hw_6_2006_REVISED_solution

hw_6_2006_REVISED_solution - ChE 3015 Homework#6 Due on...

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1 ChE 3015 Homework #6 – Due on Class #15, Monday 2/20/2006 1. PID Control of Gravity Drained Tank (10 points) Note: This problem builds directly on Workshop #6 PID Control of Heat Exchanger Temperature. For the gravity drained tank process, consider a case where the design level in the lower tank is 4 m and the disturbance flow rate is normally about 2 L/min. The set point is expected to remain constant for extended periods of time but the disturbance flow may range from 0-4 L/min. a. Perform the necessary open loop dynamic modeling studies to determine a first order plus dead time (FOPDT) model that describes process operation near the design operating conditions. Do this with a doublet test. Recall that there is an error in Control Station concerning the value of the ± 3 σ noise level on the gravity-drained tank. The correct value of ± 3 σ = 0.05 meters whereas Control Station erroneously reports this as 0.5 meters. You do not need to turn in a graph of this. Use the K p , τ p , and θ p values first in the ITAE for Disturbance Changes tuning correlation (SEE ATTACHED TABLE) and then in the ITAE for Set Point changes tuning correlation and compute the tuning parameters for a PID controller. Summarize your results for part (a) in the form of a table with the format: K p , m/% τ p , min θ p , min K c , %/m τ I , min τ D , min --- --- --- (ITAE Disturbance Criterion values) (ITAE Set Point Criterion values) b. Now implement a PID with Derivative on Measurement Controller. Test the K c , τ I , and τ D values for both PID tuning correlations from part (a) for their ability to reject disturbances. Specifically, plot the response of the process under PID control to step changes in the disturbance from 2 L/min to 4 L/min and then from 2 L/min to 0 L/min. You should generate 2 plots – one for the tuning parameters from the ITAE disturbance criterion and one for the tuning parameters from the ITAE set point criterion. On each plot, show the process variable, controller output, and the disturbance. Label each plot appropriately . Put both plots on a single page along with the plot below from part (c). Compare the performance of the two correlations and write your observations on the same page with the Table from part (a). c. The design objective for the controller is that it should minimize the magnitude of the overshoot and undershoot that occurs in the 2 Æ 4 Æ 2 L/min disturbance change. Choose the one of the two tuning parameter sets from part (b) that best meets this objective. Starting with this “best” case, run three tuning cases where you use your best K c and τ I but use 0.5, 1, and 2 times your τ D predicted by the tuning criterion.
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