Parametric robust control by quantitative feedback theory

Abstract

The problem of performance robustness, especially in the face of significant parametric uncertainty, has been increasingly recognized as a predominant issue of engineering significance in many design applications. Quantitative feedback theory is very effective for dealing with this class of problems even when there exist hard constraints on closed-loop response. In this paper, single-input/single-output quantitative feedback theory is viewed formally as a sensitivity constrained multiobjective optimization problem whose solution cannot be obtained analytically but (when feasible) can be obtained graphically. In contrast to the more recent robust control methods where phase uncertainty information is often neglected, the direct use of parametric uncertainty and phase information in quantitative feedback theory results in a significant reduction in the cost of feedback. An example involving a standard quantitative feedback theory problem is included for completeness. Nomenclature A:=B = A is defined by B A -B = A is approximately equal toB e,r = relative degree of transfer function G H = H*° controller G Q = quantitative feedback theory controller H°° = Banach space of bounded analytic functions LOO = Banach space of essentially bounded Baire functions RH°° = Banach space of bounded analytic functions with elements from the ring of stable, proper real rational functions (unit of RH°° = an element of RH°° whose inverse 6 RH°°) S H = H°° sensitivity function SQ = quantitative feedback theory sensitivity function || • || oo = norm on LOO 0 = compact parameter space with elements a o;,X = radian frequency

Automatic loop shaping of QFT robust controllers with multi-objective specifications via nonlinear quadratic inequalities

“…The transfer function between the voltage input and the rotor position is: (34) where the parametric uncertainty is given by:…”

“…UANTITATIVE Feedback Theory (QFT) - [12], [21][22][23][24][25][26], [28][29][30], [34] and [37][38][39]-is a robust frequency domain control design methodology which has been successfully applied to many practical problems of different domains - [11], [13], [17] and [26]-. One feature that distinguishes QFT from other frequency-domain methods is its ability to deal directly with uncertainty models and robust performance criteria in a very transparent way.…”