A Fuzzy Control Scheme for General Class of Nonlinear Systems

Abstract

This paper develops a stable fuzzy control scheme for a general class of nonlinear systems. Using the concept of local design and global interpolation, the developed scheme starts by probing the operating region of an unknown nonlinear system to determine a set of local points. Simple linear controllers are designed around these local points. The global control is then formed by interpolating these local controllers through a fuzzy modeling algorithm. One of the important features is that the fuzzy modeling algorithm used is adaptive in nature. which refines repeatedly the initial set of local points and interpolate to form a sequence of updated global controllers until the performance of the control system is satisfactory. The second feature is that such an adaptive design process can be shown to deliver a stable fuzzy controller. The analysis has been carried out to derive the conditions under which the stability of the overall control system are maintained. It appears that with the appropriate choices of learning parameters, there will be a guaranteed stability of the close-loop system. The third feature of the proposed scheme is that almost nothing is assumed about the dynamics of the nonlinear system to be controlled during the construction of the controller, This is unlike many of the nonlinear control techniques which require a detailed process model h order to design the control system. An illustrative example is also included to show the control system performance for the pH control, which is a typical nonlinear control problem.