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

Abstract

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.

Automatic synthesis of feedforward elements in quantitative feedback theory

“…[7][8][9] This contrasts with the considerable effort that has been put into the automatic tuning of QFT feedback controllers. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Abbreviations: 2DOF, two-degree-of-freedom; QFT, quantitative feedback theory.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.…”