Exponential Stabilization of the Inertia Wheel Pendulum Using Dynamic Surface Control

This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlinear controller design, fusing the recently introduced Dynamic Surface Control and the Control Lyapunov Function method, is presented as the solution. Stability is analyzed using concepts from Singular Perturbation Theory. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations.