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Unformatted text preview: tput, Y(s). For the controller to achieve good disturbance rejection, it is obvious that ε(s) 2 of 7 Copyright 2002 Sensitivity Functions should be made as small as possible by an appropriate design for the controller, Gc ( s) . In
particular, ε(s) = 0 if perfect control is achievable.
However, most physical systems are ‘strictly proper’. In terms of their transfer-function
representation, this means that the denominator of the transfer function is always of higher
order than the numerator. Thus,
lim Gc ( s) G p ( s) = 0 s→∞ In the frequency domain, this becomes
lim Gc ( jω )G p ( jω ) = 0 ω →∞ Hence,
lim ε( jω ) = lim ω →∞ 1
ω →∞ 1 + G ( jω ) G ( jω )
p Thus, on the one hand, ε( jω ) has to be close to zero for ideal disturbance rejection, while on
the other, at high frequencies, ε( jω ) is one! What the results are telling us is that perfect control cannot be achieved over the whole
frequency range. Indeed, the analysis shows that perfect control can only be achieved over a
small range of frequenc...
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This note was uploaded on 02/11/2014 for the course EECS 320 taught by Professor Philips during the Spring '06 term at University of Michigan.
- Spring '06