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The authors illustrate how the nonadaptive part of the desired compensation adaptive law (DCAL) is a special case of a class of controllers that can be used to obtain a global stability result for the trajectory following problem for robot manipulators. This class of robot controllers is a simple linear proportional derivative (PD) controller plus additional nonlinear terms that are used to compensate for uncertain nonlinear dynamics. To analyze the stability of this class of controllers, Lyapunov's second method is used to derive a global uniform ultimate boundedness (GUUB) stability result for the tracking error. How the controller gains can be adjusted to obtain better tracking performance in spite of the uncertainty present in the robot manipulator dynamic equation is shown.>
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Dawson et al. (1992) studied this question.
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