Stability Analysis of Fuzzy Control Loops

Abstract

Stability of feedback control systems is a main problem in control theory but also in control engineering. It is well known that the feedback loop is the basic structure to track reference signals and to regulate systems in spite of external perturbations. The feedback structure decreases the sensitivity to parameter variation and external disturbances, however the feedback could strongly affect the stability of the system. Thus, an unstable system can be stabilized by means of an appropriated feedback control loop. On the other hand, an open-loop stable system could be destabilized by means of feedback. The interest of the stability studies in fuzzy control has become a controversial question in the fuzzy logic literature. However, in many fuzzy logic industrial control applications, the practical interest of stability analysis cannot be questioned due to safety and reliability requirements. In fact, external disturbances and unexpected parameter changes are usually present in practical control system. Then, before efforts are made to satisfy any conventional control system performance related to speed or accuracy, the ability of a system to come to an equilibrium after external or internal disturbances (stability) is needed. Applications in power plants, chemical plants, vehicles, robots and many others require that the feedback control systems will satisfy this property, i.e., will be stable in all the possible working conditions. Furthermore, in many cases, it is very difficult to assess stability only by experimentation in several working conditions. Then, some tools to generalize the analysis and to be able to guarantee the stability of fuzzy control systems are required.