CN105353618B - A kind of constraint tracking and controlling method of batch injection moulding process - Google Patents
A kind of constraint tracking and controlling method of batch injection moulding process Download PDFInfo
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Abstract
The invention discloses a kind of constraint tracking and controlling method of batch injection moulding process.The present invention establishes state-space model by gathering inputoutput data, further combined with process state variables and output error, establishes the state-space model of batch process, and then devises the controller of an improved constraint trace model PREDICTIVE CONTROL.The present invention can be very good to handle the problem of batch process X factor causes, and ensure that form is simple and meets the needs of actual industrial process.
Description
Technical Field
The invention belongs to the technical field of automation, and relates to a constraint tracking control method for a batch injection molding process.
Background
In practical industrial control, as the requirements for product specifications and operation become higher, the operating conditions become more and more complex. These complex operating conditions, in turn, increase the probability of unknown factors in the system. In actual production, there are many unavoidable unknown factors that affect the operation of the process and degrade the control performance, which undoubtedly will have an influence on the product quality. Some control methods have emerged during batch processing. For example, control methods such as iterative learning control, fault-tolerant control, robust model predictive control, etc., but the key problem of improving the control performance of model mismatch still remains to be researched. Therefore, in order to solve the problems of unknown factor disturbance and model mismatch in batch process control and ensure that the system has certain robustness and stability, it is necessary to provide a new control method for constrained model predictive control designed based on the robust control principle.
Disclosure of Invention
The invention aims to provide a constraint tracking control method for a batch injection molding process aiming at the problem of model mismatch caused by unknown factors in the batch production process so as to maintain the closed loop stability of a controller and obtain good control performance. The method establishes a state space model by collecting input and output data, further establishes a state space model of batch processes by combining process state variables and output errors, and further designs an improved controller for predictive control of a constraint tracking model. The method can well treat the problems caused by unknown factors in the batch process, ensures simple form and meets the requirements of actual industrial processes.
The technical scheme of the invention is that a constraint tracking control method for a batch injection molding process is established by means of data acquisition, model establishment, prediction mechanism, optimization and the like, and the control performance of the system under the condition of model mismatch caused by unknown disturbance can be effectively improved by using the method.
The method comprises the following steps:
step 1, establishing a state space model of a controlled object in a batch process, specifically:
1.1, firstly, acquiring input and output data in a batch process, and establishing a state space model of a controlled object by using the data, wherein the form is as follows:
wherein A is m ,B m ,C m Respectively a system matrix, an input matrix and an output matrix, x m (k) U (k), y (k) are the state, input and output of the model at time k, respectively.
1.2, adding a difference operator delta into the step 1.1 to obtain a state space model form after model conversion:
where Δ is the difference operator.
1.3 chooses the reference output r (k), then the tracking error e (k) is as follows:
e(k)＝y(k)-r(k)
combining step 1.2 can further result in:
e(k)＝e(k-1)+C m A m Dx m (k)+C m B m Du(k)
1.4 selecting new state variables:
z(k)＝[Δx m (k) e(k)] T
the state space model obtained in step 1.2 is then converted into a state space model containing state variables and tracking error variables in the following form:
z(k+1)＝Az(k)+BΔu(k)
Δy(k+1)＝Cz(k+1)
wherein, the first and the second end of the pipe are connected with each other,
C＝[C m 0]
0 is a zero vector of appropriate dimensions in the a and C matrices.
Step 2, designing a batch process controller of the controlled object, which specifically comprises the following steps:
2.1 in order to track the reference values under the constraint conditions and maintain the desired control performance in the unknown process, an objective function J of the controlled object is selected ∞ (k) The form is as follows:
wherein z (k + i | k), Δ u (k + i | k), and y (k + i | k) are the predicted state at time k to time k + i, the predicted increment input, andpredicted outputs, Q, R are the weighting coefficients of the state variables and input increments, respectively, du max ,y max Is the maximum boundary value of the input increment and the output.
2.2 to obtain the minimum objective function, the following state feedback is chosen, in the form of
Δu(k+i|k)＝F(k)z(k+i|k)
Wherein F (k) is a state feedback coefficient.
2.3 defines the following quadratic function:
V(z)＝z T P(k)z
with the constraint of
V(z(k+i+1|k))-V(z(k+i|k))
≤-[z(k+i|k) T Qz(k+i|k)+Δu(k+i|k) T RΔu(k+i|k)]
Wherein, P (k) >0.
2.4 combining step 2.1 and step 2.3, the quadratic function satisfies the following constraint:
J ∞ (k)≤V(z(k))≤γ
V(z(∞))＝0 ， z(∞)＝0
wherein γ is J ∞ (k) The maximum boundary value.
