Bode Integral Limitation For Irrational Systems
Abstract
Bode integrals of sensitivity and sensitivitylike functions along with complementary sensitivity and complementary sensitivitylike functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we investigate the Bode integral and evaluate what happens when a fractional order ProportionalIntegralDerivative (PID) controller is used in a feedback control system. We extend our analysis to when fractal PID controllers are applied to irrational systems. We split this into two cases: when the sequence of infinitely many right half plane openloop poles doesn't have any limit points and when it does have a limit point. In both cases, we prove that the structure of the Bode Integral is similar to the classical version under certain conditions of convergence. We also provide a sufficient condition for the controller to lower the Bode sensitivity integral.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.10879
 arXiv:
 arXiv:2211.10879
 Bibcode:
 2022arXiv221110879C
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 93Axx
 EPrint:
 13 pages, 7 figures