Geometric-PBC based Control of 4-DOF Underactuated Overhead Crane System

The control of 4-DOF underactuated overhead crane system poses a challenging control problem as it has extra degree of freedom (DOF) compared to its popular 3DOF variant. The extra DOF represents strong state coupling and hence more complicated system dynamics. We propose Geometric Passivity Based Control (PBC) methodology for synthesis of nonlinear stabilising feedback control law. The structure of the split tangent space is modified along the actuated direction in such a way that the power flow is established between the controller and the un-actuated subsystems. The passivating outputs of the modified system are identified which are utilized for energy shaping of the system. The nonlinear control law thus obtained achieves the control objective of precise payload positioning with elimination of payload swings. The main advantage of proposed nonlinear design methodology is that obviates the need of solving PDE’s or obtaining nonlinear transformations to synthesize the control law. The simulation results are presented to validate the nonlinear control law. The system parameters and constraints on input forces are considered to represent the experimental setup of 4-DOF overhead crane system.