An Efficient Algorithm for Computing QFT Bounds

Abstract

An important step in Quantitative Feedback Theory (QFT) design is the translation of closed-loop performance specifications into QFT bounds. These bounds, domains in a Nichols chart, serve as a guide for shaping the nominal loop response. Traditionally, QFT practitioners relied on manual manipulations of plant templates on Nichols charts to construct such bounds, a tedious process which has recently been replaced with numerical algorithms. However, since the plant template is approximated by a finite number of points, the QFT bound computation grows exponentially with the fineness of the plant template approximation. As a result, the designer is forced to choose between a coarse approximation to lessen the computational burden and a finer one to obtain more accurate QFT bounds. To help mitigate this tradeoff, this paper introduces a new algorithm to more efficiently compute QFT bounds. Examples are given to illustrate the numerical efficiency of this new algorithm.