Stabilizing Control of an Underactuated 2-dimensional Tora with Only Rotor Angle Measurement

One dimensional 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, a novel underactuated 2-dimensional TORA (2DTORA), which has one actuated rotor and two unactuated translational carts, is presented. The analysis of controllability around the system’s equilibriums yielded the controllable equilibriums and the constraint on physical parameters. To stabilize the system to its controllable equilibriums from any initial conditions, we propose a simple linear controller containing the rotor angle and angular velocity. The controller was derived from a proper Lyapunov function, including the system’s total energy, that was used to show the passivity property of the system. In addition, a high pass filter was adopted to approximately differentiate the rotor angle so that an estimated angular velocity was used in the controller rather than measuring the actual rotor angular velocity. As a result, only the angle measurement is required for the designed feedback controller to stabilize the underactuated system. Finally, simulation results verify our control design and analysis.