Abstract
SUMMARYWe consider here motion control of the end‐point of a one‐link flexible manipulator. The partial differential equations of motion are derived from Hamilton's principle and include the effect of ‘centrifugal stiffening’ arising from the presence of axial forces, as well as other non‐linear terms. The desired trajectory is assumed to be given prior to the execution of motion. An optimal control law which minimizes a performance index that trades off the tracking precision and the terminal position accuracy versus control effort is obtained. This control law is composed of a feedforward term that depends on the desired trajectory and a full state feedback term with a time‐varying gain matrix. Since the optimal control law requires the availability of the full state vector, the output feedback is considered as an alternative. We propose to determine the output feedback control law by minimizing the least squares difference between the feedback portions of the optimal control input and the actual input. The basic structure of the optimal control law, which includes the feedback and feedforward terms, is preserved. The results of simulations demonstrate that when the outputs are carefully selected, the performance of the system with the output feedback can closely approach that of the optimal system with full state feedback.
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