CN103605284A - Dynamic matrix control optimization-based waste plastic cracking furnace pressure controlling method - Google Patents

Abstract

Disclosed in the invention is a dynamic matrix control optimization-based waste plastic cracking furnace pressure controlling method. The method comprises the following steps that: on the basis of step response data of a waste plastic cracking furnace pressure object, a mode of the furnace pressure object is established and a basic object characteristic is dug out; on the basis of the characteristic of dynamic matrix control, a parameter of a corresponding proportional-integral (PI) controller set; and PI controlling is carried out on a waste plastic cracking furnace temperature object. According to the dynamic matrix control optimization-based waste plastic cracking furnace pressure controlling method, good controlling performances of the PI controlling and the dynamic matrix control are combined, thereby effectively overcoming defects of the traditional controlling method. And meanwhile, the development and application of the advanced control algorithm can be promoted.

Description

The cracking waste plastics stove hearth pressure control method that dynamic matrix control is optimized

Technical field

The invention belongs to technical field of automation, relate to a kind of cracking waste plastics stove furnace pressure proportional integral (PI) control method of optimizing based on dynamic matrix control (DMC).

Background technology

Along with the maximization of modern industry process and complicated, some traditional control methods are more and more difficult to meet industrial actual demand.Although some Advanced process control technology can be enhanced productivity in theory greatly, due to aspects such as hardware, cost, enforcement difficulty, be difficult to be applied, so occupy at present the PID that remains of main flow, control.The common adoption rate integration of control (PI) of cracking waste plastics stove furnace pressure is controlled at present.Dynamic matrix control is a kind of as advanced control method, to model, require low, calculated amount is few, the method of processing time delay is simple, if can be by Dynamic array control algorithm and the combination of PI technology, the performance of dynamic matrix control is assigned to PI and controls, that will be conducive to the raising of production efficiency more, also can promote the advanced development of controlling simultaneously.

Summary of the invention

The object of the invention is the application weak point for existing advanced control method, provide a kind of cracking waste plastics stove furnace pressure PI control method of optimizing based on dynamic matrix control, to obtain better working control performance.The method, by controlling in conjunction with dynamic matrix control and PI, has obtained a kind of PI control method with dynamic matrix control performance.The method has not only been inherited the premium properties of dynamic matrix control, the simple needs that also can meet actual industrial process of Simultaneous Forms.

The inventive method first step response data based on cracking waste plastics stove furnace pressure object is set up the model of furnace pressure object, excavates basic plant characteristic; Then according to the characteristic of dynamic matrix control, go the parameter of adjusting corresponding PI controller; Finally cracking waste plastics stove fire box temperature object being implemented to PI controls.

Technical scheme of the present invention is by data acquisition, sets up dynamic matrix, sets up forecast model, predicts the means such as mechanism, optimization, establish a kind of PI control method of optimizing based on dynamic matrix control, utilized the method can effectively improve precision and the stability of control.

The step of the inventive method comprises:

Step (1). by the real-time step response data of process object, set up the model of controlled device, concrete grammar is:

A. give step input signal of controlled device, record the step response curve of controlled device.

B. step response curve a step being obtained carries out filtering processing, then fits to a smooth curve, records step response data corresponding to each sampling instant on smooth curve, and first sampling instant is T _s, adjacent two sampling instant interludes are T _s, sampling instant is sequentially T _s, 2T _s, 3T _sthe step response of controlled device will be at some moment t _nafter=NT, tend to be steady, work as a _i(i > N) and a _nerror and measuring error while having the identical order of magnitude, can think a _nbe approximately equal to the steady-state value of step response.Set up the model vector a of object:

a＝[a ₁,a ₂,…a _N] ^Τ

Wherein Τ is transpose of a matrix symbol, and N is modeling time domain.

Step (2). the PI controller of design controlled device, concrete grammar is:

A. utilize the model vector a obtaining to set up the dynamic matrix of controlled device above, its form is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

Wherein, A is P * M rank dynamic matrix of controlled device, a _ithe data of step response, the optimization time domain that P is Dynamic array control algorithm, the control time domain that M is Dynamic array control algorithm, M < P < N.

