CN104102130A - Batch process infinite time domain linear secondary fault-tolerant control method of state space model - Google Patents

Abstract

The invention provides a batch process infinite time domain linear secondary fault-tolerant control method of a state space model. According to the invention, by combining a process state variable and an output error, the state space model of a batch process is established, and then an improved infinite time domain linear secondary fault-tolerant controller is designed. According to the invention, actuator faults and unknown disturbances in the batch process can be well processed, which ensures a simple form and meets the need of an actual industrial process.

Description

Batch process Infinite horizon linear quadratic fault tolerant control method of state-space model

Technical field

The invention belongs to technical field of automation, relate to a kind of batch process Infinite horizon linear quadratic fault tolerant control method of state-space model.

Background technology

In actual industrial is controlled, along with more and more higher to the requirement of product specification and handling safety, operating conditions also just becomes and becomes increasingly complex.The operating conditions that these are complicated, has increased the probability that the system failure occurs accordingly.In these system failures, actuator failures is common a kind of fault, can affect the operation of technological process and reduce control performance.Although occurred the control methods such as some fault diagnosises and control method, iterative learning control (ILC), Model Predictive Control (MPC) in batch processed process, the key issue of improving the control performance of unmatched models and actuator failures still requires study.Therefore, propose a kind of new fault tolerant control method to solve the problem of actuator failures in batch process control, and guarantee that system control performance is necessary.

Summary of the invention

The object of the invention is the problem for the actuator failures that may occur in batch process, provide a kind of batch process Infinite horizon linear quadratic fault tolerant control method of state-space model, to maintain the closed loop stability of controller and to have good control performance.The method, by cohesive process state variable and output error, has been set up a batch status of processes spatial model, and then has been designed an improved Infinite horizon linear quadratic fault-tolerant controller.The method can well process actuator failures and unknown disturbance problem in batch process, and the form that guaranteed is simple and meet the needs of actual industrial process.

Technical scheme of the present invention is to set up, predict the means such as mechanism, optimization by data acquisition, model, batch process Infinite horizon linear quadratic fault tolerant control method of having established a kind of state-space model, utilizes the method can effectively improve the control performance of system in unknown disturbance and actuator failures situation.

The step of the inventive method comprises:

Step (1). set up the state-space model of controlled device in batch process, concrete grammar is:

A. first gather the inputoutput data of batch process, utilize these data to set up this batch of status of processes model, form is as follows:

$\left\{\begin{array}{c}x(k+1)=\stackrel{\‾}{A}x\left(k\right)+\stackrel{\‾}{B}u(k-d)\\ y\left(k\right)=\stackrel{\‾}{C}x\left(k\right)+w\left(k\right)\end{array}\right.$

Wherein, x (k) ∈ R ⁿ, y (k) ∈ R, u (k) ∈ R is respectively k batch status of processes, output and input constantly, and d is the time lag of batch process, and w (k) ∈ R is measurement noise, be respectively the system matrix of suitable dimension.

B. the model in step a is further processed into following form:

$\left\{\begin{array}{c}\mathrm{\Δx}(k+1)=\stackrel{\‾}{A}\mathrm{\Δx}\left(k\right)+\stackrel{\‾}{B}\mathrm{\Δu}(k-d)\\ \mathrm{\Δy}\left(k\right)=\stackrel{\‾}{C}\mathrm{\Δx}\left(k\right)\end{array}\right.$

Choose state variable as follows:

Δx _m(k)＝[Δx(k)Δu(k-1)Δu(k-2)…Δu(k-d)] ^Τ

Thereby obtain a batch status of processes spatial model, form is as follows:

Δx _m(k+1)＝A _mΔx _m(k)+B _mΔu(k)

Δy(k)＝C _mΔx _m(k)

Wherein,

B _m＝[010…0] ^T

$C_m=\left[\begin{array}{ccccc}\stackrel{\‾}{C}& 0& 0& \·\·\·& 0\end{array}\right]$

Δ is difference operator, and Τ is transpose of a matrix symbol, with 0be the null vector of suitable dimension.

C. convert the state-space model obtaining in step b to comprise state variable and output tracking error Extended state space model, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Wherein,

$z(k+1)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m(k+1)\\ e(k+1)\end{array}\right],z\left(k\right)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m\left(k\right)\\ e\left(k\right)\end{array}\right]$

$A=\left[\begin{array}{cc}{A}_m& 0\\ C_m{A}_m& 1\end{array}\right],B=\left[\begin{array}{c}{B}_m\\ C_m{B}_m\end{array}\right]$

e(k)＝y(k)-y _r(k)

Y (k), y _r(k) be respectively k real output value and tracking setting value constantly, e (k) is k output error constantly.

