Inherent Design Limitations for Linear Sampled-data Feedback
Systems
Jim S. Freudenberg, Rick H. Middleton and Julio H.
Braslavsky
Abstract
There is a well-developed theory describing inherent design
limitations for linear time invariant feedback systems consisting
of an analog plant and analog controller. This theory describes
limitations on achievable performance present when the plant has
nonminimum phase zeros, unstable poles, and/or time delays. The
parallel theory for linear time invariant discrete time systems is
less interesting because it describes system behavior only at
sampling instants. In this paper, we develop a theory of design
limitations for sampled-data feedback systems wherein we consider
the response of the analog system output. To do this, we use
the fact that the steady state response of a hybrid feedback system
to a sinusoidal input consists of a fundamental component at the
frequency of the input together with infinitely many harmonics at
frequencies spaced integer multiples of the sampling frequency away
from the fundamental. This fact allows us to define fundamental
sensitivity and complementary sensitivity functions that relate the
fundamental component of the response to the input signal. These
sensitivity and complementary sensitivity functions must satisfy
integral relations analogous to the Bode and Poisson integrals for
purely analog systems. The relations show, for example, that design
limitations due to nonminimum phase zeros of the analog plant
constrain the response of the sampled-data feedback system
regardless of whether the discretized system is minimum phase and
independently of the choice of hold function.
Keywords: Sampled-data systems, Design constraints,
Frequency response.
35 pages
47 references
125 Kb