B. set up the current k of controlled device model prediction initial response value y constantly _m(k)

First obtain the model predication value y after k-1 moment access control increment Delta u (k-1) _p(k-1):

y _P(k-1)＝y _M(k-1)+A ₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0(k+1|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right]$

Y ₁(k|k-1), y ₁(k+1|k-1) ..., y ₁(k+N-1|k-1) represent respectively controlled device at k-1 constantly to k, k+1 ..., the model predication value after k+N-1 moment access control increment Delta u (k-1), y ₀(k|k-1), y ₀(k|k-1) ... y ₀(k+N-1|k-1) represent that k-1 is constantly to k, k+1 ..., k+N-1 initial predicted value constantly, A ₀for the matrix that step response data is set up, Δ u (k-1) is k-1 input control increment constantly.

Then obtain the k model predictive error value e (k) of controlled device constantly:

e(k)＝y(k)-y ₁(k|k-1)

Wherein, y (k) represents the real output value of the controlled device that k records constantly.

Further obtain the modified value y of k model output constantly _cor(k):

y _cor(k)＝y _M(k-1)+h*e(k)

Wherein,

$y_{\mathrm{cor}}\left(k\right)=\left[\begin{array}{c}{y}_{\mathrm{cor}}\left(k\right|k)\\ y_{\mathrm{cor}}(k+1|k)\\ .\\ .\\ .\\ y_{\mathrm{cor}}(k+N-1|k)\end{array}\right],h=\left[\begin{array}{c}1\\ \mathrm{\&alpha;}\\ .\\ .\\ .\\ \mathrm{\&alpha;}\end{array}\right]$

Y _cor(k|k), y _cor(k+1|k) ... y _cor(k+N-1|k) represent that respectively controlled device is in the modified value of k moment model, the weight matrix that h is error compensation, α is error correction coefficient.

The last initial response value y that obtains k model prediction constantly _m(k):

y _M(k)＝Sy _cor(k)

Wherein, S is the state-transition matrix on N * N rank,

C. calculate controlled device at M continuous controlling increment Δ u (k) ..., the prediction output valve y under Δ u (k+M-1) _pM, concrete grammar is:

y _PM(k)＝y _p0(k)+AΔu _M(k)

$y_{\mathrm{PM}}\left(k\right)=\left[\begin{array}{c}{y}_M(k+1|k)\\ y_M(k+2|k)\\ .\\ .\\ .\\ y_M(k+P|k)\end{array}\right],y_{P0}\left(k\right)=\left[\begin{array}{c}{y}_0(k+1|k)\\ y_0(k+2|k)\\ .\\ .\\ .\\ y_0(k+P|k)\end{array}\right],\mathrm{\&Delta;}{u}_M\left(k\right)=\left[\begin{array}{c}\mathrm{\&Delta;u}\left(k\right)\\ \mathrm{\&Delta;u}(k+1)\\ .\\ .\\ .\\ \mathrm{\&Delta;u}(k+M-1)\end{array}\right]$

Wherein, y _p0(k) be y _m(k) front P item, y _m(k+1|k), y _m(k+2|k) ..., y _m(k+P|k) be k constantly to k+1, k+2 ..., k+P model prediction output valve constantly.

D. make the control time domain M=1 of controlled device, choose the objective function J (k) of controlled device, form is as follows:

minJ(k)＝Q(ref(k)-y _PM(k)) ²+rΔu ²(k)=Q(ref(k)-y _P0(k)-AΔu(k)) ²+rΔu ²(k)

ref(k)＝[ref ₁(k),ref ₂(k),…,ref _P(k)] ^Τ

ref _i(k)＝β ⁱy(k)+(1-β ⁱ)c(k),Q＝diag(q ₁,q ₂,…,q _P)

Wherein, Q is error weighting matrix, q ₁, q ₂..., q _pparameter value for weighting matrix; β is softening coefficient, and c (k) is setting value; R=diag (r ₁, r ₂... r _m) for controlling weighting matrix, r ₁, r ₂... r _mfor controlling the parameter of weighting matrix, the reference locus that ref (k) is system, ref _i(k) be the value of i reference point in reference locus.