Step (2). the Infinite horizon linear quadratic fault-tolerant controller of design controlled device, concrete grammar is:

A. the objective function J that chooses batch process, form is as follows:

$J=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}[z{\left(k\right)}^T\mathrm{Qz}\left(k\right)+\mathrm{\Δ}{u}^T\left(k\right)\mathrm{R\Δu}\left(k\right)]$

Q＝diag{q _jx1,q _jx2,…,q _jxn,q _ju1,q _ju2,…,q _jud,q _je}

Wherein, Q, R are respectively the weight matrix of process status and input, and Q is symmetric matrix, q _jx1..., q _jxnfor the weight coefficient of process status, q _ju1..., q _judfor the weight coefficient of process input, q _jeweight coefficient for output error.

B. according to the objective function in a, solve controlled quentity controlled variable u (k)

Δu(k)＝-R ^-1B ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞Az(k)

K _∞＝A ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞A+Q

＝A ^ΤK _∞A-A ^ΤK _∞B(R+B ^TK _∞B) ^-1B ^ΤK _∞A+Q

u(k)＝u(k-1)+Δu(k)

Wherein, R ^-1represent weighted input inverse of a matrix matrix.

C. the controlled quentity controlled variable u obtaining in b step (k) is acted on to controlled device.

D. at next constantly, according to a, to the step of c, continue to solve new controlled quentity controlled variable u (k+1), and circulate successively.

The present invention proposes a kind of batch process Infinite horizon linear quadratic fault tolerant control method of state-space model.The method has been set up Extended state space model, and has designed controller under Infinite horizon, has effectively improved the performance of traditional control method and the system that guaranteed still has good control effect in unknown disturbance and actuator failures situation.

Embodiment

It is example that the injection speed of take in injection moulding process is controlled:

It is a typical batch of process that injection speed in injection moulding process is controlled, and regulating measure is the valve opening of control ratio valve.

Step (1). set up the state-space model of injection speed, concrete grammar is:

A. first gather the inputoutput data of injection process, utilize these data to set up the state model of injection process, form is as follows:

$\left\{\begin{array}{c}x(k+1)=\stackrel{\‾}{A}x\left(k\right)+\stackrel{\‾}{B}u(k-d)\\ y\left(k\right)=\stackrel{\‾}{C}x\left(k\right)+w\left(k\right)\end{array}\right.$

Wherein, x (k) ∈ R ⁿ, y (k) ∈ R, u (k) ∈ R is respectively k state, injection speed and the valve opening of injection process constantly, the time lag that d is injection process, w (k) ∈ R is measurement noise, be respectively the system matrix of suitable dimension.

B. the model in step a is further processed into following form:

$\left\{\begin{array}{c}\mathrm{\Δx}(k+1)=\stackrel{\‾}{A}\mathrm{\Δx}\left(k\right)+\stackrel{\‾}{B}\mathrm{\Δu}(k-d)\\ \mathrm{\Δy}\left(k\right)=\stackrel{\‾}{C}\mathrm{\Δx}\left(k\right)\end{array}\right.$

Choose state variable as follows:

Δx _m(k)＝[Δx(k)Δu(k-1)Δu(k-2)…Δu(k-d)] ^Τ

Thereby the state-space model that obtains injection process, form is as follows:

Δx _m(k+1)＝A _mΔx _m(k)+B _mΔu(k)

Δy(k)＝C _mΔx _m(k)

Wherein,

B _m＝[010…0] ^T

Δ is difference operator, and Τ is transpose of a matrix symbol, with 0be the null vector of suitable dimension.

C. convert the state-space model obtaining in step b to comprise state variable and output tracking error Extended state space model, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Wherein,

$z(k+1)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m(k+1)\\ e(k+1)\end{array}\right],z\left(k\right)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m\left(k\right)\\ e\left(k\right)\end{array}\right]$

$A=\left[\begin{array}{cc}{A}_m& 0\\ C_m{A}_m& 1\end{array}\right],B=\left[\begin{array}{c}{B}_m\\ C_m{B}_m\end{array}\right]$

e(k)＝y(k)-y _r(k)

Y (k), y _r(k) be respectively k real output value and the speed tracking setting value of speed constantly, e (k) is the k output error of speed constantly.

Step (2). the Infinite horizon linear quadratic fault-tolerant controller of design injection speed, concrete grammar is:

A. the objective function J that chooses injection process, form is as follows:

$J=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}[z{\left(k\right)}^T\mathrm{Qz}\left(k\right)+\mathrm{\Δ}{u}^T\left(k\right)\mathrm{R\Δu}\left(k\right)]$

Q＝diag{q _jx1,q _jx2,…,q _jxn,q _ju1,q _ju2,…,q _jud,q _je}

Wherein, Q, R are respectively the weight matrix of process status and input, and Q is symmetric matrix, q _jx1..., q _jxnfor the weight coefficient of process status, q _ju1..., q _judfor the weight coefficient of process input, q _jeweight coefficient for output error.

