CN105353618A - Constraint tracking control method for batch injection molding process - Google Patents

Abstract

The invention discloses a constraint tracking control method for a batch injection molding process. The method comprises the steps: building a state space model by collecting input and output data, building a state space model of a batch process by further combining a process state variable and an output error, and then designing an improved controller for prediction control over a constraint tracking model. The method can well handle problems caused by unknown factors during a batch process, the form is simple, and needs of an actual industrial process are satisfied.

Description

The constraint tracking and controlling method of a kind of batch of injection moulding process

Technical field

The invention belongs to technical field of automation, relate to the constraint tracking and controlling method of a kind of batch of injection moulding process.

Background technology

Actual industrial control in, along with to product specification and operation requirements more and more higher, operating conditions also becomes and becomes increasingly complex.The operating conditions of these complexity, adds the probability that system X factor occurs accordingly.In actual production, there is a lot of inevitably X factor, can affect the operation of technological process and reduce control performance, this will have an impact to product quality undoubtedly.Some control methods have been there are in batch processed process.Such as, the control methods such as iterative learning control, faults-tolerant control, Robust Model Predictive Control, but the key issue improving the control performance of unmatched models still requires study.Therefore, for solving the problem of X factor disturbance and model mismatch in batch process controls, and the system that ensures has certain robustness and stability, the control method proposing a kind of Constrained Model Predictive Control gone out based on robust control principle design is newly necessary.

Summary of the invention

The object of the invention is in batch production process because X factor causes the problem of model mismatch, provide the constraint tracking and controlling method of a kind of batch of injection moulding process, to maintain the closed loop stability of controller and to obtain good control performance.The method exports data by Gather and input and sets up state-space model, further combined with process state variables and output error, sets up the state-space model of batch process, and then devises the controller of the constraint trace model PREDICTIVE CONTROL that is improved.The method can well process the problem that batch process X factor causes, and the form that ensure that is simple and meet the needs of actual industrial process.

Technical scheme of the present invention is set up by data acquisition, model, predicted the means such as mechanism, optimization, establish the constraint tracking and controlling method of a kind of batch of injection moulding process, the control performance in utilize the method effectively to improve model mismatch situation that system causes at unknown disturbance.

The step of the inventive method comprises:

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

First 1.1 gather the inputoutput data in batch process, and utilize these data to set up the state-space model of controlled device, form is as follows:

$\left\{\begin{array}{c}{x}_m(k+1)=A_m{x}_m\left(k\right)+B_{m}u\left(k\right)\\ y(k+1)=C_m{x}_m(k+1)\end{array}\right.$

Wherein, A _m, B _m, C _mbe respectively system matrix, input matrix and output matrix, x _mk (), u (k), y (k) are respectively state, the input and output of k moment model.

1.2 will add difference operator Δ in step 1.1, obtain the state-space model form after model conversion:

$\left\{\begin{array}{c}{\mathrm{\Δx}}_m(k+1)=A_m{\mathrm{\Δx}}_m\left(k\right)+B_m\mathrm{\Δ}u\left(k\right)\\ \mathrm{\Δ}y(k+1)=C_m{\mathrm{\Δx}}_m(k+1)\end{array}\right.$

Wherein, Δ is difference operator.

1.3 choose with reference to exporting r (k), and so tracking error e (k) is as follows:

e(k)＝y(k)-r(k)

Integrating step 1.2 can obtain further:

e(k)＝e(k-1)+C _mA _mDx _m(k)+C _mB _mDu(k)

1.4 choose new state variable:

z(k)＝[Δx _m(k)e(k)] ^T

Then the state-space model obtained in step 1.2 is converted to the state-space model comprising state variable and tracking error variable, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Δy(k+1)＝Cz(k+1)

Wherein,

$A=\left[\begin{array}{cc}{A}_m& 0\\ C_m{A}_m& 1\end{array}\right];B=\left[\begin{array}{c}{B}_m\\ C_m{B}_m\end{array}\right];$ C＝[C _m0]

0 is the null vector of suitable dimension in A and C matrix.

The batch process controller of step 2, design controlled device, specifically:

2.1 in order to track reference value under constraint condition, and in Unknown Process, keep the control performance of expectation, chooses the objective function J of controlled device _∞(k), form is as follows:

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

$\left\{\begin{array}{c}\left|\mathrm{\Δ}u(k+i|k)\right|\≤{\mathrm{\Δu}}_{\max }\\ \left|y(k+i|k)\right|\≤y_{\max }\end{array}\right.$

Wherein, z (k+i|k), Δ u (k+i|k), y (k+i|k) is respectively the k moment and exports the predicted state in k+i moment, the input of prediction increment and prediction, and Q, R are the weight coefficient of state variable and input increment respectively, Du _max, y _maxit is the maximum value boundary value of input increment and output.