E. controlled quentity controlled variable u (k) is converted:

u(k)＝u(k-1)+K _p(k)(e ₁(k)-e ₁(k-1))+K _i(k)e ₁(k)

e(k)＝c(k)-y(k)

U (k) is updated to the parameter that the objective function in steps d solves in PI controller to be obtained:

u(k)＝u(k-1)+w(k) ^ΤE(k)

w(k)＝[w ₁(k),w ₂(k)] ^Τ

w ₁(k)＝K _p(k)+K _i(k)，w ₂(k)＝-K _p(k)

E(k)＝[e ₁(k),e ₁(k-1)] ^Τ

Wherein, Kp (k), K _i(k) be respectively k ratio, the differential parameter of PI controller constantly, e ₁(k) be the error between k moment reference locus value and real output value, Τ is transpose of a matrix symbol.

Comprehensive above-mentioned formula, can obtain:

$w\left(k\right)=\frac{{(\mathrm{ref}\left(k\right)-y_{P0}\left(k\right))}^T\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

Further can obtain:

K _p(k)＝-w ₂(k)

K _i(k)＝w ₁(k)-K _P(k)

F. obtain the parameter K of PI controller _p(k), K _i(k) after, form controlled quentity controlled variable u (k) and act on controlled device, u (k)=u (k-1)+K _p(k) (e ₁(k)-e ₁(k-1))+K _i(k) e ₁(k).

H. at next constantly, according to b, to the step in f, continue to solve the parameter k that PI controller is new _p(k+1), k _i(k+1) value, successively circulation.

The present invention proposes a kind of cracking waste plastics stove fire box temperature PI control method of optimizing based on dynamic matrix control, combine the good control performance of PI control and dynamic matrix control, effectively improve the deficiency of traditional control method, also promoted development and the application of advanced control algorithm simultaneously.

Embodiment

The cracking waste plastics stove furnace pressure process control of take is example:

The process that cracking waste plastics stove furnace pressure object lags behind for band, regulating measure adopts the aperture that regulates stack damper.

Step (1). by the real-time step response data of cracking waste plastics stove furnace pressure object, set up the model of controlled device, concrete grammar is:

A. give step input signal of cracking waste plastics stove burner hearth, record its step response curve.

B. corresponding step response curve is carried out to filtering processing, then fit to a smooth curve, record step response data corresponding to each sampling instant on smooth curve, first sampling instant is T _s, adjacent two sampling instant interludes are T _s, sampling instant is sequentially T _s, 2T _s, 3T _sthe response a of baffle opening _iwill be at some moment t _nafter=NT, tend to be steady, work as a _i(i > N) and a _nerror and measuring error while having the identical order of magnitude, can think a _nbe approximately equal to step response steady-state value.Set up the model vector a of object:

a＝[a ₁,a ₂,…a _N] ^Τ

Wherein Τ is transpose of a matrix symbol, and N is modeling time domain.

Step (2). the PI controller of design cracking waste plastics stove furnace pressure, concrete grammar is:

A. utilize the model vector a obtaining to set up the dynamic matrix of cracking waste plastics stove furnace pressure above, its form is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

Wherein, A is P * M rank dynamic matrix of cracking waste plastics stove furnace pressure, a _ithe data of the baffle opening of cracking waste plastics stove furnace pressure, the optimization time domain that P is Dynamic array control algorithm, the control time domain that M is Dynamic array control algorithm, M < P < N.

B. set up the current k of cracking waste plastics stove furnace pressure initial predicted value y constantly _m(k)

First obtain k-1 moment baffle opening and increase the model predication value y after Δ u (k-1) _p(k-1):

y _P(k-1)＝y _M(k-1)+A ₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0(k+1|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right]$

Y ₁(k|k-1), y ₁(k+1|k-1) ..., y ₁(k+N-1|k-1) represent respectively cracking waste plastics stove furnace pressure at k-1 constantly to k, k+1 ..., k+N-1 adds the model predication value after Δ u (k-1), y constantly ₀(k|k-1), y ₀(k|k-1) ... y ₀(k+N-1|k-1) represent that k-1 is constantly to k, k+1 ..., the initial predicted value of k+N-1 cracking waste plastics stove furnace pressure constantly, A ₀for the matrix of being set up by cracking waste plastics stove furnace pressure step response data, Δ u (k-1) is the baffle opening controlling increment of k-1 cracking waste plastics furnace pressure power constantly.

