Design of stabilizing controllers for underactuated TORA system

Translational oscillator with a rotational actuator (TORA) is an underactuated nonlinear mechanical system with two degrees of freedom (DOF). This paper discusses the stabilizing control problems for this system. Two stabilizing control strategies are presented based on Lyapunov theory and backstepping idea. The first strategy uses the backstepping idea to construct a Lyapunov function. The nonnegativity of the Lyapunov function guarantees the stabilizing control objective of the TORA to be achieved. The second one transforms the system into a cascade system. And the stabilization of the system is ensured by the cascade backsteeping theory. Simulation results demonstrate the validity of our developed control methods.