}\left(k\right)h^l,$ d _iBe setting value polynomial expression exponent number, c _Il(k) be the setting value multinomial coefficient; y ₁(k) ..., y _q(k) be current time q process object real output value; ${\mathrm{\α}}_i=e^{-\frac{T_s}{T_{\mathrm{ri}}}},$ I=1 ..., q, T _sBe the sampling period, T _RiFor following the tracks of the i bar reference locus Expected Response time.

(e) adopt following optimization aim:

$J=\underset{j=1}{\overset{H}{\mathrm{\Σ}}}\underset{i=1}{\overset{q}{\mathrm{\Σ}}}{[{\tilde{y}}_i(k+h)-y_{\mathrm{ri}}(k+h)]}^2$

Wherein: ${\tilde{y}}_i(k+h)=y_{\mathrm{mi}}(k+h)+e_i(k+h);$

(f) by finding the solution above-mentioned optimization problem, promptly by finding the solution $\frac{\∂J}{{\∂\mathrm{\μ}}_{\mathrm{ij}}\left(k\right)}=0,$ Just can obtain matrix of coefficients:

$\left[\begin{array}{c}{\mathrm{\μ}}_{11}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{1N}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{q1}\left(k\right)\\ \·\\ \·\\ \·\\ {\mathrm{\μ}}_{\mathrm{mN}}\left(k\right)\end{array}\right]=-Z^{-1}\·M\·{\left[\begin{array}{c}v\left(\mathrm{1,1}\right)\\ \·\\ \·\\ \·\\ v(1,p)\\ \·\\ \·\\ \·\\ v(s,1)\\ \·\\ \·\\ \·\\ v(s,q)\end{array}\right]}_{\mathrm{Hq}\×1}$

Wherein:

$M={\left[\begin{array}{ccccccc}{T}_{11}(h_1,1)& \·\·\·& T_{11}(h_1,p)& \·\·\·& T_{11}(h_s,1)& \·\·\·& T_{11}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{1N}(h_1,1)& \·\·\·& T_{1N}(h_1,p)& \·\·\·& T_{1N}(h_s,1)& \·\·\·& T_{1N}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{m1}(h_1,1)& \·\·\·& T_{m1}\left(h_{1,}p\right)& \·\·\·& T_{m1}(h_s,1)& \·\·\·& T_{m1}(h_s,p)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ T_{\mathrm{mN}}(h_1,1)& \·\·\·& T_{\mathrm{mN}}(h_1,p)& \·\·\·& T_{\mathrm{mN}}(h_s,1)& \·\·\·& T_{\mathrm{mN}}(h_s,p)\end{array}\right]}_{\mathrm{mN}\×\mathrm{Sq}}$

$Z={\left[\begin{array}{ccccccc}{w}_{11}\left(\mathrm{1,1}\right)& \·\·\·& w_{1N}\left(\mathrm{1,1}\right)& \·\·\·& w_{m1}\left(\mathrm{1,1}\right)& \·\·\·& w_{\mathrm{mN}}\left(\mathrm{1,1}\right)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(1,N)& \·\·\·& w_{1N}(1,N)& \·\·\·& w_{m1}(1,N)& \·\·\·& w_{\mathrm{mN}}(1,N)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,1)& \·\·\·& w_{1N}(m,1)& \·\·\·& w_{m1}(q,1)& \·\·\·& w_{\mathrm{mN}}(q,1)\\ \·& & \·& & \·& & \·\\ \·& \·\·\·& \·& \·\·\·& \·& \·\·\·& \·\\ \·& & \·& & \·& & \·\\ w_{11}(m,N)& \·\·\·& w_{1N}(m,N)& \·\·\·& w_{m1}(q,N)& \·\·\·& w_{\mathrm{mN}}(q,N)\end{array}\right]}_{\mathrm{mN}\×\mathrm{mN}}$

Wherein:

$w_{\mathrm{ij}}(t,R)=\underset{l=1}{\overset{S}{\mathrm{\Σ}}}\underset{\mathrm{\ρ}=1}{\overset{p}{\mathrm{\Σ}}}{T}_{\mathrm{tR}}(h_l,\mathrm{\ρ})\·T_{\mathrm{ij}}(h_l,\mathrm{\ρ});$

i＝1，…，m；j＝1，…，N；t＝1，…，m；R＝1，…，N

$v(i,j)=-r_j\left(h_i\right)+y_j\left(k\right)-y_{\mathrm{mj}}\left(k\right)+{{\mathrm{\α}}_j}^{h_i}\·[c_j\left(k\right)-y_j\left(k\right)]-\underset{l=1}{\overset{d_j}{\mathrm{\Σ}}}{c}_{\mathrm{jl}}\left(k\right)h_i^l.$

i＝1，…，S；j＝1，…，q

$\left[\begin{array}{c}{r}_1\left(h\right)\\ \·\\ \·\\ \·\\ r_q\left(h\right)\end{array}\right]=C_m\mathrm{\Φ}\left(h\right)X_m\left(k\right)=\left[\begin{array}{ccc}{r}_{11}\left(h\right)& \·\·\·& r_{1n}\left(h\right)\\ \·& & \·\\ \·& \·\·\·& \·\\ \·& & \·\\ r_{q1}\left(h\right)& \·\·\·& r_{\mathrm{qn}}\left(h\right)\end{array}\right]\·\left[\begin{array}{c}{x}_{m1}\left(k\right)\\ \·\\ \·\\ \·\\ x_{\mathrm{mn}}\left(k\right)\end{array}\right],$

$T_{\mathrm{il}}(h,s)=\underset{t=0}{\overset{h-1}{\mathrm{\Σ}}}{g}_{\mathrm{si}}(h-1-t)\·f_l\left(t\right);$ i＝1，…，m；l＝1，…，N；s＝1，…，q，

$C_m\mathrm{\Φ}\left(i\right)B_m={\left[\begin{array}{ccc}{g}_{11}\left(i\right)& \·\·\·& g_{1m}\left(i\right)\\ \·& \·& \·\\ \·& \·& \·\\ \·& \·& \·\\ g_{q1}\left(i\right)& \·\·\·& g_{\mathrm{qm}}\left(i\right)\end{array}\right]}_{q\×m},$ i＝0，…，h-1.

Thereby obtain matrix of coefficients μ (k).

(g) therefore obtain multi-variable linear system Predictive function control rate: V (k+h)=μ (k) f (h).

4, a kind of multivariable nonlinearity Predictive function control method based on the Hammerstein model according to claim 1 is characterized in that describedly finding the solution and implement the optimal control law step according to multivariable nonlinearity Predictive function control device:

(h) algorithm initialization: the correlation parameter of the parameter of given model, basis function and multivariable nonlinearity Predictive function control device;

(i) read in k process output valve Y (k) constantly, and k, k+H _j, j=1 ..., q setting value constantly;

(j) calculate k+h _j, h _j=1 ..., H _jReference locus value Y constantly _r(k+h _j);

(k) optimization is found the solution and is obtained k intermediate controlled amount V constantly _m(k);

(l) find the solution the root of Nonlinear System of Equations, obtain current controlled quentity controlled variable U (k);

(m) calculate Y _m(k+1) and carry out U (k);

(n) make k=k+1 change step (j).

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