A robust controller design method for a flexible manipulator with a time varying payload and parameter uncertainties

Abstract

A new robust controller design method is proposed to obtain a less conservative feedback controller, and applied to a single-link flexible manipulator. The objective is to maximize the control performance guaranteeing the robust stability when regulating the tip position of the flexible manipulator in the presence of a large time varying payload and parameter uncertainties such as stiffness, joint friction. Descriptor form representation, which allows separate treatment of payload uncertainty from other parametric uncertainties, is used to reduce the conservatism of the conventional robust control approaches. Uncertainty of the payload included in the left-hand side inertia matrix and the uncertain parameters included in the right-hand side damping and stiffness matrices are treated with polytopic and descaling techniques, respectively. Using aforementioned techniques, the robust LQ controller design problem for a flexible manipulator is formulated based on the guaranteed cost approach. Then, the formulated problem has been solved by LMIs.