Modelling and μ-synthesis control of flexible manipulators

A dynamical model for a flexible manipulator is derived using the Timoshenko beam theory and the assumed mode method. A control design model is subsequently obtained. The linear model is qualitatively compared to the original model and the discrepancies are quantified in terms of uncertainty weights and included in the control design process. The μ-synthesis control design technique is then used to synthesize robust controllers for the flexible robot arm using different feedback signals. The designed controllers have lead to good tip tracking especially when a sensor is placed at the tip. The derived controllers are robust to unmodelled dynamics, input and actuation uncertainties, and noise.