SYNTHESIS OF FIXED ORDER STABILIZING CONTROLLERS USING FREQUENCY RESPONSE MEASUREMENTS
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In this paper, a method is proposed for synthesizing sets of stabilizing controllers of strictly proper, delay-free, Single Input, Single Output Linear Time Invariant (LTI) plants directly from their empirical frequency response data and from some coarse information about them. The coarse information that is required is the following: the number of non minimum phase zeros of the plant and the frequency range beyond which the phase response of the LTI plant does not change appreciably and the amplitude response goes to zero. It is assumed that the LTI plant does not have purely imaginary zeros or poles. The method of synthesizing stabilizing controllers involves the use of generalized Hermite-Biehler theorem for rational functions for counting the roots and the use of recently developed Sum-of- Squares techniques for checking the non-negativity of a polynomial in an interval through the Markov-Lucaks theorem. The method does not require an explicit analytical model of the plant that must be stabilized or the order of the plant, rather, it only requires an empirical frequency response data of the plant. The method also allows for measurement errors in the frequency response of the plant. Copyright 2006 IFAC.
