Second order sliding mode tracking controller for inertia wheel pendulum

A second order sliding mode control is developed to solve the tracking control problem for an inertia wheel pendulum. The periodic motion of the pendulum will be at the upright position around the unstable equilibrium point of the unforced system. A two relay controller (TRC) produces oscillations at the scalar output of an underactuated system where the desired amplitude and frequency are reached by choosing the controller gains properly. In this paper, a reference model is developed, based on the two-relay controller, to generate a set of desired trajectories for the inertia wheel pendulum and then design a robust tracking controller. Poincaré-map based design was used to obtain the corresponding parameter values of the TRC. A second order sliding mode tracking controller will be capable to track the prescribed reference trajectory. Performance issues of the constructed controller are illustrated in an experimental study.