2.2 in order to obtain minimum target function, and choose following feedback of status, form is as follows

Δu(k+i|k)＝F(k)z(k+i|k)

Wherein, F (k) is feedback of status coefficient.

2.3 are defined as follows quadratic function:

V(z)＝z ^TP(k)z

Its constraint condition is

V(z(k+i+1|k))-V(z(k+i|k))

≤-[z(k+i|k) ^TQz(k+i|k)+Δu(k+i|k) ^TRΔu(k+i|k)]

Wherein, P (k) >0.

2.4 integrating step 2.1 and steps 2.3, quadratic function meets following constraint condition:

J _∞(k)≤V(z(k))≤γ

V(z(∞))＝0 _，z(∞)＝0

Wherein, γ is J _∞(k) maximum boundary value.

Constraint condition in step 2.4 is converted to by 2.5

$\left[\begin{array}{cc}1& z{\left(k\right)}^T\\ z\left(k\right)& S\end{array}\right]\≥0,$ S>0

Wherein, S=γ P (k) ^-1

2.6 based on step 1.4, step 2.2 and step 2.3, then the constraint condition of step 2.5 can be write as following form further:

z(k+i|k) ^T[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]z(k+i|k)≤0

Meet following constraint condition:

[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]≤0

Further constraint condition is converted to MATRIX INEQUALITIES form:

$\left[\begin{array}{cccc}S& {\mathrm{SA}}^T+Y^T{B}^T& {\mathrm{SQ}}^{1/2}& Y^T{R}^{1/2}\\ AS+BY& S& 0& 0\\ Q^{1/2}S& 0& \mathrm{\γ}I& 0\\ R^{1/2}Y& 0& 0& \mathrm{\γ}I\end{array}\right]\≥0$

Wherein, P (k)=γ S ^-1, Y=F (k) S, I are the vector of unit length of suitable dimension.

Bound for objective function in step 2.1 can be expressed as by 2.7 further:

$\left[\begin{array}{cc}X& Y\\ Y^T& S\end{array}\right]\≥0,X\≤{\mathrm{\Δu}}_{max}^2$

$\left[\begin{array}{cc}Z& C(AS+BY)\\ {(AS+BY)}^T{C}^T& S\end{array}\right]>0,Z\≤y_{max}^2$

2.8 integrating steps 2.5, the MATRIX INEQUALITIES in step 2.6 and step 2.7, tries to achieve feedback of status coefficient F (k).

2.9 can obtain optimum input increment Delta u (k) by step 2.2 and step 2.8, and then try to achieve optimal control law u (k), and form is as follows:

u(k)＝u(k-1)+Δu(k)

2.10 at subsequent time, continues to solve new input increment Delta u (k+1), and circulate successively according to step 2.1 to step 2.9.

Beneficial effect of the present invention: the batch process constraint tracking and controlling method that the present invention proposes a kind of state-space model, the method establishes state-space model and devise controller under constraint condition, effectively raises the performance of traditional control method and has good control effects in the model mismatch situation that causes at unknown disturbance of the system that ensure that.

Embodiment

Control for the injection speed in injection moulding process:

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

The state-space model of controlled device in step 1, foundation batch injection moulding process, concrete grammar is:

First 1.1 gather the inputoutput data in batch process, and utilize these data to set up the state-space model of controlled device, form is as follows:

$\left\{\begin{array}{c}{x}_m(k+1)=A_m{x}_m\left(k\right)+B_{m}u\left(k\right)\\ y(k+1)=C_m{x}_m(k+1)\end{array}\right.$

Wherein, A _m, B _m, C _mbe respectively system matrix, input matrix and output matrix, x _mk (), u (k), y (k) are respectively state, the input and output of k moment model.

1.2 will add difference operator Δ in step 1.1, obtain the state-space model form after model conversion:

$\left\{\begin{array}{c}{\mathrm{\Δx}}_m(k+1)=A_m{\mathrm{\Δx}}_m\left(k\right)+B_m\mathrm{\Δ}u\left(k\right)\\ \mathrm{\Δ}y(k+1)=C_m{\mathrm{\Δx}}_m(k+1)\end{array}\right.$

Wherein, Δ is difference operator.

1.3 choose with reference to exporting r (k), and so tracking error e (k) is as follows:

e(k)＝y(k)-r(k)

Integrating step 1.2 can obtain further:

e(k)＝e(k-1)+C _mA _mΔx _m(k)+C _mB _mΔu(k)

Wherein, y (k) is that model exports.

