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In this paper a new controller for the end-effector trajectory tracking (EETT) of multilink flexible manipulators (MLFM) is introduced. The new controller is derived utilizing the concept of the integral manifold of the singularly perturbed differential equations. Based on the new controller, to reduce the end-effector trajectory tracking error, a corrective term of order e 2 has to be added to the computed torque command (CTC) of the rigid link counterpart of the MLFM, where the parameter e = 1 / 2 π f and f is the smallest non-zero natural frequency (first natural frequency) of the MLFM in the specified range of operation of the manipulator. The implementation of the new controller does not require measurement of the time derivative of the links’ lateral deflections, which may be practically impossible. This is achieved since the time derivative of the links’ lateral deflections is estimated by using an observer, which is designed based on the gain-scheduling technique. The stability of the proposed controller is proven using the Lyapunov criterion. Simulation results showed the effectiveness of the new controller. One of the main contributions of this work is in the derivation of a new EETT controller for the MLFM, based on the integral manifold concept, which: (1) requires the fewest corrective terms in addition to the CTC and (2) its calculation effort is minimized. |
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