Optimal Nonlinear Control for a 2D Under-Actuated Crane System Based on Harmony Search Algorithm

Container crane is an under-actuated system, which is why it is much more difficult to control such systems. In this paper, partial feedback linearization and sliding mode controllers are employed to control a 2D container crane with varying cable length. Since, the dynamic model of the system cannot present the real one and the system contains some uncertainties, a controller is designed to reduce the effect of model uncertainties and external disturbances. Since the considered system is under-actuated, in order to design controller, first, dynamics of the system is divided into two parts, actuated and under-actuated. Then, stability of the controllers is discussed. An objective function is considered as the combination of integral of absolute error and rate of variation of control signal. The introduced objective function is minimized employing Harmony Search and particle swarm optimization algorithms and optimum values for parameters of the designed controllers are determined to make it possible to compare performance of the mentioned controllers in their optimum conditions. Simulation results show suitable performance of the designed controllers by harmony search algorithm for the 2D crane in the presence of mass uncertainty, actuator disturbances and sensor noises.