LAUSR

Interconnection and damping assignment passivity-based control (IDA-PBC) has been successfully applied to many mechanical, electrical, and electromechanical systems. For the control of such systems, existing IDA-PBC methods have concentrated on systems with underactuation degree one, such as the ball and beam system, the vertical takeoff and landing aircraft, and the pendulum on a cart. In this paper, we focus on the application of the IDA-PBC methodology to the regulation control of a three-dimensional (3D) overhead crane system with underactuation degree two. The goal of this study is to design and analyze a regulation controller that can drive the cart to the desired position precisely and eliminate the payload swing effectively. To achieve this challenging objective, we first find an ingenious way to solve partial differential equations for constructing a Lyapunov function candidate. Then, we devise a nonlinear controller on the basis of the constructed Lyapunov function and analyze the stability of the closed-loop system by using Lyapunov techniques and LaSalle’s invariance principle. Finally, both simulation and experimental results demonstrate the proposed strategy can achieve excellent positioning accuracy and significant swing elimination, and a comparison study between the proposed method and the existing PBC method is included as well.