Two relay based control for orbital stabilization of inertia wheel pendulum—The bounded input case

We study the orbital stabilization problem of an inertia wheel pendulum (IWP) where a two-relay controller will be used to induce oscillations at the pendulum. The main focus of the paper is the consideration of the viscous friction force and saturation of the actuator. A two relay controller produces oscillations at the scalar output of the plant where the desired amplitude and frequency are reached by choosing its gains but now we consider the bounded input restriction in the design. Condition in frequency and amplitude will be explicitly given leading to permissible controller parameter design. Performance issues of the controller constructed are illustrated in an experimental study.