Analytic Loop Shaping Methods in Quantitative Feedback Theory

Abstract

Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.

Automatic loop shaping in fractional-order QFT controllers using particle swarm optimization

“…defines the allowed regions for 4) Designing a prefilter: The final step in QFT is to design the prefilter, F(s), such that the performance specifications are satisfied.…”

“…There was no guarantee of convergence and rational function approximation was ultimately needed to obtain an analytical expression for the loop. Thompson and Nwokah [4] proposed that automatic loop shaping was achieved using nonlinear programming techniques where the QFT bounds were over bounded by disks. With the continuation of this work, Borguesani et al [5] proposed an automatic loop shaping technique via linear programming.…”

Automatic loop-shaping of QFT robust controllers

“…Quantitative Feedback Theory ( [26][27][28][29][30] and [38]) is a robust frequency domain control design methodology which has been successfully applied in many practical problems of different domains [10][11][12][13][14][15][16][17][18][19][20][21]. 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.…”

Automated Synthesis of Fixed Structure QFT Controller using Interval Constraint Satisfaction Techniques

“…Traditionally, this synthesis was done manually by the designer, relying on design experience and skill. Recently, several researchers have attempted to automate this step, see, for instance, Bryant and Halikias (1995); Chait et al (1999); Gera and Horowitz (1980); Garcia-Sanz and Guillen (2000); Nataraj and Tharewal (2007); Nataraj and Kubal (2007); Thomspon and Nwokah (1994).…”

“…The method, however, needs a rational function approximation to obtain an analytical expression for the loop transfer function, and straight line approximations for the nonlinear QFT bounds. Thomspon and Nwokah (1994) proposed a method based on nonlinear programming techniques wherein the templates of the uncertain plant are approximated by overbounding rectangles. Such a template approximation leads to overbounding in the constraints derived for the optimization.…”