1.4 choose new state variable:

z(k)＝[Δx _m(k)e(k)] ^T

Then the state-space model obtained in step 1.2 is converted to the state-space model comprising state variable and tracking error variable, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Δy(k+1)＝Cz(k+1)

Wherein,

$A=\left[\begin{array}{cc}{A}_m& 0\\ C_m{A}_m& 1\end{array}\right];B=\left[\begin{array}{c}{B}_m\\ C_m{B}_m\end{array}\right];$ C＝[C _m0]

0 is the null vector of suitable dimension in A and C matrix.

Batch injection moulding process controller of step 2, design controlled device, concrete steps are:

2.1 in order to track reference value under constraint condition, and in Unknown Process, keep the control performance of expectation, chooses the objective function J of controlled device _∞(k), form is as follows:

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

$\left\{\begin{array}{c}\left|\mathrm{\Δ}u(k+i|k)\right|\≤{\mathrm{\Δu}}_{\max }\\ \left|y(k+i|k)\right|\≤y_{\max }\end{array}\right.$

Wherein, z (k+i|k), Δ u (k+i|k), y (k+i|k) is respectively the k moment and exports the predicted state in k+i moment, the input of prediction increment and prediction, and Q, R are the weight coefficient of state variable and input increment respectively, Δ u _max, y _maxit is the maximum value boundary value of input increment and output.

2.2 in order to obtain minimum target function, and choose following feedback of status, form is as follows

Δu(k+i|k)＝F(k)z(k+i|k)

Wherein, F (k) is feedback of status coefficient.

2.3 are defined as follows quadratic function:

V(z)＝z ^TP(k)z

Its constraint condition is

V(z(k+i+1|k))-V(z(k+i|k))≤-[z(k+i|k) ^TQz(k+i|k)+Δu(k+i|k) ^TRΔu(k+i|k)]

Wherein, P (k) >0.

2.4 integrating step 2.1 and steps 2.3, quadratic function meets following constraint condition:

J _∞(k)≤V(z(k))≤γ

V(z(∞))＝0 _，z(∞)＝0

Wherein, γ is J _∞(k) maximum boundary value.

Constraint condition in step 2.4 is converted to by 2.5

$\left[\begin{array}{cc}1& z{\left(k\right)}^T\\ z\left(k\right)& S\end{array}\right]\≥0,$ S>0

Wherein, S=γ P (k) ^-1

2.6 based on step 1.4, step 2.2 and step 2.3, then the constraint condition of 2.5 can be write as following form further:

z(k+i|k) ^T[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]z(k+i|k)≤0

Meet following constraint condition:

[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]≤0

Further constraint condition is converted to MATRIX INEQUALITIES form:

$\left[\begin{array}{cccc}S& {\mathrm{SA}}^T+Y^T{B}^T& {\mathrm{SQ}}^{1/2}& Y^T{R}^{1/2}\\ AS+BY& S& 0& 0\\ Q^{1/2}S& 0& \mathrm{\γ}I& 0\\ R^{1/2}Y& 0& 0& \mathrm{\γ}I\end{array}\right]\≥0$

Wherein, P (k)=γ S ^-1, Y=F (k) S, I are the vector of unit length of suitable dimension.

Bound for objective function in step 2.1 can be expressed as by 2.7 further:

$\left[\begin{array}{cc}X& Y\\ Y^T& S\end{array}\right]\≥0,X\≤{\mathrm{\Δu}}_{max}^2$

$\left[\begin{array}{cc}Z& C(AS+BY)\\ {(AS+BY)}^T{C}^T& S\end{array}\right]>0,Z\≤y_{max}^2$

2.8 integrating steps 2.5, the MATRIX INEQUALITIES in step 2.6 and step 2.7, tries to achieve feedback of status coefficient F (k).

2.9 can obtain optimum input increment Delta u (k) by step 2.2 and step 2.8, and then try to achieve optimal control law u (k), and form is as follows:

u(k)＝u(k-1)+Δu(k)

2.10 at subsequent time, continues to solve new input increment Delta u (k+1), and circulate successively according to step 2.1 to step 2.9.

