Fuzzy-PID Controllers vs. Fuzzy-PI Controllers M. Santos*, S. Dormido**, J. M. de la Cruz* *Dpto. de Informática y Automática. Facultad de Físicas. (UCM) **Dpto. de Informática y Automática. Facultad de Ciencias. (UNED) Ciudad Universitaria s/n. 28040-MADRID (Spain). FAX: (34)-1-3944687 e-mail: msantos@eucmax.sim.ucm.es Abstract The synthesis of a control system includes both the controller selection and the adjustment of its parameters. In some cases, the type of controller might be more complex or more general, like PID instead PI or PD, to improve the control system performance. In all cases, the tuning problem must be satisfactorily solved. On the other hand, Fuzzy Control has made possible the establishment of intelligent control. However, Fuzzy Logic Controllers (FLC) are only used in simple configurations and their analytic knowledge is still poor. In this paper, a quantitative and qualitative study of fuzzy controllers is done for the most complete case of a Fuzzy-PID. The FLC-PID analytic performance is summarized in terms of its three input variables, which allows us to obtain initial values for the FLC-PID scale factors in terms of the classical PID parameters. This initial tuning has been tested for several systems and a qualitative tuning has also been established. The advantages of the derivative term are also examined. 1. Introduction The need for simple advanced control alternatives especially arises in the Control Process area, where most of the real processes are generally complex and difficult to model [1]. The application of Fuzzy Logic to a wide range of control applications has made possible the establishment of intelligent control in these areas [4], [5]. Its appeal, from the Process Control Theory point of view, lies in the fact that this technique provides a good support for translating the heuristic knowledge of the skilled operator, expressed in linguistic terms, into computer algorithms. Fuzzy Control solves real problems, previously not tackled due to their complexity or to lack of information [9]. However, Fuzzy Logic Controllers (FLC) are usually applied with poor analytic knowledge of their behavior and only in simple configurations. In fact, they normally perform like PI or PD. FLC-PI controllers are quite simple, though they are the most widely used in practice and provide similar results to conventional controllers. But in some applications it may be useful to employ more general controllers, which make it easier to reach the system specifications and improve their performance, though they can be also more difficult to tune. The complete study of fuzzy controllers should involve all the terms of conventional controllers. The third control action must be included so as to consider the FLC-PID case. Though the derivative term is not commonly included -neither in the conventional case-, this allows us to complete the development of Fuzzy controllers in a similar way that of the classical ones. It also makes it possible to obtain certain conclusions about their stability and specifications. But the main problem in the synthesis of a control system is not only the selection of a specific controller but also the adjustment of its parameters, to verify certain given specifications for the controlled process. In this paper an analytic study of the FLC-PID is carried out in section 2, which allows us to establish an equivalence between the FLC-PID and a conventional PID; thus a tuning method is proposed for these fuzzy controllers and is then evaluated. The qualitative analysis is done in section 3. The behavior of these controllers is compared with the FLC-PI type in section 4 and some general conclusions are summarized in the last section. 2. Analytic study of the FLC-PID controller The aim of a controller is to reach or maintain a process in a specific state, by monitoring a set of variables and selecting the adequate control actions. The Fuzzy-PID controller performs like its classical homonym, but both the input variables and the control action are given in linguistic terms. The analytic development of fuzzy controllers allows us to explain the influence of each tuning parameter on the system