hw_5_2006_solution

hw_5_2006_solution - ChE 3015 Homework #5 - Due on Class #...

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ChE 3015 Homework #5 - Due on Class # 14, Friday 2/17/2006 1. PI vs P-Only Control of Heat Exchanger ( 20 points ) Note: This problem is designed to illustrate: i. the differences between P and PI control & characterization of controller performance ii. the effect of process nonlinearity on closed loop response under PI control iii. the use of the test matrix method to fine tune a PI controller For the Heat Exchanger process, consider a case where the design or expected operating temperature is 150 o C but may range from 135 o C to 165 o C. The disturbance flow rate is expected to remain steady at 5 L/min. a. (open loop tests) Perform the necessary open loop dynamic modeling studies to determine a first order plus dead time (FOPDT) model which describes process operation near the design operating conditions. Do this with a step test and a doublet test using in both cases changes on either side of the set point with magnitude 10%U bias . For the step test , design a test similar to that illustrated by Figure 1 in the solution to HW#3. Put the FOPDT parameters derived from the step test in the format of the table shown below [preferably in the form of a Word document]. For the doublet test , specify the values of %CO and the minimal expected change in exit temperature you expect to see for each part of the test and write these values on the same page with the Table shown below. Also, write in the table the FOPDT parameters derived from the doublet test. [Hint for designing the doublet test – see Figure 6.6, p.57 of PPC and also consider how we designed the doublet test in HW#4] Using the IMC Standard tuning criterion , calculate values of (K c ) P for a Proportional controller and (K c ) PI and τ I for a PI controller and put them in the Summarize your results for part (a) in the form of a table with the format: Test type K p , o C/% τ p , min θ p , min (K c ) P , %/ o C (K c ) PI , %/ o C τ I , min Step --- --- --- --- --- --- Doublet --- --- --- --- --- --- ) We will denote the values of K c and τ I for a PI controller derived from the doublet test in part (a) as K c * and τ I *, respectively. Using the values of (K c ) P for a Proportional controller and the values K c * and τ I * for a PI controller, test the set point tracking capability of this controller by plotting the response of the process to step changes in the set point from 150 o C up to 165 o C and back again to 150 o C. For the PI controller test, use the “Integral with Anti-Reset Windup” option. Run the P and PI tests consecutively and plot on one figure; title it “ HW #5, Part b ”. On the same page containing the table
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hw_5_2006_solution - ChE 3015 Homework #5 - Due on Class #...

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