Design Of A Sliding Mode Controller For A Tora System

Abstract

This paper presents the design of a sliding mode controller for an uncertain model of a TORA system (Translational Oscillations with a Rotational Actuator) as a two DOF underactuated mechanical system. The switching function is selected to make the TORA system an asymptotically stable mass-spring system with a nonlinear damping effect when the sliding mode controller constrains the state to the sliding manifold. This sliding mode controller is derived here according to a new formula consisting of continuous and discontinuous parts. The main obstacle in the controller design is the uncertainty in the switching function, which appears in the controller formula. The sliding controller is found effective in bringing the system state to the neighborhood of the equilibrium point in spite of the uncertainty in the switching function. In addition, the chattering problem is solved via the use of approximate signum function.