Generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties
Shih‐Feng Yang · International Journal of Robust and Nonlinear Control · 2010
Abstract This paper presents an efficient algorithm for the generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties. For a plant withmaffinely dependent uncertainties, it is shown that whether a point in the Nichols chart lies in the QFT bound for a robust tracking specification at a given frequency can be easily tested by computing the maxima and minima ofm2m−1univariate functions corresponding to the edges of the parameter domain box. This test procedure is then utilized along with a pivoting procedure to trace out the boundary of the QFT bound with a prescribed accuracy or resolution. The developed algorithm has the advantages that (1) it is efficient in the sense that it requires less floating point operations than other existing algorithms in the literature; (2) it can avoid the unfavorable trade‐off between the computational burden and the accuracy of the computed QFT bounds that has arisen in the application of many existing QFT‐bound generation algorithms; (3) the maximum allowable error of the computed QFT bound can be prespecified; and (4) it can compute QFT bounds with multi‐valued boundaries. Numerical examples are given to illustrate the proposed algorithm and its computational superiority. Copyright © 2010 John Wiley & Sons, Ltd.