Then obtain the k model predictive error value e (k) of cracking waste plastics furnace pressure power constantly:

e(k)＝y(k)-y ₁(k|k-1)

Wherein, y (k) represents the real output value of the cracking waste plastics furnace pressure power that k records constantly.

Further obtain the k modified value y of the model output of cracking waste plastics furnace pressure power constantly _cor(k):

y _cor(k)＝y _M(k-1)+h*e(k)

Wherein,

$y_{\mathrm{cor}}\left(k\right)=\left[\begin{array}{c}{y}_{\mathrm{cor}}\left(k\right|k)\\ y_{\mathrm{cor}}(k+1|k)\\ .\\ .\\ .\\ y_{\mathrm{cor}}(k+N-1|k)\end{array}\right],h=\left[\begin{array}{c}1\\ \mathrm{\&alpha;}\\ .\\ .\\ .\\ \mathrm{\&alpha;}\end{array}\right]$

Y _cor(k|k), y _cor(k+1|k) ... y _cor(k+N-1|k) represent that respectively cracking waste plastics stove furnace pressure is in the modified value of k moment model, the weight matrix that h is error compensation, α is error correction coefficient.

Last obtains cracking waste plastics stove furnace pressure at the initial predicted value y of k moment model _m(k):

y _M(k)＝Sy _cor(k)

Wherein, S is the state-transition matrix on N * N rank,

C. calculate cracking waste plastics stove furnace pressure at M continuous controlling increment Δ u (k) ..., the prediction output valve y under Δ u (k+M-1) _pM, concrete grammar is:

y _PM(k)＝y _P0(k)+AΔu _M(k)

Wherein,

$y_{\mathrm{PM}}\left(k\right)=\left[\begin{array}{c}{y}_M(k+1|k)\\ y_M(k+2|k)\\ .\\ .\\ .\\ y_M(k+P|k)\end{array}\right],y_{P0}\left(k\right)=\left[\begin{array}{c}{y}_0(k+1|k)\\ y_0(k+2|k)\\ .\\ .\\ .\\ y_0(k+P|k)\end{array}\right],\mathrm{\&Delta;}{u}_M\left(k\right)=\left[\begin{array}{c}\mathrm{\&Delta;u}\left(k\right)\\ \mathrm{\&Delta;u}(k+1)\\ .\\ .\\ .\\ \mathrm{\&Delta;u}(k+M-1)\end{array}\right]$

Y _p0(k) be y _m(k) front P item, y _m(k+1|k), y _m(k+2|k) ..., y _m(k+P|k) be cracking waste plastics stove furnace pressure at k constantly to k+1, k+2 ..., k+P model prediction output valve constantly.

D. time domain M=1 is controlled in order, and chooses the objective function J (k) of cracking waste plastics stove furnace pressure, and form is as follows:

minJ(k)＝Q(ref(k)-y _PM(k)) ²+rΔu ²(k)=Q(ref(k)-y _P0(k)-AΔu(k)) ²+rΔu ²(k)

ref(k)＝[ref ₁(k),ref ₂(k),…,ref _P(k)] ^Τ

ref _i(k)＝β ⁱy(k)+(1-β ⁱ)c(k),Q＝diag(q ₁,q ₂,…,q _P)

Wherein, Q is error weighting matrix, q ₁, q ₂..., q _pparameter value for error weighting matrix; β is softening coefficient, and c (k) is the setting value of cracking waste plastics stove furnace pressure; R=diag (r ₁, r ₂... r _m) for controlling weighting matrix, r ₁, r ₂... r _mfor controlling the parameter of weighting matrix, ref (k) is the reference locus of cracking waste plastics stove furnace pressure, ref _i(k) be the value of i reference point in reference locus.

