Stabilisation designs for the inertia wheel pendulum using saturation techniques

In this article, three new global stabilisation designs are presented for the inertia wheel pendulum (IWP) using saturation techniques. The first controller is obtained using a twice differentiable saturation function and the backstepping technique. Without using the backstepping technique, the other two controllers are achieved in such a way that the IWP is equivalently transformed into a feedforward system with higher order terms, and then corresponding saturated controllers are put forward. The central idea of the latter two designs is to attenuate the higher order terms by selecting small saturation levels. For the three designs, global asymptotical stability is proven in a bottom-up manner, by showing that the closed-loop system has no finite escape time and reduces to an asymptotically stable dynamics. Simulation results show that the proposed control laws are effective.