2.5 converting the constraints in step 2.4 into
S>0
Wherein, S = gamma P (k) -1
2.6 based on step 1.4, step 2.2 and step 2.3, the constraints of step 2.5 can be further written as follows:
z(k+i|k) T [(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]z(k+i|k)≤0
the following constraints are satisfied:
[(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]≤0
the constraints are further converted into a matrix inequality form:
wherein, P (k) = γ S -1 Y = F (k) S, I is a unit vector of appropriate dimensions.
2.7 the constraints of the objective function in step 2.1 can be further expressed as:
2.8 combining the matrix inequalities in step 2.5, step 2.6 and step 2.7, the state feedback coefficient F (k) is obtained.
2.9 the optimal input increment Δ u (k) is obtained from step 2.2 and step 2.8, and the optimal control law u (k) is obtained, which is as follows:
u(k)＝u(k-1)+Δu(k)
2.10 at the next instant, continue to solve for the new input delta u (k + 1) according to steps 2.1 to 2.9 and loop through.
The invention has the beneficial effects that: the invention provides a batch process constraint tracking control method of a state space model, which establishes the state space model and designs a controller under constraint conditions, thereby effectively improving the performance of the traditional control method and ensuring that the system has good control effect under the condition of model mismatch caused by unknown disturbance.
Detailed Description
Taking the injection speed control in the injection molding process as an example:
the injection speed control in the injection molding process is a typical batch process, and the adjusting means is to control the valve opening of the proportional valve.
Step 1, establishing a state space model of a controlled object in a batch injection molding process, wherein the specific method comprises the following steps:
1.1 firstly, acquiring input and output data in a batch process, and establishing a state space model of a controlled object by using the data, wherein the form is as follows:
wherein A is m ,B m ,C m Respectively a system matrix, an input matrix and an output matrix, x m (k) U (k), y (k) are the state, input and output of the model at time k, respectively.
1.2, adding a difference operator delta into the step 1.1 to obtain a state space model form after model conversion:
where Δ is the difference operator.
1.3 chooses the reference output r (k), then the tracking error e (k) is as follows:
e(k)＝y(k)-r(k)
combining step 1.2 can further result in:
e(k)＝e(k-1)+C m A m Δx m (k)+C m B m Δu(k)
where y (k) is the model output.
1.4 selecting new state variables:
z(k)＝[Δx m (k) e(k)] T
the state space model obtained in step 1.2 is then converted into a state space model containing state variables and tracking error variables in the following form:
z(k+1)＝Az(k)+BΔu(k)
Δy(k+1)＝Cz(k+1)
wherein the content of the first and second substances,
C＝[C m 0]
0 is a zero vector of appropriate dimensions in the a and C matrices.
Step 2, designing a batch injection molding process controller of the controlled object, which comprises the following specific steps:
2.1 in order to track the reference values under the constraint conditions and maintain the desired control performance in the unknown process, an objective function J of the controlled object is selected ∞ (k) The form is as follows:
wherein z (k + i | k), Δ u (k + i | k), and y (k + i | k) are the predicted state, predicted increment input, and predicted output of time k to time k + i, Q and R are the weight coefficients of the state variable and input increment, respectively, and Δ u is the weight coefficient of the state variable and input increment, respectively max ,y max Is the maximum boundary value of the input increment and the output.
2.2 to obtain the minimum objective function, the following state feedback is chosen, in the form of
Δu(k+i|k)＝F(k)z(k+i|k)
Wherein F (k) is a state feedback coefficient.
2.3 defines the following quadratic function:
V(z)＝z T P(k)z
with the constraint of
V(z(k+i+1|k))-V(z(k+i|k))≤-[z(k+i|k) T Qz(k+i|k)+Δu(k+i|k) T RΔu(k+i|k)]
Wherein, P (k) >0.
2.4 combining step 2.1 and step 2.3, the quadratic function satisfies the following constraint:
J ∞ (k)≤V(z(k))≤γ
V(z(∞))＝0 ， z(∞)＝0
wherein γ is J ∞ (k) The maximum boundary value.
2.5 converting the constraints in step 2.4 into
S>0
Wherein, S = gamma P (k) -1
2.6 based on step 1.4, step 2.2 and step 2.3, then the constraint of 2.5 can be further written as follows:
z(k+i|k) T [(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]z(k+i|k)≤0
the following constraints are satisfied:
[(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]≤0
the constraints are further converted into a matrix inequality form:
wherein, P (k) = γ S -1 Y = F (k) S, I is a unit vector of appropriate dimensions.
2.7 the constraints of the objective function in step 2.1 can be further expressed as:
2.8 combining the matrix inequalities in step 2.5, step 2.6 and step 2.7, the state feedback coefficient F (k) is obtained.
