Orbitally stabilizing control for the underactuated translational oscillator with rotational actuator system: Design and experimentation

Underactuated translational oscillator with rotational actuator systems are simplified mechatronic systems introduced to investigate the despin maneuver phenomenon for dual-spin spacecrafts in mechanical engineering. The conventional research work for translational oscillator with rotational actuator systems mainly focuses on stabilizing control of equilibrium points. In this article, an orbitally stabilizing control strategy is proposed to steer oscillating movements of a translational oscillator with rotational actuator system. Based on the natural periodicity of translational oscillator with rotational actuator system self-sustained oscillation, the dynamics is analyzed to derive the periodically orbital functions of the translational oscillator with rotational actuator system. Then, a proper control Lyapunov function following the principle of energy conservation is designed to obtain orbitally stabilizing controller for target periodical oscillation orbits of the translational oscillator with rotational actuator system. Finally, the validity of the presented control strategy is demonstrated via the simulations and experiments.