Fuzzy logic-based tuning of the boundary layer thickness of the variable structure controller

Abstract

The variable structure control (VSC) is a simple and powerful nonlinear controller, but it leads to a high frequency chattering on the control input. To decrease the chattering phenomenon of the VSC, a boundary layer is commonly introduced. Then its thickness requires a compromise between the steady state error and the chattering amplitude. In this paper, we propose a new VSC that tunes the boundary layer thickness using the fuzzy logic system. The tuning methods presented are two: One uses absolute error and its derivative as fuzzy input variables, which decreases the number of tuning rules as compared with using common fuzzy variables of error and change of error. The other uses only a single fuzzy variable of a distance. This variable is derived by the property of two-dimensional rule table which is composed of absolute error and its derivative. Since the second method uses a single variable for tuning the thickness, the number of tuning rules is greatly decreased. Furthermore, we obtain the good tracking performance which is almost the same as that of the first method. To ensure the control performance in both cases, we perform computer simulations using an inverted pendulum as a controlled plant.