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-This paper presents a robust position controller for a one degree-of-freedom (DOF) mechanical system using only position measurement. In order to alleviate the performance degradation owing to various uncertainties, a two-stage design method is studied by employing a proportional integral observer (PIO). In the first stage, a baseline backstepping controller is designed for a nominal system without accounting for uncertainties. The PIO is developed for estimating both the velocity information for the backstepping controller and an equivalent input disturbance for a feedforward compensation using the estimated uncertainty. It is shown that the estimation errors with the proposed PIO can be made arbitrarily small in a finite time. If the system suffers from undesirable actuator nonlinearities, however, it might be necessary to estimate the velocity and the disturbance with different rates of convergence. The proposed method combines the predesigned backstepping controller and dual PIOs to reduce mechanical vibrations as well as steady-state errors. The performance of the proposed method is tested through comparative computer simulations and experiments using a laboratory prototype.

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