Virtual constraints based control design of an inclined Translational Oscillator with Rotational Actuator System

Abstract

Translational oscillator with rotational actuator (TORA) system, whose translational and rotational movements occur in horizontal planes, is a benchmark of underactuated mechanical systems for studying of control techniques. Currently, the research work of the benchmark mainly focuses on stabilizing control of equilibrium points of the dynamical system. The problem of steering TORA to arbitrary points in its state space is rarely studied. In this paper, the movements of the TORA system are extended to inclined planes and dynamics of the inclined TORA system is presented firstly. Following that, a trajectory tracking control method based on virtual constraints is proposed to steer the oscillations of the inclined TORA system. A virtual constraints based method is presented to generate periodic trajectories which pass through desired point; and a Lyapunov based control design is proposed to track the generated trajectories. Finally, the performance and feasibility of the proposed control design methodology are illustrated and analyzed according to numerical simulations.