Adaptive Control for Jib Crane with Nonlinear Uncertainties

This paper presents a robust LQ control system with Model Reference Adaptive Control (MRAC) law for a jib crane. Our approaches show that the robust control performance is improved in the presence of nonlinear uncertainties by adding MRAC law into the usual robust control system. The proposed system is synthesized as follows. Firstly, the process to design a robust LQ controller in the framework of the redundant descriptor representation is considered. The robust LQ controller is designed for uncertainties, which can be linearly treated in controller synthesis. Secondly, the adaptive law with a-modification is designed into the robust LQ control loop. The adaptive law is considered for nonlinear uncertainties. The feature of this study is to deal with nonlinear uncertainties, which can not be linearly treated in robust LQ controller synthesis, by adding the adaptive law. The exponential stability for the homogeneous system is analyzed through solving quadratic stability condition. Finally, the effectiveness of the proposed system is verified by comparing with the robust LQ controller without MRAC law in simulations with using the jib crane.