Efficient Algorithm for the Generation of QFT Bounds for Plants With Affinely Dependent Uncertainties

[+] Author and Article Information
Shih-Feng Yang

Department of Information Management, Transworld Institute of Technology, Douliou City, Yunlin County 640, Taiwanysf@tit.edu.tw

J. Dyn. Sys., Meas., Control 129(4), 550-555 (Mar 22, 2007) (6 pages) doi:10.1115/1.2745883 History: Received July 24, 2006; Revised March 22, 2007

This paper presents an efficient algorithm for the generation of quantitative feedback theory (QFT) bounds for plants with affinely dependent uncertainties. For a plant with m affinely dependent uncertainties, it is shown that whether a point in the complex plane lies in the QFT bound for a frequency-domain specification at a given frequency can be tested by checking if m2m1 one-variable quadratic equations corresponding to the edges of the domain box are all non-negative on the interval [0,1]. 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 can avoid the unfavorable trade-off between the computational burden and the accuracy of QFT bounds. Moreover, it is efficient in the sense that no root-finding and iterative procedures are required. Numerical examples are given to illustrate the proposed algorithm and its computational superiority.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

The feedback control system

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Figure 2

Triangulation of the complex plane for the pivoting procedure

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Figure 3

The QFT bound on the nominal loop transmission for the plant output disturbance rejection specification Ws(ω)=1.2 at ω=1.5 for the plant in example 1

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Figure 4

The QFT bound on the nominal loop transmission for the plant output disturbance rejection specification Ws(w)=1.2 at w=5 for the plant in example 2



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