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TECHNICAL PAPERS

Automatic Loop Shaping of Structured Controllers Satisfying QFT Performance

[+] Author and Article Information
O. Yaniv

Department of Electrical Engineering Systems,  Tel Aviv University, Tel Aviv 69978, Israelyaniv@eng.tau.ac.il

M. Nagurka

Department of Mechanical and Industrial Engineering,  Marquette University, Milwaukee, WI 53201mark.nagurka@marquette.edu

J. Dyn. Sys., Meas., Control 127(3), 472-477 (Sep 26, 2004) (6 pages) doi:10.1115/1.1985441 History: Received April 22, 2004; Revised September 26, 2004

This paper presents a robust noniterative algorithm for the design of controllers of a given structure satisfying frequency-dependent sensitivity specifications. The method is well suited for automatic loop shaping, particularly in the context of Quantitative Feedback Theory (QFT), and offers several advantages, including (i) it can be applied to unstructured uncertain plants, be they stable, unstable or nonminimum phase, (ii) it can be used to design a satisfactory controller of a given structure for plants which are typically difficult to control, such as highly underdamped plants, and (iii) it is suited for design problems incorporating hard restrictions such as bounds on the high-frequency gain or damping of a notch filter. It is assumed that the designer has some idea of the controller structure appropriate for the loop shaping problem.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

A MISO feedback system

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Figure 2

Boundary of all (a,b) pairs satisfying inequality 4,5 for example (1). The a, b pair for which ab is minimum is marked by (∘).

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Figure 3

Several QFT bounds satisfying inequality 4 and the open-loop transfer function L(s) for the pair a, b for which ab is minimum

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Figure 4

Several QFT bounds satisfying inequality 4 at different frequencies and the open-loop transfer function for the optimal triplet a, b, c for which abc is minimum

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Figure 5

Several QFT bounds satisfying inequality 4 and the open-loop transfer function for which the controller HFG is minimum (nominal plant is the one with the largest resonance frequency, here 105 rad∕s)

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Figure 6

Several QFT bounds satisfying inequality 4 and the system’s open-loop transfer function (for k=1) for which the controller HFG is minimum

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Figure 7

A SISO two degree-of-freedom feedback system

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