Assignment_4_2007_Solutions

1s e 01s h s f1 s f2 s 5s 1 5s 1 assuminggf

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Unformatted text preview: equat ion, 2. Analyze the range o f controller gains that makes the clo sed­loop system stable using Routh’s Criterion and Root­Locus. 3. Design a PI controller using the ZN method 4. Analyze the gain and phase margins using ZN settings 5. Adjust the controller gain to achieve a gain margin of 2.5 6. Compare and discuss the performance of the resulting controllers Solution: We have the fo llowing model for the process and disturbance transfer funct ions: e -0.1s e 0.1 s h ( s) = F1 (s ) + F2 ( s ) 5s + 1 5s + 1 Assuming, g f ( s = g m = 1 , the characterist ic equat ion beco mes ) e -0. 1s k c 5 + 1 s (5 + 1) + e - 0. 1 s k c = 0 s This is an irrational transfer funct ion, so in order to use the Routh’s Criterion, we need to transform the po lyno mial into a rational one. This is acco mplished by a first­order Pade approximat ion. 1 + g p g c = 0 = 1 + 1 - 0.1s 1 + 0.1s Consequent ly, the characterist ic equat ion beco mes, (1 - 0.1s ) k = 0 ( 5s + 1) + c (1 + 0.1s ) or ( 5s + 1) (1 + 0.1s ) + (1 - 0.1s )kc = 0 e 0.1 s » This is now a polyno mial equat ion. Expressing this equation in the standard form yield...
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This note was uploaded on 01/12/2014 for the course CHE 4198 taught by Professor Hjortso,m during the Fall '08 term at LSU.

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