Again since most physical processes are strictly

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: close as possible to 1 by an 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). The trade-off Notice that when...
View Full Document

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.

Ask a homework question - tutors are online