Approach angle-based switching function for sliding mode control design

This paper investigates a novel continuous switching function for a sliding mode controller. This novel continuous switching function incorporates the state trajectory approach angle, which is a measure of the orientation of the state trajectory with respect to the sliding surface. By incorporating the state approach angle into the switching function, the overall sliding mode controller guarantees that the system achieves asymptotic stability, with only a slight amount of system chattering. The novel switching function overcomes the shortcomings of a pure discontinuous switching function (excessive system chattering) and a traditional continuous switching function (does not ensure asymptotic stability). In addition, a hybrid sliding mode control structure, such as fuzzy-sliding mode control, is avoided. A sliding mode controller that utilizes the proposed switching function is applied to the classic nonlinear inverted pendulum. The effectiveness of the sliding mode controller is shown via the results of a simulation.