斜面上TORA系统的动力学与控制设计

he 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. Based on Lagrange Equations, dynamics of the TORA is achieved by selecting position of a cart and rotor angle as the general coordinates and torque acting on the rotor as general force. According to the analysis of equilibriums and their controllability, 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 developed dynamics and stabilizing controller.