0
TECHNICAL BRIEFS

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

Abstract

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 $m2m−1$ 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.

<>

Figures

Figure 1

The feedback control system

Figure 2

Triangulation of the complex plane for the pivoting procedure

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

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

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections