In this paper an adaptive optimal controller is constructed to perform servo tasks on mechanical systems that exhibit friction. Two adaptive optimal controllers, i.e., (i) a staticgain optimal controller and (ii) a gain-scheduled optimal controller, are derived by choosing a proper Lyapunov function based on a polytopic linear model. The controllers are compared to a classic PID-controller by means of experiments on a rotating arm subjected to friction. The gain-scheduled controller performs better with respect to static errors than the static-gain controller for positioning tasks. The servo error after setpoint is equal for both the PID-controller and the gain-scheduled controller, where the tracking behaviour of the PID-controller outperforms the optimal controllers. For velocity reversals the differences between the two proposed controllers are similar as for the servo task and the performance of the gain-scheduled controller and the PID-controller are comparable.
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