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U of M College of Engineering Control Seminar Series Sponsored by Eaton, Ford, General Motors, and Whirlpool |
Fundamental Limitations in Communications
And Feedback Control
Professor James
Freudenberg
University of Michigan
Department of Electrical Engineering
and Computer Science
Abstract:
The rapid growth of communications and networking technology has prompted many researchers to study the limitations imposed on a feedback control system by the presence of a communication channel in the feedback loop. The fields of communication and control each have theories of fundamental limitations -- the Shannon theory of reliable communication, and the theory of feedback tradeoffs based on the work of Bode. It is difficult to reconcile these theories because of their different treatment of time delay: delay is detrimental to a feedback system but is required for reliable communication.
In joint work with Rick Middleton and Julio Braslavsky, we are motivated by the observation that the bit rate limit in the Shannon theory is derived from properties of an analog AWGN communication channel, specifically its bandwidth and noise and transmission power, or signal to noise ratio (SNR). We thus compute the minimal SNR required to stabilize an unstable plant over a noisy channel. By computing the capacity of a channel with this SNR, we are able to compare our results with those of Nair and Evans, who compute the minimal bit rate required to stabilize over a noise free digital channel. For the state feedback case our results agree, as they do for output feedback with no delay and a minimum phase plant. If NMP zeros or delay is present, the SNR required for stabilization is greater, as one would expect from control practice.
Extensions of this work to
include performance as well as stabilization have interesting connections to
Wiener filtering, which we shall discuss, time permitting.
3:30 – 4:30 p.m.