CN114859720B - Dissipative economic model predictive control method for large-time-lag forming system - Google Patents
Dissipative economic model predictive control method for large-time-lag forming system Download PDFInfo
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Abstract
The invention relates to a control problem of a molding system, and mainly relates to an application of a novel Economic Model Predictive Control (EMPC) method in the molding system. Aiming at the problem that the economic index and the stability index in a control system are difficult to balance due to the characteristics of nonlinearity, large time lag and strong coupling of the system in the molding system, the invention discloses a predictive control method for a dissipative economic model of a large time lag molding system, which reasonably presumes the molding system to ensure the closed-loop stability of the control system. The technical scheme of the invention is that the method for predicting and controlling the dissipative economic model of the large-time-lag forming system mainly comprises the following steps: 1) The time lag time of the system is amplified to an original system model to construct a time lag amplifying model; 2) Reasonably designing economic performance indexes of the system according to the molding system augmentation model; 3) Constructing a terminal-free cost economic model prediction controller according to the time lag augmentation model and the Turnpike economic index; 4) And the real-time performance of the EMPC controller is regulated by designing an adaptive prediction time domain through error feedback. The invention can effectively solve the problem that the economic performance and the stability of the molding system are restricted, and ensure the economic, rapid and stable operation of the molding closed-loop control system.
Description
Technical Field
The invention relates to a predictive control method for a dissipative economic model of a large-time-lag forming system, and belongs to the field of control algorithm application.
Background
The molding industry is an important component of the development of modern scientific industry and is an important expression of entity economy and comprehensive national force. In the control of the molding system, hysteresis of the molding system is common and the hysteresis is different due to the fact that the physical and chemical changes in the molding system cannot be suddenly changed, the signal transmission needs time and the like. In the molding control system, if the controlled object has pure hysteresis, the control difficulty of the system is increased, the control quality is deteriorated, the stability of the system is also reduced, the delay time is longer, the system is unstable, and the quality of the product is difficult to guarantee.
Large-time-lag molding systems have been a difficult problem in industrial control due to their complex nature. In addition, the molding industrial system is generally a nonlinear system, the internal mechanism structure is complex, the model is inaccurate, and the interference of environmental factors is more remarkable, which can influence the stability, the rapidity and the accuracy of the control strategy.
In view of the characteristics of non-linearity, large time lag, uncertainty, multiple interferences and the like common in molding systems, model Predictive Control (MPC) is widely applied as a control method with low system model precision requirements but accurate control. In recent years, economic Model Predictive Control (EMPC) algorithm with required economic targets as direct optimization targets has been rapidly developed, and is widely applied in industrial systems
However, the control algorithm of the traditional EMPC controller is complex, the economic performance and the stability performance are balanced, the algorithm complexity and the steady state error are simultaneously optimized, and further improvement on the traditional EMPC control algorithm is needed.
Disclosure of Invention
The invention aims to provide a predictive control method for a dissipative economic model of a large-time-lag forming system, which overcomes the defects in the background art.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a large time lag molding system dissipative economic model prediction control method is characterized by comprising the following steps:
step 1, the EMPC controller determines a nominal model and control time lag time of a control system of a molding system, and obtains a time lag augmentation control model of the molding system;
step 2, the controller designs a turnpike characteristic non-terminal cost economic performance index according to a molding system time lag augmentation model;
step 3, the EMPC controller calculates the optimal control input at the current moment according to the time lag augmentation model of the forming system at the moment k and the designed economic index;
step 4, the EMPC controller inputs the control input quantity obtained in the step 3 into a molding system, and obtains a system error at the current moment;
and 5, the EMPC controller calculates an adaptive prediction time domain at the time of k+1 according to the error obtained at the time of k, and returns to the step 3.
The nominal model of the molding system and the control time lag time needed by the EMPC controller are obtained in advance through methods such as model identification or mechanism derivation, and the time lag time is amplified into the nominal model of the molding system through the ratio of the time lag time to the sampling time;
the economic index of the forming system designed in the EMPC controller means that an optimal economic function of an economic model prediction control optimal problem must meet a Turnpike assumption so as to meet the requirement that the optimal control problem has no terminal cost, and the optimal economic function is transmitted to the step 3;
the EMPC controller solves the optimal control problem according to the time lag augmentation model in the step 1, the economic optimization index function in the step 2 and the self-adaptive prediction time domain obtained at the last moment, obtains the optimal control input quantity and transmits the optimal control input quantity to the step 4;
the EMPC controller inputs the optimal control input quantity calculated in the step 3 into a large-time-lag forming system to obtain a system error at the current moment, and the system error is transmitted to the step 5;
and the EMPC controller calculates the self-adaptive prediction time domain of the next moment according to the system error of the current moment, and returns to the step 3.
Drawings
FIG. 1 is a system control block diagram of a dual-mode economic model predictive robust control method for a large-time-lag molding system according to the present invention
Detailed Description
The molding system is composed of the following parts. The bottom is a cooling tank. The cooling water is recycled from the outside through two valves, so that the stable cooling water temperature is maintained. And slowly putting the molding liquid material into a cooling tank for cooling at a set speed by a motor. Hot air is continuously blown to the riser to ensure that molding materials in the riser hopper arranged on the die cannot solidify. As the material in the mold solidifies, its volume decreases and the molding material in the feeder hopper can flow into the mold void, preventing shrinkage porosity, cavities and cracks in the product.
