A dead-beat servo problem

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Abstract
The problem of tracking a reference variable from a given class is considered for discrete-time linear single-input-output plants. The plant and the reference are both described by an input/output relation, such as a difference equation, and the objective is to track exactly in a minimum time. This dead-beat servo problem is solved hero by applying polynomial techniques. The optimal control law is shown to contain both feed-back and feed-forward terms and it is obtained by solving two linear polynomial equations. The entire design procedure is remarkably simple and efficient.

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