Optimal Loop Synthesis in Quantitative Feedback Theory

Thompson, David F.; Nwokah, O.D.I.

doi:10.23919/acc.1990.4790808

Cited by 13 publications

(13 citation statements)

References 5 publications

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“…w'and Z-plane representations must be faidy close up lirn F(w') = 1 (32) to w = 105 (rad/sec). The frequency response of F(w') w•.--0 and F(z) are plotted in Fig.…”

Section: Y(s) =C(b)x(s)mentioning

confidence: 99%

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Symposium Proceedings on Quantitative Feedback Theory Held in Fairborn, Ohio on 2-4 August 1992.

Houpis¹,

Chandler²

1992

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“…w'and Z-plane representations must be faidy close up lirn F(w') = 1 (32) to w = 105 (rad/sec). The frequency response of F(w') w•.--0 and F(z) are plotted in Fig.…”

Section: Y(s) =C(b)x(s)mentioning

confidence: 99%

“…1. From (32) and (41), we can easily construct the forbidden region in the u -v plane by considering inequality (39) at each frequency. Denote…”

Section: Eementioning

confidence: 99%

Symposium Proceedings on Quantitative Feedback Theory Held in Fairborn, Ohio on 2-4 August 1992.

Houpis¹,

Chandler²

1992

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

García-Sanz

Molins

2010

Proceedings of the IEEE 2010 National Aerospace &Amp; Electronics Conference

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This paper introduces a new methodology to synthesize automatically robust controllers in the Quantitative Feedback Theory (QFT) framework. The method avoids the classical gridding of the controller's phase, and deals with multi-objective specifications and parametric uncertainty in the plant model. By tacking the required robust stability and robust performance specifications, and grouping them into two nonlinear quadratic inequalities, the method derives a nonlinear and frequency-dependent expression for the controller magnitude, which is independent of the controller phase. Then, by evaluating this expression for every frequency of interest, and using a least-square-type algorithm with phase constraints to find the parameters of an a priory fix order controller structure, the method finds automatically the most appropriate controller parameters to meet all the multi-objective specifications for all the plants within the uncertainty. The method is exemplified with a DC motor control application.

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“…All of these problems yield a collection of linear models obtained by a linearization of the parametrically dependent Received Oct. 29,1990; revision received May 13, 1991 nonlinear differential equation set about a finite number of different operating points. This problem class is often endowed with hard stability and performance constraints such as on rise time and overshoot.…”

Section: Introductionmentioning

confidence: 99%

“…(39) is satisfied with equality. Any optimum loop transmission function L opt that solves the QFT optimization problem(27)(28)(29) must lie on dtf^c/)) Vtoe[0 oo) 28. ' 33 The generation of dB p (w 9 <t>) proceeds as follows.…”

mentioning

confidence: 99%

Parametric robust control by quantitative feedback theory

Nwokah

Jayasuriya

Chait

1992

Journal of Guidance, Control, and Dynamics

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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

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Optimal Loop Synthesis in Quantitative Feedback Theory

Cited by 13 publications

References 5 publications

Symposium Proceedings on Quantitative Feedback Theory Held in Fairborn, Ohio on 2-4 August 1992.

Symposium Proceedings on Quantitative Feedback Theory Held in Fairborn, Ohio on 2-4 August 1992.

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

Parametric robust control by quantitative feedback theory

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