2.9 the optimal input increment Δ u (k) is obtained from step 2.2 and step 2.8, and the optimal control law u (k) is obtained, which is as follows:
u(k)＝u(k-1)+Δu(k)
2.10 at the next instant, continue to solve for the new input delta u (k + 1) according to steps 2.1 through 2.9, and loop through.
Claims (1)
1. A constraint tracking control method for a batch injection molding process is characterized by comprising the following specific steps:
step 1, establishing a state space model of a controlled object in a batch process, specifically:
1.1, firstly, acquiring input and output data in a batch process, and establishing a state space model of a controlled object by using the data, wherein the form is as follows:
wherein, A m ,B m ,C m Respectively a system matrix, an input matrix and an output matrix, x m (k) U (k), y (k) are respectively the state, input and output of the model at the moment k;
1.2 adding a difference operator delta in the step 1.1 to obtain a state space model form after model conversion:
where Δ is a difference operator;
1.3 choose the reference output r (k), then the tracking error e (k) is as follows:
e(k)＝y(k)-r(k)
combining the step 1.2 to further obtain:
e(k)＝e(k-1)+C m A m △x m (k)+C m B m △u(k)
1.4 selecting new state variables:
z(k)＝[△x m (k) e(k)] T
the state space model obtained in step 1.2 is then converted into a state space model containing state variables and tracking error variables in the following form:
z(k+1)＝Az(k)+B△u(k)
△y(k+1)＝Cz(k+1)
wherein the content of the first and second substances,
0 is a zero vector of appropriate dimensions in the A and C matrices;
step 2, designing a batch process controller of the controlled object, which specifically comprises the following steps:
2.1 in order to track the reference values under the constraint conditions and to maintain the desired control performance in the unknown process, an objective function J of the controlled object is selected ∞ (k) The form is as follows:
wherein z (k + i | k), Δ u (k + i | k), and y (k + i | k) are the predicted state, predicted increment input, and predicted output of the time k to the time k + i, Q, R are the weight coefficients of the state variable and input increment, respectively, and Δ u max ,y max Is the maximum boundary value of the input increment and the output;
2.2 to obtain the minimum objective function, the following state feedback is chosen, in the form of
△u(k+i|k)＝F(k)z(k+i|k)
Wherein F (k) is a state feedback coefficient;
2.3 defines the following quadratic function:
V(z(k))＝z(k) T P(k)z(k)
with the constraint of
V(z(k+i+1|k))-V(z(k+i|k))
≤-[z(k+i|k) T Qz(k+i|k)+△u(k+i|k) T R△u(k+i|k)]
Wherein, P (k) >0;
2.4 combining step 2.1 and step 2.3, the quadratic function satisfies the following constraint:
J ∞ (k)≤V(z(k))≤γ
V(z(∞))＝0，z(∞)＝0
wherein γ is J ∞ (k) A maximum boundary value;
2.5 converting the constraints in step 2.4 into
Wherein S = gamma P (k) - 1
2.6 based on step 1.4, step 2.2 and step 2.3, the constraints of step 2.5 can be further written as follows:
z(k+i|k) T [(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]z (k + i | k) ≦ 0 satisfies the following constraint:
[(A+BF(k)) T P(k)(A+BF(k))-P(k)+F(k) T RF(k)+Q]≤0
the constraints are further converted into a matrix inequality form:
wherein, P (k) = γ S -1 Y = F (k) S, I is a unit vector of appropriate dimensions;
2.7 the constraints of the objective function in step 2.1 are further expressed as:
2.8, combining the matrix inequalities in the step 2.5, the step 2.6 and the step 2.7 to obtain a state feedback coefficient F (k);
2.9 the optimal input increment Δ u (k) is obtained from step 2.2 and step 2.8, and the optimal control law u (k) is obtained, which has the following form:
u(k)＝u(k-1)+△u(k)
2.10 at the next instant, continue to solve for the new input increment Δ u (k + 1) according to steps 2.1 through 2.9, and cycle through.
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| CN107765549A (en) * | 2017-10-12 | 2018-03-06 | 杭州电子科技大学 | A kind of New Iterative learning control method of batch industrial process |
| CN107976942B (en) * | 2017-11-22 | 2020-11-24 | 海南师范大学 | 2D constraint fault-tolerant control method for intermittent process of infinite time domain optimization |
| CN107918283B (en) * | 2017-12-12 | 2021-03-26 | 海南师范大学 | Design method of anti-interference hybrid stable controller in batch injection molding process |
| CN112180738B (en) * | 2020-10-22 | 2022-04-19 | 辽宁石油化工大学 | Robust fuzzy prediction control method for nonlinear injection molding asynchronous switching process |
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