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Assignment 5 Solutions 2009

935andti1 as can be seen fro m the different plots

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Unformatted text preview: = o f f ) 14 7.5 14 5.0 14 2.5 14 0.0 Cont r olle r Out p ut 40 35 30 25 1 68 1 71 1 74 177 180 183 Time (mins ) 1 86 1 89 1 92 19 5 198 T u n i n g : G a i n = ­ 1 . 9 4 , R e s e t T i m e = 1 . 0 0 , S a m p l e T i m e = 1 . 0 0 Figure 24: Closed­loop response ( in CStation) for set point change (kC = ­1.935 and tI = 1) C o n t ro l S t a t io n : C a s e S t u d ie s Cont r olle r Out p ut Pr o c e s s Va r i a b l e /Se tp o in t P r o c e s s : H e a t E x c h a n g e r C o n t . : P I D ( P = D A , I = A R W , D = o f f , F = o f f ) 14 0.0 40 2 19 2 22 2 25 228 231 234 Time (mins ) 2 37 2 40 2 43 24 6 249 T u n i n g : G a i n = ­ 1 . 9 4 , R e s e t T i m e = 1 . 0 0 , S a m p l e T i m e = 1 . 0 0 Figure 25: Closed­loop response ( in CStation) for disturbance change (kC = ­1.935 and tI =1) As can be seen fro m the different plots the responses obtained fro m APC_Tool (using the linear model) co mpared well wit h those obtained using the full nonlinear model. Decreasing the value of the Integral act ion does not seem to be a good idea since the controller beco mes too oscillatory. 4. For the blending process (see Cont inuing Problem), and using the transfer funct ions developed in Chapter 5, we would like to implement a feedback control scheme to control the level o f the tank using F1 as manipulated input. F2 , in this case, is a disturbance: 1. Write the characterist icequat ion, 2. Analyze the range of controller gains that makes the closed­loop 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...
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