An Effective Two-time Scale Composite Control Contraction Based Chaotic Trajectory Tracking of Two-link Flexible Manipulator

In this paper, a two-link flexible manipulator n-dimensional model is developed using the assumed modes method. Based on this model, the manipulator dynamics are segregated into two subsystems by the two-time scale decomposition method of singular perturbation. Subsequently, a contraction-based control theory and a backstepping control of composite controller are investigated for the desired chaotic trajectory tracking along with tip deflection vibration suppression. In the two subsystems, the slow subsystem is involved in the modelling of the joint angles, and the fast subsystem is for corrected flexible modes of vibration suppression. In order to guarantee strict stability, Lyapunov's stability is realized for closed-loop system uniform boundedness. Thus, by choosing the control parameters appropriately, the system states converge to a neighborhood of asymptotic stability. Eventually, extensive validation by comparative simulations of the Quanser model of the two-link flexible manipulator is carried out to demonstrate and indicate the effectiveness of the proposed composite controller in terms of faster tip deflection vibration suppression and better trajectory tracking.