Assignment 5 Solutions 2009

# 9 9 7 s s e 1 9 8 figure15model fitting

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Unformatted text preview: olling the temperature with the cooling water as the manipulated variable. 1. 2. 3. 4. Find the characterist ic equat ion Find the ultimate controller gain ( k cu ) Design a PID controller using the Cohen and Coon and ZN tuning methods Analyze the closed­loop response against set­point and disturbances changes Solution: Performing the experiments in Control Station we have: C o n t ro l S t a t io n : D e s ig n T o o ls M o d e l : F i r s t O r d e r P l u s D e a d T i m e ( F O P D T ) F i l e N a m e : e x _ 1 . t x t M anipulat ed V ar iable P r oc es s V ariable 1 40 1 39 1 38 1 37 4 5.0 4 2.5 4 0.0 0 5 10 1 5 20 25 Time 30 35 40 45 50 G a i n ( K ) = ­ 0 . 4 7 6 1 , T i m e C o n s t a n t ( T 1 ) = 0 . 8 6 9 8 , D e a d T i m e ( T D ) = 0 . 9 6 7 6 G o o d n e s s o f F i t : R ­ S q u a r e d = 0 . 9 9 7 , S S E = 1 . 9 8 Figure 15: Model fitting for manipulated variable C o n t ro l S t a t io n : D e s ig n T o o ls M an ipu lat e d V ariable P r oc e s s V ar iab le M o d e l : S O P D T w i t h L e a d T i m e F i l e N a m e : e x _ 2 . t x t 1 40 .50 1 40 .25 1 40 .00 1 39 .75 1 2.0 1 1.5 1 1.0 1 0.5 1 0.0 0 5 10 1 5 2 0 25 Time 30 35 4 0 4 5 50 K = ­ 0 . 1 8 6 , T 1 = 0 . 6 9 8 , T 2 = 0 . 6 9 8 , T D = 1 . 1 0 , T L = ­ 3 . 3 4 G o o d n e s s o f F i t : R ­ S q u a r e d = 0 . 8 0 6 9 , S S E = 2 . 1 5 Figure 16: Model fitting for disturbance variable Ident ification o f the input­output model fro m the experiments leads to a process model given by: y = - 0 476 -0. 967 s . e - 0 186 3 34 + 1 e -1. 10 s . ( - . s ) u + d 0 863 + 1 . s ( .698 + 1 (9 698 + 1 0 s ) . s ) Incorporation the process model into APC_Tool environment and using a P­Control we find the ult imate controller gain for this process (kCU = 4.3 and PU=3) Figure 17: Closed­loop response with P­controller (kCU=­4.3) The ZN setting give us kC = ­1.935 and tI = 2.5. Testing the ZN controller settings in the mode l within APC_Tool g...
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