Lyapunov theory based robust control of complicated nonlinear mechanical systems with uncertainty

This paper presents a robust control approach for nonlinear uncertain crane systems with a three DOF framework. We deal with an overhead crane in which a trolley located on the top is moved to x- and y-axes independently. We first approximate the nonlinear system model through feedback linearization transformation to simply construct a PD control and then design a robust control system for compensating control deviation feasibly occurring due to modeling error or system perturbation in practice. An adaptive control rule is analytically derived by using Lyapunov stability theory given bounds of system perturbation. We accomplish numerical simulation for evaluating the proposed methodology and demonstrate its superiority by comparing with the traditional control strategy.