Robust performance characterization of PID controllers in the frequency domain

In this paper a method is introduced for finding all proportional integral derivative (PID) controllers that satisfy a robust performance constraint for a given single-input-single-output transfer function of any order with time-delay. This problem can be solved by finding all achievable PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is that it only depends on the frequency response of the system and does not require the plant transfer function coefficients. If the plant transfer function is given, the procedure is still appropriate. The ability to include the time-delay in the nominal model of the system will often allow for designs with reduced conservativeness in the plant uncertainty and an increase in size of the set of all PID controllers that robustly meet the performance requirements.

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