On the energy shaping plus damping injection control of mechanical systems

This paper presents a tutorial about a controllers design method based on the energy shaping plus damping injection for the control of mechanical systems. A unified theoretical framework is provided to solve different control objectives such as: position regulation and speed regulation for both class of mechanical systems and, trajectory tracking for the case of fully actuated mechanical systems. Also, the energy regulation is formulated as a new control objective to generate controlled oscillations in both fully actuated mechanical systems and underactuated mechanical systems. In addition, some design criteria are addressed: dynamic friction compensation, exclusion of speed measurement and, inclusion of actuator dynamics. Finally, as examples of application, recent results published in the literature on the design of controllers for torque-driven robot manipulators, an inertia wheel pendulum, and a cart-pendulum system, are presented.