How Do I Choose the Best Workflow Model?

In the Optimal control model, the strategy adopted by the operator in the operation is considered, that is, the operator shows different operations according to different instructions and different task requirements. In the optimal control model, the operator perceives a series of displayed parameter quantities and implements control so that the cost of the system, the functional value (J), is minimized.

A control operation model for humans. In the optimal control model, J is a key component in the optimal control model, and its value can usually be expressed by the following formula:

The integration value in parentheses is required to be reduced to a minimum, which is a weighted combination of the square of the error value and the square of the control speed. The relative values of these two items depend on the relative importance of the control accuracy e and the control cost u. But this importance varies from person to person and from time to time.

Control model

Optimal control theory is a major branch of modern control theory, focusing on the basic conditions and

In order to solve the optimal control problem, it is necessary to establish

The realization of optimal control is inseparable from the optimization technology, which is the research and solution

So-called

Optimal control model online optimization method

The offline optimization method based on object mathematical model is an ideal method. This is because although the industrial process (object) is designed to run continuously under certain normal working conditions, factors such as environmental changes, aging of catalysts and equipment, and changes in raw material components have caused disturbances to the industrial process, so Working conditions are not optimal. ^[2]

Common ways to solve such problems.

(1) Design method of local parameter optimization and global optimization

The basic idea of the local parameter optimization method is to adjust the adjustable parameters of the controller according to the difference between the reference model and the output of the controlled process, so that the integral of the squared output error is minimized. This allows the controlled process and the reference model to be precisely aligned as quickly as possible.

In addition, the combination of static and dynamic optimization, and variable local optimization is the overall optimization. The overall optimality is reflected by the overall objective function. The overall optimization consists of two parts: one is a static optimization (or offline optimization), and its objective function is constant over a period of time or a certain range; the other is a dynamic optimization (or online optimization) It refers to the optimization of the entire industrial process. The industrial process is a dynamic process. To keep a system always in an optimized state, it is necessary to eliminate all kinds of interference at any time and coordinate the local optimization parameters or field controllers to achieve the entire system optimal.

(2) Rolling optimization algorithm in predictive control

Predictive control, also known as Model-based Control, is a new type of optimized control algorithm that arose in the late 1970s. However, it is different from the usual discrete optimal control algorithms. Instead of using a constant global optimization goal, it uses a rolling limited time domain optimization strategy. This means that the optimization process is not performed offline once, but repeatedly online. The locality of this finite target makes it ideally only a global suboptimal solution, but its rolling implementation can take into account the uncertainties caused by model mismatches, time variations, interference, etc. The new optimization is always based on reality, so that the control remains practically optimal. This heuristic rolling optimization strategy takes into account the effects of ideal optimization and actual uncertainty in the future for a sufficient period of time. In a complex industrial environment, this is more practical and effective than optimal control based on ideal conditions.

The optimization mode of predictive control has distinctive characteristics: its discrete form of limited optimization goals and the implementation process of rolling advancement enable dynamic optimization in the entire process of control, and static parameter optimization in each step of control. With this thinking, you can handle more complex situations, such as constraints, multi-objective, non-linear and even non-parametric. Learning from the hierarchical thinking in planning, you can also layer goals according to their importance and type, and implement different levels of optimization. Obviously, the idea of hierarchical decision-making and artificial intelligence methods in large system control can be introduced into predictive control to form a multi-layer intelligent predictive control model. This multi-layer intelligent predictive control method will overcome the shortcomings of the predictive control algorithm of a single model and is one of the important directions of current research.

(3) Steady-state hierarchical control

For the control of complex large industrial processes (objects), a distributed control mode is often used. At this time, the computer's online steady-state optimization often uses a hierarchical control structure. This structure has both a control layer and an optimization layer, and the optimization layer is a two-level structure composed of a local decision unit level and a coordinator. The optimization process is: each decision unit responds to the sub-process optimization in parallel, and the optimization process is coordinated by the upper-level decision unit (coordinator). Each decision unit and coordinator find the optimal solution by iterating with each other. The important contributions of Polish scholar Findeisen and others must be mentioned here.

Because the more accurate mathematical models of industrial processes are not easy to obtain, and industrial processes (objects) tend to be non-linear and slow time-varying, Polish scholar Findesien proposed that the solution obtained by the model in the optimization algorithm is an open-loop optimization solution. In the design phase of on-line steady-state control of large industrial processes, open-loop solutions can be used to determine the optimal operating point. However, in practical use, this solution may not be able to make the industrial process in the optimal working conditions, but will also violate constraints. The new idea they proposed is: extract the steady-state information of the associated variables from the actual process and feed it back to the upper-level coordinator (global feedback) or local decision unit (local feedback), and use it to modify the optimal solution based on the model To bring it closer to the true optimal solution.