E. the stack damper aperture controlled quentity controlled variable u (k) of cracking waste plastics stove burner hearth is converted:

u(k)＝u(k-1)+K _p(k)(e ₁(k)-e ₁(k-1))+K _i(k)e ₁(k)

e(k)＝c(k)-y(k)

And u (k) is updated to the objective function in steps d, and further solving the parameter in the PI controller of cracking waste plastics stove furnace pressure, can try to achieve:

u(k)＝u(k-1)+w(k) ^ΤE(k)

w(k)＝[w ₁(k),w ₂(k)] ^Τ

w1(k)＝K _p(k)+K _i(k)，w ₂(k)＝-K _p(k)

E(k)＝[e ₁(k),e ₁(k-1)] ^Τ

Wherein, K _p(k), K _i(k) be respectively ratio, the differential parameter of PI controller, e ₁(k) be the error between k moment reference locus value and real output value, Τ is transpose of a matrix symbol.

Comprehensive above-mentioned formula, can obtain:

$w\left(k\right)=\frac{{(\mathrm{ref}\left(k\right)-y_{P0}\left(k\right))}^T\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

Further can obtain:

K _p(k)＝-w ₂(k)

K _i(k)＝w ₁(k)-K _P(k)

F. obtain the parameter K of PI controller _p(k), K _i(k), after, form controlled quentity controlled variable u (k)=u (the k-1)+K of stack damper aperture _p(k) (e ₁(k)-e ₁(k-1))+K _i(k) e ₁(k), act on cracking waste plastics stove burner hearth.

G. at next constantly, according to b, to the step in f, continue to solve the parameter K that PI controller is new _p(k+1), K _i(k+1) and successively circulate.

Claims (1)

1. the cracking waste plastics stove hearth pressure control method that dynamic matrix control is optimized, is characterized in that the concrete steps of the method are:

Step (1). by the real-time step response data of process object, set up the model of controlled device, concrete grammar is:

1-a., to step input signal of controlled device, records the step response curve of controlled device;

The step response curve that 1-b. obtains step 1-a carries out filtering processing, then fits to a smooth curve, records step response data corresponding to each sampling instant on smooth curve, and first sampling instant is T _s, adjacent two sampling instant interludes are T _s, sampling instant is sequentially T _s, 2T _s, 3T _sthe step response of controlled device will be at some moment t _nafter=NT, tend to be steady, work as a _i, i > N, with a _nerror and measuring error while having the identical order of magnitude, can think a _nbe approximately equal to the steady-state value of step response; Set up the model vector a of object:

a＝[a ₁,a ₂,…a _N] ^Τ

Wherein Τ is transpose of a matrix symbol, and N is modeling time domain;

Step (2). the PI controller of design controlled device, concrete grammar is:

2-a. utilizes the model vector a obtaining to set up the dynamic matrix of controlled device above, and its form is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

Wherein, A is P * M rank dynamic matrix of controlled device, a _ithe data of step response, the optimization time domain that P is Dynamic array control algorithm, the control time domain that M is Dynamic array control algorithm, M < P < N;

2-b. sets up the current k of controlled device model prediction initial response value y constantly _m(k)

First obtain the model predication value y after k-1 moment access control increment Delta u (k-1) _p(k-1):

y _P(k-1)＝y _M(k-1)+A ₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0(k+1|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right]$

Y ₁(k|k-1), y ₁(k+1|k-1) ..., y ₁(k+N-1|k-1) represent respectively controlled device at k-1 constantly to k, k+1 ..., the model predication value after k+N-1 moment access control increment Delta u (k-1), y ₀(k|k-1), y ₀(k|k-1) ... y ₀(k+N-1|k-1) represent that k-1 is constantly to k, k+1 ..., k+N-1 initial predicted value constantly, A ₀for the matrix that step response data is set up, Δ u (k-1) is k-1 input control increment constantly;

Then obtain the k model predictive error value e (k) of controlled device constantly:

e(k)＝y(k)-y ₁(k|k-1)

Wherein, y (k) represents the real output value of the controlled device that k records constantly;

Further obtain the modified value y of k model output constantly _cor(k):

y _cor(k)＝y _M(k-1)+h*e(k)

Wherein,

$y_{\mathrm{cor}}\left(k\right)=\left[\begin{array}{c}{y}_{\mathrm{cor}}\left(k\right|k)\\ y_{\mathrm{cor}}(k+1|k)\\ .\\ .\\ .\\ y_{\mathrm{cor}}(k+N-1|k)\end{array}\right],h=\left[\begin{array}{c}1\\ \mathrm{\&alpha;}\\ .\\ .\\ .\\ \mathrm{\&alpha;}\end{array}\right]$

