Dynamics and energy-based control of TORA system on a slope

The Translational Oscillators with Rotating Actuator (TORA) is an underactuated system which has one actuated rotor and one unactuated translational cart. This paper focuses on dynamics and control design of an underactuated TORA on a slope. Lagrange Equations are employed to achieve the dynamics of the TORA on a slope by selecting position of a cart and rotor angle as the general coordinates and torque acting on the rotor as general force. Based on the passivity of the system, a control Lyapunov function including system energy is designed. Consequently, a stabilizing controller is yielded based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of the dynamic analysis and stabilizing controller.