The Research Of Fuzzy PID Control Based On Quotient Space

With the progress of The Times and the improvement of industrial level, industrial control system becomes more and more complex. Industrial control system not only shows the highly nonlinear and uncertainty, but also has the characteristics of strong coupling, the incompleteness of information and large time-delay and so on. And the constraint conditions of industrial control system is also more and more strict. There exists many problems in the process of industrial control with the conventional control method and we unable to get satisfactory control effect. Therefore, it promotes the improvement of the industrial control technology and method. Many advanced industrial control technology arises.Fuzzy control is an important part of intelligent control in the modern control theory. Fuzzy control is a control theorem based on fuzzy set theory. It is based on language rules and fuzzy reasoning. The method that is most commonly used is PID control. It does not have the advantage of simple structure and easy to operate, but also have strong robustness, the steady state without anti static advantage. So a new method formed called fuzzy PID control that combines the fuzzy control and PID control. On the one hand, fuzzy control can make up for the shortage of PID control that it is not applicable to the controlled object of nonlinear and the mathematical model without precise. On the other hand, the fuzzy control can’t accurately control the controlled objects. So it has the weakness of rough control effect and the low accuracy. PID control also improve these advantages. In short, the fuzzy PID control not only has the characteristics of strong adaptability and flexible control, but also has higher accuracy and rapidity.Though the subject of granular computing arises late, it develops rapidly. Granular computing not only combines the essence of rough set and artificial intelligence, but also combines the results of fuzzy sets and theory of data mining, and other research results. Granular computing has changed the traditional calculating model of searching the precise solution.It can not only study the uncertainty and fuzzy objects, but also study the vast and imprecise data by computing the approximate solution. Therefore, granular computing is different from the traditional concept of computing. It is a new concept of processing information and computing model. It is more convenient and scientific for processing information. At the present time, the computing theory based on quotient space theory, the computing theory based on rough set theory and the computing theory based on fuzzy logic theory are the most important theories in the granular computing.Quotient space theory is a very important component part in the granular computing theory. It describes a problem with a triple (X, f, T).In this paper, we combine the quotient space theory and the PID control theory by using the quotient space theory to solve the problem. Therefore, a new method is formed that we use fuzzy control to solve the problem at a coarse granularity and use PID control at a fine granularity. It solves the problem of the fuzzy control rules index explosion and improve the precision and speed of the whole control system.Double inverted pendulum system is not only a nonlinear and unstable control system, as well as a control system with multivariate and rapid change. When we use the conventional fuzzy control theory to control it, there will be a problem of the fuzzy rules index explosion because of the multivariate. In this paper, we use the fuzzy PID controller based on the quotient space theory for double inverted pendulum system and constitute two levels of coarse and fine layers. We use the fuzzy control at the level of coarse granularity to realize the stability of the system and use the PID control at the level of fine granularity to obtain the ideal control performance. Finally, use the MATLAB7.0to simulate the double inverted pendulum system.