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appropriate choice of controller. Again, since most physical processes are strictly proper in
the open-loop, i.e.
lim Gc ( s) G p ( s) = 0 s→∞ this means that, in the frequency domain, 4 of 7 Copyright 2002 Sensitivity Functions lim η( jω ) = lim ω →∞ ω →∞ Gc ( jω )G p ( jω ) [ 1 + G c ( jω ) G p ( jω ) =0 As in the case of the sensitivity function, ε(jω), the desired value of the complementary
sensitivity function, η(jω), can be achieved only near low frequencies.
A plot of η( jω ) for the same system that gave rise to ε( jω ) is shown below: Figure 3. Complementary Sensitivity function of a feedback loop with a PI controller and a
1st-order system without delay
Effects of measurement noise
If there is process noise, i.e. N ( s) ≠ 0 , then
η( s) = G c ( s) G p ( s ) [1 + G ( s)G ( s)]
c p = Y ( s)
R ( s) − N ( s) Thus the structure of η( s) is identical to the noise free case for the feedback loop that we are
considering (Figure 1).
Notice that when...
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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