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Article

Robust Performance Limitations and Design of Controlled Delayed Systems

[+] Author and Article Information
O. Yaniv

Faculty of Engineering, Department of Electrical Engineering Systems, Tel Aviv University, Tel Aviv 69978, Israel e-mail: yaniv@eng.tau.ac.il

M. Nagurka

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

J. Dyn. Sys., Meas., Control 126(4), 899-904 (Mar 11, 2005) (6 pages) doi:10.1115/1.1849246 History: Received November 29, 2003; Revised February 25, 2004; Online March 11, 2005
Copyright © 2004 by ASME
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Figures

Grahic Jump Location
Region of (a,b) values for M=1.46, equivalent to at least 40 deg phase margin (PM) and at least 4.5 dB gain margin (GM) for K=1 (both shaded regions). Lower shaded region is for M=1.46 with additional 6 dB plant gain uncertainty (K=2).
Grahic Jump Location
Boundary curves of (a,b) values that satisfy (1) with K=1 for L of (6) and change of variables (7). Marked on the right of each curve is its M value and corresponding lower bound of phase margin (PM) and gain margin (GM in dB) for K=1, according to (3) and (4).
Grahic Jump Location
Boundary curves of (a,b) values that satisfy (1) with K=1 where L is replaced by L(Z) of (16). Marked on the right of each curve is its M value and corresponding lower bound of phase margin (PM) and gain margin (GM in dB) for K=1, according to (3) and (4).
Grahic Jump Location
Nichols plot for M=1.46 and K=3.16, corresponding to at least 40 deg phase margin and at least 14.5 dB gain margin (4.5 dB due to M and 10 dB due to plant gain uncertainty). Frequencies are marked in rad/s for chosen Ts=0.001 s. The open-loop transfer function must not enter the shaded region in order to satisfy the gain and phase margin constraints.
Grahic Jump Location
Maximum a,ab and crossover frequency (rad/s) versus M and its associated guaranteed phase margin (deg) (indicated at top) for the approximate solution.
Grahic Jump Location
Boundary curves of (a,b) values showing comparison between exact and approximate solutions for M=1.93 (phase margin, PM, of at least 30 deg) and for M=1.18 (PM of at least 50 deg). Gain margin, GM, indicated in dB.

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