VS-control with time-varying sliding sector - Design and application to pendulum

In general, a Variable Structure (VS) system is designed with a sliding mode. Recently a sliding sector, designed by an algebraic Riccati equation, has been proposed to replace the sliding mode for chaffering-free VS controllers. In this paper we extend the design algorithm for the sliding sector to a time-varying sliding sector. The time-varying sliding sector is defined by functions dependent on both state and time, hence time-varying uncertainty can be considered. The VS controller is designed to stabilize an uncertain system, quadratically. The design procedure for real systems is introduced via an implementation to the control of "Furuta pendulum". To enhance the stability it is necessary to compensate the time-varying nonlinear static friction of the actuator adequately, hence this problem is a good example to demonstrate the performance of the proposed VS control method. In the experiment, it will be shown that the VS control with the time-varying sliding sector is superior to an orthodox chattering-free VS control.