Backstepping boundary control of a wave PDA with spatially distributed time invariant unknown disturbances and its application to an overhead crane model

Abstract

The aim of this thesis is to control the speed of a payload carried by an overhead crane with the control input provided from the top end of the crane cable. It is assumed that the only measurement available to the controller is from the top end where the cable is attached to the crane car. The motion of the crane model is limited to one horizontal dimension. First, a controller is designed for a simplified mathematical model. The disturbance is assumed to be time invariant, the weight of the crane cable is neglected and the length of the cable is normalized. The exponential stability of this simplified model with the designed controller is proven. Then, the controller is applied to the real crane model with the necessary transformations. Performance of the controller in both cases is shown using numerical simulations in MATLAB. The models are simulated using semi-discretization method for the simplified model and Crank-Nicolson method for the crane model. Perfect reference tracking and disturbance cancellation is achieved under constant disturbances. However, in the presence of time varying effects, the model is stabilized but does not converge perfectly. This result is theoretically expected.