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Unformatted text preview: there is process noise, in terms of process inputs and outputs, η( s) is now
also affected by N(s). In this case, η( s) has to be made small so as reduce the influence of
5 of 7 Copyright 2002 Sensitivity Functions random inputs on system characteristics. In other words, we want η( s) ≈ 0 or equivalently,
ε ( s) ≈ 1. Compare this with the noise free situation where we require η( s) ≈ 1 or ε ( s) ≈ 0 .
This illustrates the compromise that often has to be made in control systems design: good setpoint tracking and disturbance rejection has to be traded off against suppression of process
noise.
Summary
From the above discussion, we can make the following observations:
• Both ε ( s) and η( s) have minimum values equal to 0 and maximum values equal to 1
• When there is no measurement noise,
⇒ For perfect disturbance rejection, ε ( s) = 0 .
⇒ For perfect setpoint tracking, η( s) = 1 .
⇒ Perfect disturbance rejection also implies perfect setpoint tracking, since
η( s) ∆ 1 − ε ( s) , i.e. perfect overall control. This can be illustrated by plotting both
sensitivity and complementary sensitivity functions on the same graph, as shown in
Figure 4. Figure 4. Sensitivity and Complementary Sensitivity functions of a feedback loop with a PI
controller and a 1storder system without delay
6 of 7 Copyright 2002 Sensitivity Functions • When measurement noise is present
⇒ η( s) ≈ 0 or equivalently, ε ( s) ≈ 1 so as to reduce the influence of random inputs on
system performance 7 of 7 Copyright 2002...
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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
 Philips

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