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QFT bounds for robust stability specifications defined on the open‐loop function
Author(s) -
RicoAzagra J.,
GilMartínez M.,
Rico R.,
Maisterra P.
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3908
Subject(s) - control theory (sociology) , phase margin , quantitative feedback theory , stability (learning theory) , loop gain , upper and lower bounds , minimum phase , frequency response , loop (graph theory) , stability theory , open loop controller , robust control , robustness (evolution) , maximization , computer science , transfer function , mathematics , mathematical optimization , bandwidth (computing) , control system , closed loop , control engineering , control (management) , engineering , nonlinear system , voltage , artificial intelligence , amplifier , computer network , mathematical analysis , chemistry , operational amplifier , biochemistry , machine learning , combinatorics , electrical engineering , gene , quantum mechanics , physics
Summary In the framework of quantitative feedback theory, this paper develops a new method to compute robust stability bounds. This is of special interest when stability is defined directly on the open‐loop function. Thus, ignorance of the plant gain and phase shift can be specifically and independently considered. Furthermore, upper and lower stability margins for both gain and phase can be chosen. However, classical quantitative feedback theory stability specifications are defined as constraining the peak magnitude of closed‐loop functions, which lack the said flexibility. Once the upper tolerance has been defined, all stability margins are determined. Moreover, confining the most restrictive stability margin may result in other excessive margins. However, the stability bounds of the new approach guard just the required distance from the open‐loop frequency response to the critical point. This allows maximization of the available feedback in the functional bandwidth and minimization of the cost of feedback beyond the crossover frequency, provided that the open‐loop frequency response is shaped to closely follow the stability bounds. It should be noted that the new bound computation algorithm performs few and simple arithmetic operations. This makes it far more efficient than traditional methods. The flight altitude control of an unmanned aerial vehicle is proposed as a practical example to show the new method's potential benefits.