Energy Shaping for Tracking Control of 4-DOF Crane

摘要

In this paper the nonlinear tracking control methodology is proposed for 4-DOF (degree of freedom) overhead crane system using energy shaping. The 4-DOF underactuated overhead crane system has an extra DOF compared with the popular 3-DOF variant. The 4-DOF crane modeling represents strong state coupling and more complicated system dynamics which makes it challenging control problem. The control methodology begins with the first step of decoupling the crane dynamics into two subsystems using collocated partial feedback linearization. The passivating outputs of the modified subsystems are identified which are further utilized for energy shaping to obtain the nonlinear state feedback control law which effectively achieves the objective of trajectory tracking with fast elimination of payload swings. The energy shaping procedure obviates the need for solving PDEs to derive the control law. The trajectory tracking control law represents generalization of the position regulation problem. The simulation results are presented to validate the control law and superior performance is demonstrated over the existing control methodologies.