Coupling-Energy-Based Antiswing PD Control for a General <i>n</i> -Link Pendulum–Cart System: Theory and Experimental Validation

In this article, we study the antiswing control of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>-link pendulum–cart system with viscous friction at each joint of the pendulum. We justify the necessity of using this system to model the dynamic characteristics of the overhead crane under various operational conditions. We introduce a new concept of the horizontal translational kinetic energy of the center of mass (COM) of the system as a basis to construct a new coupling energy and a new coupling displacement signal for enhancing the coupling between the actuated cart and the unactuated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>-link pendulum. Based on the coupling energy and the signal, we present an energy-based antiswing controller for the system and theoretically demonstrate the asymptotic stability of the downward equilibrium point (DEP), where the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>-link pendulum extends straight downward and the cart remains in a desired position. The energy-based controller features a simple structure with clear physical meanings. Moreover, we provide a method to determine the coupling gain and two control gains. Through hardware experiments implemented on a two-link pendulum–cart platform, we validate the effectiveness and robustness of our presented controller.