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In this paper, we present a speed regulator for a force-driven cart-pole system. The proposed controller allows bringing the pole towards its upright position, while the cart moves asymptotically at desired constant speed, recovering the position regulation when we assign a desired constant position of the cart. The main motivation for addressing speed regulation is to broaden the scope of control of underactuated mechanical systems, because so far, the control of this class of mechanical systems has been focused primarily on position regulation; and therefore, there is few information and results available on broader control objectives, such as speed regulation. In particular, we design a speed regulator for the cart-pole system, as this system is one of the more representative test benches of underactuated mechanical system found in many automatic control research laboratories. Another novelty is the introduction of an alternative energy shaping approach for the velocity control design of a class of underactuated mechanical systems. A complete asymptotic stability analysis based on the Lyapunov theory and the Barbashin–Krasovskii theorem is presented. Local asymptotic stability is concluded. Simulation results upon a force-driven cart-pole model illustrate the performance of the proposed controller.

A speed regulator for a force-driven cart-pole system