Since the molding effect of the molding system is mainly affected by temperature, in this example, the temperature of the cooling water tank is used as the state variable x, and the flow rate of the water inlet/outlet valve is used as the molding system input u.
The molding system model is set as the following relation:
x(k+1)＝Ax(k)+Bu(k)+B τ u(k-τ)
wherein the input time delay is tau times of the sampling period time, A is a state matrix, B is an input transmission matrix at the current moment, B τ The transfer matrix is input for a time delay.
Let the augmentation vector z (k) = [ x (k) T u(k-1) T …u(k-τ) T ]The nominal system described above may then be converted to a time-lapse augmented form as shown below:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the predictive control method for the dissipative economic model of the large-time-lag forming system needs to consider the Optimal Control Problem (OCP) of the following formula:
x(k+1|t)＝f(x(k|t),u(k|t)),k＝0,...,N-1
x(0|t)＝x(t)
x(k|t),u(k|t) T ∈X×U,k＝0,...,N-1
wherein V is N (x (t)) does not contain terminal constraints.
According to the above OCP problem, an economic index function l is designed that satisfies the Turnpike property (i.e., satisfies strict dissipation, index accessibility, steady-state local n-step accessibility) e 。
Model for increasing time lag
And economic performance index l e Is brought into the OCP problem and is based on the adaptive prediction time domain N obtained at time k-1 a Performing optimizing calculation in (k-1), and finding out l when the constraint condition is satisfied e The input u (k) value when the function takes the minimum value is used as the input value of the molding system at the next moment.
U (k) is input into the molding system and an error ε (k) is calculated from the difference in system response from the set steady-state point.
When the EMPC controller satisfies Turnpike property, the feedback control system has recursive feasibility and the nature of actual stability and steady state error decrease as the prediction horizon increases. In order to accelerate the steady-state speed of a closed-loop control system of a forming system and reduce steady-state errors of the system as far as possible, an adaptive prediction time domain N is calculated according to the error epsilon (k) a (k) Satisfies the following formula:
wherein the method comprises the steps of
[]Represents a rounding function, ε is the error between the output and the reference signal, ε ini ，ε min Respectively the primary error and the minimum error, N max ，N ini The maximum predicted time domain and the initial predicted time domain, respectively.
The adaptive prediction time domain N obtained in the kth step a (k) Returning to the step 3, and performing k+1 steps of calculation.
It is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (1)
1. A large time lag molding system dissipative economic model prediction control method is characterized by comprising the following steps:
step 1, determining a nominal model and control time lag time of a control system of a molding system, and obtaining a time lag augmentation control model of the molding system;
step 2, designing a turnpike-based non-terminal cost economic performance index according to a time delay augmentation control model of the molding system by using a dissipative Economic Model Predictive Control (EMPC) method of the large time delay molding system;
step 3, the EMPC controller calculates the optimal control input at the current moment according to the time lag augmentation model of the forming system at the moment k and the designed economic index;
step 4, the EMPC controller inputs the control input quantity obtained in the step 3 into a molding system, and obtains a system error at the current moment;
step 5, the EMPC controller calculates an adaptive prediction time domain at the time of k+1 according to the error obtained at the time of k, and returns to the step 3;
the nominal model and the control time lag time of the molding system required by the EMPC controller in step 1 are obtained in advance through a model identification and mechanism derivation method, and the time lag time is amplified into the nominal model of the molding system through the ratio of the time lag time to the sampling time; the nominal model is expressed as the relation x (k+1) =ax (k) +bu (k) +b τ u (k-tau), wherein the temperature of the cooling water tank is taken as a state variable x, the flow of the water inlet and outlet valve is taken as a forming system input u, the input time delay is tau times of the sampling period time, A is a state matrix, B is an input transmission matrix at the current moment, and B τ Inputting a transmission matrix for time delay; the time lag augmentation form model of the molding system is expressed as
Wherein (1)>
Step 2, optimizing economic function l of economic index and economic model prediction control optimal problem used in EMPC controller e The turnpike assumption must be satisfied, that is, strict dissipation, index accessibility, steady-state local n-step accessibility are satisfied, so as to meet the requirement that the optimal control problem has no terminal cost, and the requirement is transmitted to the step 3; the design optimization economic function needs to consider the following Optimal Control Problem (OCP):
wherein V is N (x (t)) is free of terminal constraints;
the EMPC controller in the step 3 solves the optimal control problem according to the time lag augmentation model in the step 1, the economic optimization index function in the step 2 and the self-adaptive prediction time domain obtained at the last moment to solve the optimal control problem and obtain the optimal control input quantity, and the optimal control input quantity is transmitted to the step 4;
inputting the optimal control input quantity calculated in the step 3 into a large-time-lag forming system by the EMPC controller in the step 4, obtaining a system error at the current moment, and transmitting the system error to the step 5;
and 5, the EMPC controller calculates an adaptive prediction time domain of the next moment according to the system error of the current moment, and returns to the step 3.
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