B. according to the objective function in a, solve controlled quentity controlled variable u (k)

Δu(k)＝-R ^-1B ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞Az(k)

K _∞＝A ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞A+Q

＝A ^ΤK _∞A-A ^ΤK _∞B(R+B ^TK _∞B) ^-1B ^ΤK _∞A+Q

u(k)＝u(k-1)+Δu(k)

Wherein, R ^-1represent weighted input inverse of a matrix matrix.

C. the controlled quentity controlled variable u obtaining in b step (k) is acted on to injection machine.

D. at next constantly, according to a, to the step of c, continue to solve new controlled quentity controlled variable u (k+1), and circulate successively.

Claims (1)

1. batch process Infinite horizon linear quadratic fault tolerant control method of state-space model, is characterized in that the concrete steps of the method are:

Step (1). set up the state-space model of controlled device in batch process, specifically:

A. first gather the inputoutput data of batch process, utilize these data to set up this batch of status of processes model, form is as follows:

$\left\{\begin{array}{c}x(k+1)=\stackrel{\‾}{A}x\left(k\right)+\stackrel{\‾}{B}u(k-d)\\ y\left(k\right)=\stackrel{\‾}{C}x\left(k\right)+w\left(k\right)\end{array}\right.$

Wherein, x (k) ∈ R ⁿ, y (k) ∈ R, u (k) ∈ R is respectively k batch status of processes, output and input constantly, and d is the time lag of batch process, and w (k) ∈ R is measurement noise, be respectively the system matrix of suitable dimension;

B. the model in step a is further processed into following form:

$\left\{\begin{array}{c}\mathrm{\Δx}(k+1)=\stackrel{\‾}{A}\mathrm{\Δx}\left(k\right)+\stackrel{\‾}{B}\mathrm{\Δu}(k-d)\\ \mathrm{\Δy}\left(k\right)=\stackrel{\‾}{C}\mathrm{\Δx}\left(k\right)\end{array}\right.$

Choose state variable as follows:

Δx _m(k)＝[Δx(k)Δu(k-1)Δu(k-2)…Δu(k-d)] ^Τ

Thereby obtain a batch status of processes spatial model, form is as follows:

Δx _m(k+1)＝A _mΔx _m(k)+B _mΔu(k)

Δy(k)＝C _mΔx _m(k)

Wherein,

B _m＝[010…0] ^T

$C_m=\left[\begin{array}{ccccc}\stackrel{\‾}{C}& 0& 0& \·\·\·& 0\end{array}\right]$

Δ is difference operator, and Τ is transpose of a matrix symbol, with 0be the null vector of suitable dimension;

C. convert the state-space model obtaining in step b to comprise state variable and output tracking error Extended state space model, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Wherein,

$z(k+1)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m(k+1)\\ e(k+1)\end{array}\right],z\left(k\right)=\left[\begin{array}{c}\mathrm{\Δ}{x}_m\left(k\right)\\ e\left(k\right)\end{array}\right]$

$A=\left[\begin{array}{cc}{A}_m& 0\\ C_m{A}_m& 1\end{array}\right],B=\left[\begin{array}{c}{B}_m\\ C_m{B}_m\end{array}\right]$

e(k)＝y(k)-y _r(k)

Y (k), y _r(k) be respectively k real output value and tracking setting value constantly, e (k) is k output error constantly;

Step (2). the Infinite horizon linear quadratic fault-tolerant controller of design controlled device, specifically:

A. the objective function J that chooses batch process, form is as follows:

$J=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}[z{\left(k\right)}^T\mathrm{Qz}\left(k\right)+\mathrm{\Δ}{u}^T\left(k\right)\mathrm{R\Δu}\left(k\right)]$

Q＝diag{q _jx1,q _jx2,…,q _jxn,q _ju1,q _ju2,…,q _jud,q _je}

Wherein, Q, R are respectively the weight matrix of process status and input, and Q is symmetric matrix, q _jx1..., q _jxnfor the weight coefficient of process status, q _ju1..., q _judfor the weight coefficient of process input, q _jeweight coefficient for output error;

B. according to the objective function in a, solve controlled quentity controlled variable u (k)

Δu(k)＝-R ^-1B ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞Az(k)

K _∞＝A ^Τ[I+K _∞BR ^-1B ^Τ] ^-1K _∞A+Q

＝A ^ΤK _∞A-A ^ΤK _∞B(R+B ^TK _∞B) ^-1B ^ΤK _∞A+Q

u(k)＝u(k-1)+Δu(k)

Wherein, R ^-1represent weighted input inverse of a matrix matrix;

C. the controlled quentity controlled variable u obtaining in b step (k) is acted on to controlled device;

D. at next constantly, according to a, to the step of c, continue to solve new controlled quentity controlled variable u (k+1), and circulate successively.