Nonlinear control of a trolley crane system

This paper addresses the control system design for a trolley crane system. The challenges in the control design task arise from the under-actuated nonlinear multi-input multi-output nature of the system. The trolley crane system has three-degrees of freedom that need to be controlled: the lateral and vertical positions of the load and its angular oscillations. The paper develops a nonlinear controller for the trolley crane system using Lyapunov functions and a modified version of sliding-surface control. The nonlinear controller guarantees stability of the closed-loop system and also ensures that the internal dynamics are well-behaved. Theoretical bounds are established for trajectory tracking errors. Simulation results demonstrate the performance and robustness of the developed control system