Tuning Fuzzy PID Controllers

After the development of fuzzy logic, an important application of it was developed in control systems and it is known as fuzzy PID controllers. They represent interest in order to be applied in practical applications instead of the linear PID controllers, in the feedback control of a variety of processes, due to their advantages imposed by the non-linear behavior. The design of fuzzy PID controllers remains a challenging area that requires approaches in solving non-linear tuning problems while capturing the effects of noise and process variations. In the literature there are many papers treating this domain, some of them being presented as references in this chapter. Fuzzy PID controllers may be used as controllers instead of linear PID controller in all classical or modern control system applications. They are converting the error between the measured or controlled variable and the reference variable, into a command, which is applied to the actuator of a process. In practical design it is important to have information about their equivalent input-output transfer characteristics. The main purpose of research is to develop control systems for all kind of processes with a higher efficiency of the energy conversion and better values of the control quality criteria. What has been accomplished by other researchers is reviewed in some of these references, related to the chapter theme, making a short review of the related work form the last years and other papers. The applications suddenly met in practice of fuzzy logic, as PID fuzzy controllers, are resulted after the introduction of a fuzzy block into the structure of a linear PID controller (Buhler, 1994, Jantzen, 2007). A related tuning method is presented in (Buhler, 1994). That method makes the equivalence between the fuzzy PID controller and a linear control structure with state feedback. Relations for equivalence are derived. In the paper (Moon, 1995) the author proves that a fuzzy logic controller may be designed to have an identical output to a given PI controller. Also, the reciprocal case is proven that a PI controller may be obtained with identical output to a given fuzzy logic controller with specified fuzzy logic operations. A methodology for analytical and optimal design of fuzzy PID controllers based on evaluation approach is given in (Bao-Gang et all, 1999, 2001). The book (Jantzen, 2007) and other papers of the same author present a theory of fuzzy control, in which the fuzzy PID controllers are analyzed. Tuning fuzzy PID controller is starting from a tuned linear PID controller, replacing it with a linear fuzzy controller, making the fuzzy controller nonlinear and then, in the end, making a fine tuning. In the papers (Mohan & Sinha, 2006, 2008), there are presented some mathematical models for the simplest fuzzy PID controllers and an approach to design