Claims (1)

1. a constraint tracking and controlling method for batch injection moulding process, 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:

First 1.1 gather the inputoutput data in batch process, and utilize these data to set up the state-space model of controlled device, form is as follows:

$\left\{\begin{array}{c}{x}_m(k+1)=A_m{x}_m\left(k\right)+B_{m}u\left(k\right)\\ y(k+1)=C_m{x}_m(k+1)\end{array}\right.$

Wherein, A _m, B _m, C _mbe respectively system matrix, input matrix and output matrix, x _m(k), u (k), y (k) are respectively state, the input and output of k moment model;

1.2 add difference operator Δ in step 1.1, obtain the state-space model form after model conversion:

$\left\{\begin{array}{c}\mathrm{\Δ}{x}_m(k+1)=A_m\mathrm{\Δ}{x}_m\left(k\right)+B_m\mathrm{\Δ}u\left(k\right)\\ \mathrm{\Δ}y(k+1)=C_m\mathrm{\Δ}{x}_m(k+1)\end{array}\right.$

Wherein, Δ is difference operator;

1.3 choose with reference to exporting r (k), and so tracking error e (k) is as follows:

e(k)＝y(k)-r(k)

Integrating step 1.2 obtains further:

e(k)＝e(k-1)+C _mA _mΔx _m(k)+C _mB _mΔu(k)

1.4 choose new state variable:

z(k)＝[Δx _m(k)e(k)] ^T

Then the state-space model obtained in step 1.2 is converted to the state-space model comprising state variable and tracking error variable, form is as follows:

z(k+1)＝Az(k)+BΔu(k)

Δy(k+1)＝Cz(k+1)

Wherein,

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

0 is the null vector of suitable dimension in A and C matrix;

The batch process controller of step 2, design controlled device, specifically:

2.1 in order to track reference value under constraint condition, and in Unknown Process, keep the control performance of expectation, chooses the objective function J of controlled device _∞(k), form is as follows:

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

$\left\{\begin{array}{c}\left|\mathrm{\Δ}u(k+i|k)\right|\≤{\mathrm{\Δu}}_{\max }\\ \left|y(k+i|k)\right|\≤y_{max}\end{array}\right.$

Wherein, z (k+i|k), Δ u (k+i|k), y (k+i|k) is respectively the k moment and exports the predicted state in k+i moment, the input of prediction increment and prediction, and Q, R are the weight coefficient of state variable and input increment respectively, Δ u _max, y _maxit is the maximum value boundary value of input increment and output;

2.2 in order to obtain minimum target function, and choose following feedback of status, form is as follows

Δu(k+i|k)＝F(k)z(k+i|k)

Wherein, F (k) is feedback of status coefficient;

2.3 are defined as follows quadratic function:

V(z)＝z ^TP(k)z

Its constraint condition is

V(z(k+i+1|k))-V(z(k+i|k))

≤-[z(k+i|k) ^TQz(k+i|k)+Δu(k+i|k) ^TRΔu(k+i|k)]

Wherein, P (k) >0;

2.4 integrating step 2.1 and steps 2.3, quadratic function meets following constraint condition:

J _∞(k)≤V(z(k))≤γ

V(z(∞))＝0，z(∞)＝0

Wherein, γ is J _∞(k) maximum boundary value;

Constraint condition in step 2.4 is converted to by 2.5

$\left[\begin{array}{cc}1& z{\left(k\right)}^T\\ z\left(k\right)& S\end{array}\right]\≥0,S>0$

Wherein, S=γ P (k) ^-1

2.6 based on step 1.4, step 2.2 and step 2.3, then the constraint condition of step 2.5 can be write as following form further:

z(k+i|k) ^T[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]z(k+i|k)≤0

Meet following constraint condition:

[(A+BF(k)) ^TP(k)(A+BF(k))-P(k)+F(k) ^TRF(k)+Q]≤0

Further constraint condition is converted to MATRIX INEQUALITIES form:

$\left[\begin{array}{cccc}S& {\mathrm{SA}}^T+Y^T{B}^T& {\mathrm{SQ}}^{1/2}& Y^T{R}^{1/2}\\ AS+BY& S& 0& 0\\ Q^{1/2}S& 0& \mathrm{\γ}I& 0\\ R^{1/2}Y& 0& 0& \mathrm{\γ}I\end{array}\right]\≥0$

Wherein, P (k)=γ S ^-1, Y=F (k) S, I are the vector of unit length of suitable dimension;

Bound for objective function in step 2.1 is expressed as by 2.7 further:

$\left[\begin{array}{cc}X& Y\\ Y^T& S\end{array}\right]\≥0,X\≤{\mathrm{\Δu}}_{max}^2$

$\left[\begin{array}{cc}Z& C(AS+BY)\\ {(AS+BY)}^T{C}^T& S\end{array}\right]>0,Z\≤y_{max}^2$

2.8 integrating steps 2.5, the MATRIX INEQUALITIES in step 2.6 and step 2.7, tries to achieve feedback of status coefficient F (k);

2.9 can obtain optimum input increment Delta u (k) by step 2.2 and step 2.8, and then try to achieve optimal control law u (k), and form is as follows:

u(k)＝u(k-1)+Δu(k)

2.10 at subsequent time, continues to solve new input increment Delta u (k+1), and circulate successively according to step 2.1 to step 2.9.