Single-input fuzzy-like moving sliding surface approach to the sliding mode control

A new approach to the sliding mode control of second-order nonlinear systems is introduced in continuous-time. A single-input fuzzy logic controller is used to continuously compute the slope of the sliding surface, with the result that the sliding surface is rotated in such a direction that tracking performance of the system under control is improved. The proposed fuzzy moving sliding surface approach with a one-dimensional rule base (FMSS-1D) reduces huge number of linguistic fuzzy rules significantly. However, it is shown that the input/output relation of the single-input fuzzy rule base is very close to the input/output relation of a straight line. Therefore, a single-input fuzzy-like moving sliding surface (FLMSS) approach using an approximate line function is then proposed. It is shown that the proposed control approaches have better tracking performance than the conventional sliding mode control with fixed sliding surface. The proposed moving sliding surface approaches are applied to balance an inverted pendulum on a cart. Computer simulations are presented to show the effectiveness of the proposed methods and to make a quantitative comparison with the classical sliding-mode controller with fixed sliding surface method existing in literature.