The design of variable damping in the position control of a flexible single link arm is considered. Variable damping is obtained from velocity feedback with variable gain or from actuator variation. The variable damping is related to the position of the arm. The design process begins with the development of a nondimensional mathematical model of a flexible beam with one flexural mode, an actuator, and feedback control. Optimal control/arm parameters are determined for a constant damping system. Dynamic design sensitivity analysis is used to construct a variable damping scheme. Optimal scheme parameters are determined. A variable damping scheme that applies little damping for most of the motion and a great deal of damping as the arm nears its final position emerges. Vibration suppression is controlled in an optimal fashion throughout the motion. The resulting system provides a minimum response time with negligible overshoot for the tip of the arm. Numerical simulations demonstrate the method.

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