(4) Integrated research method for system optimization and parameter estimation

The difficulty of steady-state hierarchical control is that the input and output characteristics of the actual process are unknown. The feedback correction mechanism proposed by Polish scholars can only obtain a suboptimal solution. However, its main disadvantage is that it is generally difficult to accurately estimate the degree of deviation of the suboptimal solution from the optimal solution, and the suboptimal degree of the suboptimal solution often depends on the selection of the initial point. A natural idea is to separate optimization and parameter estimation and alternate them until the iterations converge to a solution. In this way, the computer's online optimization control includes two parts of the task: the optimization based on the rough model (the rough model is usually available) and the modified model under the set point. This method is called an integrated research method for system optimization and parameter estimation. (Integrated System Optimization and Parameter Estimation)

Intelligent optimization method of best control model

For more and more complex control objects, on the one hand, the required control performance is no longer limited to one or two indicators; on the other hand, the above-mentioned various optimization methods are based on the optimization problem and have accurate mathematical models. Based on. However, many practical engineering problems are difficult or impossible to obtain accurate mathematical models. This limits the practical application of the above-mentioned classical optimization methods. With the development of fuzzy theory, neural networks and other intelligent technologies and computer technology.

Intelligent optimization methods have been valued and developed.

(1) neural network optimization method

The study of artificial neural networks originated in 1943 with the work of Mc Culloch and Pitts. In terms of optimization, Hopfield first introduced the Lyapuov energy function to judge the stability of the network in 1982, and proposed a Hopfield single-layer discrete model; Hopfield and Tank developed the Hopfield single-layer continuous model. In 1986, Hopfield and Tank directly matched electronic circuits with Hopfield models to implement hardware simulation. Kennedy and Chua proposed analog circuit models based on nonlinear circuit theory, and used the Lyapuov function of the system differential equations to study the stability of electronic circuits. These works have strongly promoted the research on neural network optimization methods.

According to the neural network theory, the minimum point of the energy function of the neural network corresponds to the stable equilibrium point of the system, so that the solution of the minimum point of the energy function is converted to the stable equilibrium point of the system. With the evolution of time, the orbit of the network always moves in the direction of decreasing energy function in space, and finally reaches the equilibrium point of the system-that is, the minimum point of the energy function. Therefore, if the stable attractor of the neural network dynamic system is considered as the minimum point of the appropriate energy function (or augmented energy function), the optimization calculation will reach a minimum point with the system flow from an initial point. If the concept of global optimization is applied to the control system, the objective function of the control system will eventually reach the desired minimum point. This is the basic principle of neural optimization calculations.

As with general mathematical planning, neural network methods also have weak points that focus on more analysis times. How to combine with structural optimization techniques such as approximate reanalysis of structures and reduce the number of iterations is one of the future research directions.

Since the Hopfield model can be applied to both discrete and continuous problems, it is expected to effectively solve the nonlinear optimization problem of mixed discrete variables commonly found in control engineering.

(2) Genetic algorithm

Genetic algorithm and genetic programming are a new search and optimization technology. It imitates the evolution and inheritance of living things, and according to the "survival of the fittest" principle, it gradually approaches the optimal solution from the initial solution. In many cases, genetic algorithms are significantly better than traditional optimization methods. This algorithm allows the problem to be solved to be non-linear and discontinuous, and can find the global optimal solution and the suboptimal solution from the entire feasible solution space, avoiding to get only the local optimal solution. This can provide us with more useful reference information for better system control. At the same time, the process of searching for the optimal solution is instructive, which avoids the dimensional disaster problem of general optimization algorithms. With the development of computer technology, these advantages of genetic algorithm will play an increasing role in the field of control.

Research shows that genetic algorithm is a structural optimization method with great potential. It is used to solve complex optimization problems such as nonlinear structural optimization, dynamic structural optimization, shape optimization, and topology optimization. It has great advantages.

(3) Fuzzy optimization method

Optimization problems have always been one of the most widely used areas of fuzzy theory.

Since Bellman and Zadeh pioneered this research in the early 1970s, their main research has focused on theoretical research in the general sense, fuzzy linear programming, multi-objective fuzzy programming, and fuzzy programming theory in stochastic programming and many practical problems. Application. The main research method is to use the a-cut of fuzzy sets or determine the membership functions of fuzzy sets to transform fuzzy programming problems into classic programming problems to solve.

The fuzzy optimization method has the same requirements as the ordinary optimization method. It still seeks a control scheme (that is, a set of design variables), satisfies the given constraints, and makes the objective function the optimal value. The only difference is that it contains fuzzy factors. Ordinary optimization can be reduced to solving a common mathematical programming problem, and fuzzy programming can be reduced to solving a fuzzy mathematical programming problem. Contains control variables, objective functions, and constraints, but the control variables, objective functions, and constraints may be vague, or one aspect may be vague and the other aspects clear. For example, fuzzy factors in the optimization design problem of fuzzy constraints are contained in constraints (such as geometric constraints, performance constraints and human constraints, etc.). The basic idea of solving fuzzy mathematical programming problems is to transform fuzzy optimization into non-fuzzy optimization, that is, ordinary optimization problems. Methods can be divided into two categories: one is to give a fuzzy solution; the other is to give a specific crisp solution. It must be pointed out that the above solutions are all proposed for fuzzy linear programming. However, most practical engineering problems are described by fuzzynonlinear programming. So some people proposed the level cut method, the bounded search method and the maximum level method, etc., and achieved some promising results.

In the field of control, fuzzy control is integrated with self-learning algorithms, fuzzy control and genetic algorithms. By improving the learning algorithm and genetic algorithm, according to a given optimization performance index, the controlled object is gradually optimized and learned, which can effectively determine Structure and parameters of fuzzy controller.