Adaptive rigid control of a rigid manipulator handling a flexible payload

An adaptive control scheme based on rigid control for a new model, in which a rigid manipulator handled a flexible payload which is simultaneously driven by an unknown force, is presented. The model of the whole system is derived. The uncertainty of the parameters of the manipulator is considered in the adaptive control scheme. The relationship between two internal forces is analyzed during the establishment of the mathematical model of the whole system. The adaptive rigid controller, which can guarantee the success of trajectory tracking while vibration is suppressed in the absence of the gravity force, is established. The disturbance aroused by part of the unknown force can be avoided using the predetermined compensation. Stability of the system is proven through Lyapunov stability theory. Simulations demonstrate the validity of the proposed controller.