Premium
GENERATION OF EXACT QFT BOUNDS FOR PLANTS WITH AFFINELY DEPENDENT UNCERTAINTIES
Author(s) -
Yang ShihFeng
Publication year - 2007
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2007.tb00432.x
Subject(s) - bivariate analysis , sensitivity (control systems) , mathematics , reduction (mathematics) , polynomial , controller (irrigation) , upper and lower bounds , set (abstract data type) , control theory (sociology) , phase margin , mathematical optimization , computer science , mathematical analysis , engineering , statistics , control (management) , agronomy , geometry , electronic engineering , artificial intelligence , biology , programming language , amplifier , computer network , operational amplifier , bandwidth (computing)
This paper presents an efficient method for the generation of exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications for plants with affinely dependent uncertainties. It is shown that, for a plant with m affinely dependent uncertainties, the exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications at a given frequency and controller phase can be computed by solving m 2 m ‐1 bivariate polynomial inequalities corresponding to the edges of the parameter domain box. Moreover, the solution set for each bivariate polynomial inequality can be computed by solving for the real roots of one fourth‐order and six second‐order polynomials. This avoids the unfavorable trade‐off between the computational burden and the accuracy of QFT bounds that has arisen in the application of many existing QFT bound generation algorithms. Numerical examples are given to illustrate the proposed method and its computational superiority.