In this paper, an adaptive control algorithm is proposed to track deterministic reference trajectories while minimizing output variance subject to both deterministic and random disturbances. The proposed algorithm contains two independent adaptive control actions. The first adaptive action tracks and rejects a set of unidentified deterministic signals using an internal model principle type controller with online adaptive frequency identification. Using a novel new implementation the IMP, the stability of the system can be ensured. The other adaptive action minimizes the output variance subject to random disturbance using an adaptive finite impulse response filter. By making use of the internal model control structure, the two adaptive control actions are decoupled in both design and implementation. The stability and performance of the proposed algorithm are analyzed and demonstrated by experimental results on a Halbach linear motor for nano-precision positioning.

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