CHE 322 Spring 2005 Final Exam

CHE 322 Spring 2005 Final Exam - Name Student...

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Unformatted text preview: Name: Student #: Q1:______Q2:____Q3:______Q4:_____QS:_____ Total UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, APRIL 2005 CHE3ZZS -— PROCESS DYNAMICS AND CONTROL Examiner — W.R. Cluett Closed Book All work to be marked must appear on front of page; Use back of page for rough work only. 1. (20 marks) Consider the following blending process where three feed streams containing components A, B and C, respectively, are being combined into one stream, first using a static mixer followed by a well—mixed blend tank. The following data has been collected from this system, by performing step changes to each control valve and measuringthe corresponding change in the flowrate through each valve (the units of the input are % valve opening and the units of the flowrates are US gallons per minute (GPM)). 51% ' 520.77 cm A 47.27: 486 GPM lé———f-7.3SEC—->‘ 422 B - A 407: 1423.5 GPM 1369 GPM . ‘é—-————'10.ZSEc—-——->‘ C 54% 51.37. ‘ 970.51 GPM MW ‘ ' K—e.1SEc——>‘ (a) Determine transfer function models that describe the dynamic relationship between the control valve and the measured flowrate through the valve for each feed stream. Present the models in standard form and state the engineering units for any parameters associated with these models. Blend Tank (b) Design PI flow controllers for each feed stream (A, B and C) such that each flow control loop has offset free performance with a closed-loop time constant (Ta) of 2 seconds. The next control objective is to control the level in the blend tank using the total flowrate of all three feed streams as the manipulated variable: ,..r ....... ® ................. ® ............. Blend Tank The level controller (LC) actually determines the total feed flowrate by adjusting the setpoints of the three controllers is such a way as to maintain a desired blend ratio of A, B and C. (c) What type of control strategy is this? Explain how this strategy is intended to work when an increase in the flowrate out of the blendtank is introduced. _ (d) In light of the desire to maintain a desired blend ratio at all times, why is it important that the three flow controllers be designed using the same TCL : as was done in part (b)? 2. (15 marks) Consider the figure below that shows a simulation of the stirred-tank heater in the process control laboratory under three different feedback temperature control strategies, where the feedback measurement for control purposes is taken from three different thermocouple locations (1, 2 and 3). The thermocouples are located in the exit water temperature line at approximately t=10, 40 and 80 sec downstream of the tank. In all simulations, the inlet water temperature increased by a unit amount at t=50 sec and the responses in the manipulated steam valve position and controlled exit water temperature are shown in the figure. (a) Indicate directly on the figure the amount of deviation in the exit water temperature from its target value of zero (deviation variables) that is unaffected by the feedback controller for each of the three different cases. (b) Indicate directly on the figure the expected change in steam valve position if a feedforward temperature controller had been used instead of the feedback strategy. Steam Valve Position 0 1 00 200 300 400 500 600 700 800 900 1 000 9 1 Q. 3 8 — Thermocouple1 CE) 05 Thermocouplez 2 ~—— ThermocoupleS +— E Q. E Q) l- . 0 1 00 200 300 400 500 600 700 800 900 1 000 Time . (c) Consider the following statement: “Control system performance depends on the dynamics of the process and on the frequency and magnitude of the disturbance.” Explain this statement in light of the simulation results for a unit step disturbance, and for the case where the inlet temperature is changing in aperiodic fashion. ' 3. ' (25 marks) Consider the following second-order process: 1 — , GP(S)_ (s+1)(s-O.1) The unit step response of this process is shown below: ) cted, based on the transfer function? Explain your (a) Is the response what you expe answer. A proportional feedback controller (GFB = KC ),, is to be used to stabilize this system. (b) Determine the range of controller gains that will stabilize this system. (0) Determine the proportional controller gain required to produce a critically- damped, stable closed-loop system. 10 (d) Sketch the output response of the closed-loop system designed in part (b) to a unit setpoint change, showing both the setpoint change and the process output response on the same sketch. Include as much detail as possible. (e) Draw the root locus diagram that shows the closed-loop pole locations for KC = 0 —-> oo . ll 4. (15 marks) A forced circulation evaporator is used to concentrate dilute liquors by evaporating solvent from a feed stream. Feed is mixed with recirculating liquor and pumped into the tube side of a vertical heat exchanger. Steam enters the shell side of the heat exchanger and condenses on the outside of the tubes. The liquor is partially vaporized as it passes through the tube side of the heat exchanger and passes into the separator. Vapor from the separator is condensed by a cooling water exchanger, while a portion of the liquid stream from the separator is withdrawn as product and the rest is recirculated to the heat exchanger. A schematic process and instrumentation (P&ID) diagram is shown below. Condensate Product. . y2 Composmon Product Feed (a) It has been decided that the level in the separator (yl) will be controlled by manipulating the product flowrate (ul). This level must be under feedback control. Explain why this is so. 12 (b) For the remaining 2x2 system, what is the importance of knowing that the system is controllable? How would you go about testing for controllability? Explain your answer. (c) Assuming you have designed a multi-loop control strategy for the remaining 2x2 system, how would you go about testing to be sure that the controlled system has integrity? Explain your answer. 13 5. (25 marks) / In this question, you are asked to design various control strategies for the system of stirred tanks shown in the figure below. The measurements and manipulated variable are shown in the figure; you may not alter them and need not use them all. The goal is to control the temperature T4 at the outlet of the last tank tightly. The major disturbance is the temperature 0f one of the feed streams, T2. l4 (a) Decide whether a single-loop feedback control strategy is possible. If yes, add the single-loop control strategy to the figure below and explain how your design will work when T2 changes. Heating medium 15 (b) Decide whether a cascade control strategy is possible. If yes, add the best cascade control strategy to the figure below and explain how your design will work when T2 changes. 16 (0) Decide whether a feedforward control strategy is possible. If yes, add the best feedforward control strategy to the figure below and explain how your design will work when T2 changes. Heating medium 17 ((1) Rank your strategies from parts (a)-(c) in terms of their potential control performance and explain your ranking. 18 (e) Describe how each strategy proposed in parts (a)-(c) would respond to a disturbance in T1. 19 ...
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