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Feedback Control in Systems Biology
book

Feedback Control in Systems Biology

by Carlo Cosentino, Declan Bates
October 2011
Intermediate to advanced content levelIntermediate to advanced
296 pages
9h 39m
English
CRC Press
Content preview from Feedback Control in Systems Biology
120 Feedback Control in Systems Biology
r→0
R→∞
Im(s)
Re(s)
FIGURE 4.5: Nyquist contour in the s-plane.
The number of unstable closed-loop poles is equal to the number of uns table
open- loop poles plus the num ber of encirclements (counted as positive in the
clockwise and negative in the counter-clockwise direction) of the origin by the
Nyquist plot of D(s).
This result follows directly by applying Cauchy’s principle of the argument
to the function D(s) with the s-plane contour given in Fig. 4.5, and noting
that
1. Z and P represent the numbers of zeros and poles, respectively, of D(s)
in the right half plane, and
2. the zeros of D(s) are the closed-lo
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Publisher Resources

ISBN: 9781439816912