ch08 - 8-1 8-2 )(11)(sUssKsYDDca++==

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Unformatted text preview: 8-1 8-2 )(11)(sUssKsYDDca++== ++)1(12sssMKDDc=)(sYa)1()1(2+++ssMKssMKDcDDc+++-++-=1)(11122sssMKssMKDDDcDDDcTaking inverse Laplace transform [ ] [ ])1(1)()/()/(-++-=--DDtDctDcaetMKeMKtyAs 0 MtKMKtycDca+=)(Ideal response, =)(sYi+21ssMKDc= 2sMKsMKcDc+MtKMKtycDci+=)(Hence )()(tytyiaas b)It may be difficult to obtain an accurate estimate of the derivative for use in the ideal transfer function. c)Yes. The ideal transfer function amplifies the noise in the measurement by taking its derivative. The approximate transfer function reduces this amplification by filtering the measurement. 8.2 a)11)()(12121211+++=++=sKsKKKsKsEsP++++=11)(1211221ssKKKKK8-3 b) Kc= K1+ K2K2= Kc-K1 D=12122112KKKKKKDD+=+=or 2121KKK+==+221KKK)1(2221-=-=KKKKSubstituting, 111)1()1()1)((KKKKKcc---=--=Then, cKK-=11c) If Kc= 3 , D= 2 , = 0.1 then, 2731.9.1-=-=K30)27(32=--=K1= 0.1 2 = 0.2 Hence K1+ K2= -27 + 30 = 3 232.302112==+KKK++=12.123)(sssGc8-4 8.3 a)From Eq. 8-14, the parallel form of the PID controller is : ++=ssKsGDIci11)(From Eq. 8-15, for 0, the series form of the PID controller is: [ ]111)(++=ssKsGDIca+++=ssKDIIDc11+++++=IDDIIDIDcssK11111Comparing Ga(s)with Gi(s)+=IDccKK1+=IDII1IDDD+=1b)Since +ID11 for all D, I, therefore ccKK, IIand DDc)For Kc= 4, I=10 min , D =2 min 8.4=cK, min12=I, min67.1=Dd)Considering only first-order effects, a non-zero will dampen all responses, making them slower. 8-5 8.4 Note that parts a), d), and e) require material from Chapter 9 to work....
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This note was uploaded on 04/10/2008 for the course CHE 242 taught by Professor Cummings during the Spring '08 term at Vanderbilt.

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ch08 - 8-1 8-2 )(11)(sUssKsYDDca++==

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