In many applications, a robot end-effector (the tip) is required to follow a prescribed trajectory. This task is not easy to achieve for a flexible-link robot because it is known that the transfer function from the joint-torque input to the tip-position output is nonminimum phase. Output redefinition techniques have been proposed so that the transfer function of the system with this new output is minimum phase and this facilitates the design of trajectory tracking controllers. There are various output functions suggested in the literature. Along this line of development, a new output function is suggested. The authors show that the zero dynamics of a single-link flexible robot is exponentially stable with the newly defined output function. Asymptotic tracking of step input, linear and second-order polynomial trajectories are achieved using controllers designed based on this new technique and the link vibrations are damped out significantly. The unique feature of the controller design technique is that the poles of the zero dynamics can be placed at any desired locations in the left half of the s-plane. This enables the suppression of undesirable vibrations while the robot tip is tracking a prescribed tip-trajectory.
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