KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec39

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec39

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1 Chapter 14 Closed-Loop Frequency Response and Sensitivity Functions Sensitivity Functions The following analysis is based on the block diagram in Fig. 14.1. We define G as and assume that G m =K m and G d = 1. Two important concepts are now defined: v p m G G G G @ 1 sensitivity function (14-15a) 1 complementary sensitivity function (14-15b) 1 c c c S G G G G T G G + + @ @
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2 Chapter 14 Comparing Fig. 14.1 and Eq. 14-15 indicates that S is the closed-loop transfer function for disturbances ( Y/D ), while T is the closed-loop transfer function for set-point changes ( Y/Y sp ). It is easy to show that: 1 (14-16) S T + = As will be shown in Section 14.6, S and T provide measures of how sensitive the closed-loop system is to changes in the process. Let | S ( j ) | and | T ( j )| denote the amplitude ratios of S and T , respectively. The maximum values of the amplitude ratios provide useful measures of robustness. They also serve as control system design criteria, as discussed below. ω ω
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3 Chapter 14 • Define M S to be the maximum value of | S ( j ) | for all frequencies: ω ω max | (ω) | (14-17) S M S j @ The second robustness measure is M T , the maximum value of
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This note was uploaded on 09/22/2009 for the course CHEMICAL CHE 401 taught by Professor Dr.muhammadal-arfaj during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec39

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