Linear parameter varying modeling and robust control of cranes

Crane systems have a widespread use to transport heavy loads and hazardous materials in factories, shipyards, nuclear facilities, industrial areas and high-rise buildings. It is one of the classic and most basic problems to locate the payload with low sway as fast as possible during the movement of such systems. Accidental situations that can occur because of swaying heavy loads and can be caused by material damage and serious injuries. For these reasons, it is important to improve the dynamics of the crane in such a way that to provide high positioning precision and speed in order to reduce the most possible damage incidents. In addition to the above performance criteria, designing controllers which having time-varying dynamics, such as cable length, and payload uncertainties is a great deal of interest. It has been deemed appropriate to design a Linear Matrix Inequalities (LMI) based Gain Scheduling (GS) control law, by considering the Linear Parametric Varying (LPV) crane model. These controllers have been compared to various control structures and the superiority of these controllers has been emphasized. In this study, the cable length is considered as scheduling parameter to enable the design of GS controller on LPV gantry crane model. The state and control output vectors are augmented by integral term of reference tracking error, to ensure positioning without steady state error. In this case, the system has been turned into an I-PD + PD control structure. The elimination of steady-state errors and the mitigation of payload oscillations are achieved using convex optimization problem by minimizing the H∞ norm of the transfer function matrix from the reference inputs to the desired outputs to be controlled. In addition, the desired transient response characteristics are ensured by using LMI regions to constrain the closed-loop poles to the prescribed locations in complex plane. The performance of the proposed GS H∞ controller with LMI region constraints analyzed by comparing with nominal counterparts with and without LMI region constraints. As an additional study, the performance of the H∞ controller, which places the poles in the LMI regions, which treats the cable length and the load mass as parametric uncertainty, is also examined. Finally, another GS control structure on the LPV model is used and the parametric uncertainty of the payload mass consider as a polytopic uncertainty to design a robust controller. The performance of this proposed controller is also compared with the nominal case and analyzed against time varying parameters as well as against parameter uncertainties.