Two-relay controller for real-time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum

A sliding mode control is developed to solve the tracking control problem for an inertia wheel pendulum. The desired trajectory is centered at the upright position where the open-loop system becomes a non-minimum-phase system. As a first step towards the solution of the tracking control problem is the reference trajectory generation where we develop a reference model, based on the two-relay controller, to generate a set of desired trajectories for the inertia wheel pendulum. The two relay controller produces oscillations at the scalar output of an underactuated system where the desired amplitude and frequency are reached by choosing its gains. The well-known second order sliding mode controller is capable of making the pendulum move tracking the prescribed reference signals determined by the trajectory generator. Performance issues of the controller constructed are illustrated in a simulation study.