Energy-based control design of an underactuated 2-dimensional TORA system

The translational oscillation with a rotational actuator (TORA) system has been used as a benchmark for motivating the study of nonlinear control techniques. In this paper, modeling and control of a novel 2-dimensional TORA (2DTORA) are presented. The 2DTORA is an underactuated mechanical system which has one actuated rotor and two unactuated translational carts. The dynamics of the 2DTORA system is derived based on Lagrange equations. The total energy of the system is employed to show the passivity property of 2DTORA, and then a simple state feedback control algorithm is developed based on a proper Lyapunov function including energy item. Finally, simulation results are demonstrated.