A Robust Controller Design Method for a Flexible Manipulator with a Time Varying Payload and Parameter Uncertainties

A new robust controller design method is proposed to obtain a less conservative feedback controller and it is 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 and joint friction. A 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 in the inertia matrix is represented by polytopic approach and the uncertain parameters in the damping and stiffness matrices are treated with descaling techniques. Using aforementioned techniques, the robust LQ controller design problem for a flexible manipulator based on the guaranteed cost approach is formulated. Then, the formulated problem is solved by LMIs.