Y _cor(k|k), y _cor(k+1|k) ... y _cor(k+N-1|k) represent that respectively controlled device is in the modified value of k moment model, the weight matrix that h is error compensation, α is error correction coefficient;

The last initial response value y that obtains k model prediction constantly _m(k):

y _M(k)＝Sy _cor(k)

Wherein, S is the state-transition matrix on N * N rank,

2-c. calculates controlled device at M continuous controlling increment Δ u (k) ..., the prediction output valve y under Δ u (k+M-1) _pM, concrete grammar is:

y _PM(k)＝y _p0(k)+AΔu _M(k)

$y_{\mathrm{PM}}\left(k\right)=\left[\begin{array}{c}{y}_M(k+1|k)\\ y_M(k+2|k)\\ .\\ .\\ .\\ y_M(k+P|k)\end{array}\right],y_{P0}\left(k\right)=\left[\begin{array}{c}{y}_0(k+1|k)\\ y_0(k+2|k)\\ .\\ .\\ .\\ y_0(k+P|k)\end{array}\right],\mathrm{\&Delta;}{u}_M\left(k\right)=\left[\begin{array}{c}\mathrm{\&Delta;u}\left(k\right)\\ \mathrm{\&Delta;u}(k+1)\\ .\\ .\\ .\\ \mathrm{\&Delta;u}(k+M-1)\end{array}\right]$

Wherein, y _p0(k) be y _m(k) front P item, y _m(k+1|k), y _m(k+2|k) ..., y _m(k+P|k) be k constantly to k+1, k+2 ..., k+P model prediction output valve constantly;

2-d. makes the control time domain M=1 of controlled device, chooses the objective function J (k) of controlled device, and form is as follows:

minJ(k)＝Q(ref(k)-y _PM(k)) ²+rΔu ²(k)=Q(ref(k)-y _P0(k)-AΔu(k)) ²+rΔu ²(k)

ref(k)＝[ref ₁(k),ref ₂(k),…,ref _P(k)] ^Τ

ref _i(k)＝β ⁱy(k)+(1-β ⁱ)c(k),Q＝diag(q ₁,q ₂,…,q _P)

Wherein, Q is error weighting matrix, q ₁, q ₂..., q _pparameter value for weighting matrix; β is softening coefficient, and c (k) is setting value; R=diag (r ₁, r ₂... r _m) for controlling weighting matrix, r ₁, r ₂... r _mfor controlling the parameter of weighting matrix, the reference locus that ref (k) is system, ref _i(k) be the value of i reference point in reference locus;

2-e. converts controlled quentity controlled variable u (k):

u(k)＝u(k-1)+K _p(k)(e ₁(k)-e ₁(k-1))+K _i(k)e ₁(k)

e(k)＝c(k)-y(k)

U (k) is updated to the parameter that the objective function in steps d solves in PI controller to be obtained:

u(k)＝u(k-1)+w(k) ^ΤE(k)

w(k)＝[w ₁(k),w ₂(k)] ^Τ

w ₁(k)＝K _p(k)+K _i(k)，w ₂(k)＝-K _p(k)

E(k)＝[e ₁(k),e ₁(k-1)] ^Τ

Wherein, Kp (k), K _i(k) be respectively k ratio, the differential parameter of PI controller constantly, e ₁(k) be the error between k moment reference locus value and real output value, Τ is transpose of a matrix symbol;

Comprehensive above-mentioned formula, can obtain:

$w\left(k\right)=\frac{{(\mathrm{ref}\left(k\right)-y_{P0}\left(k\right))}^T\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

Further can obtain:

K _p(k)＝-w ₂(k)

K _i(k)＝w ₁(k)-K _P(k)

2-f. obtains the parameter K of PI controller _p(k), K _i(k) after, form controlled quentity controlled variable u (k) and act on controlled device, u (k)=u (k-1)+K _p(k) (e ₁(k)-e ₁(k-1))+K _i(k) e ₁(k);

2-h. at next constantly, continues to solve to the step in 2-f the parameter k that PI controller is new according to 2-b _p(k+1), k _i(k+1) value, successively circulation.