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Problem 1: (a) Figure 1 shows a feedback control scheme for blending process that is subject to significant disturbances. It is desired to augment this scheme with feedforward control. Of the four potential locations for the feedforward measurement indicated in the diagram, A, B, C, or D, which would be the best? (The A values noted in the diagram correspond to the average residence time in the indicated hollow pipes). Justify your answer briefly. Composition Controller CC CA Composition Analyzer D C B A o-3 sec 0-5 sec Figure 1: Blending process. (b) Figure 2 shows a schematic diagram for a heat exchanger exit temperature control problem. The exit temperature of the process stream is influenced by the steam flowrate into the hea exchanger shell, and by the erratically varying inlet temperature of the process stream. The steam flowrate itselfis also subject to erratic fluctuations induced by unsteady, unpredictable, and unmeasured steam supply pressure. Temperature measurements are provided by two temperature sensors and accompanying transmitters indicated as TT1 and TT2 in the diagram; and steam flow measurements are provided by a flowmeter and the accompanying flow transmitter, FT, also indicated in the diagram. A flow controller, FC, a temperature controller, TC, and a feedforward controller, FFC (which can configured any way you wish), have been made available to you. You are requiredto place these controllers such that the heat exchanger system is configured for: 1. Feedforward control only, 2. Feedback control with cascade control, 3. Feedforward control augmented with feedback, 4. Feedforward, feedback, and cascade control. For each case, draw a process diagram similar to that given in Figure P2.2, showing clearly the connections between each of the controllers in question and the sensor/transmitter from which it gets its information FFC TC FC Steam TT2 TT FT Process Stream Condensate Figure 2: Heat exchanger. Problem 2 The objective in the water heating tank process shown in Figure 3 is to maintain the outlet temperature at some desired set-point Td by adjustingq, the quantity of heat sent to the tank vi a steam heating. The steam delivery pressureis P, and it experiences variations over which we have no control, but which affect 9. The following deviation variables are given: Ti - Ti = d1; p - p' = d2; T - T* = y; Td - T2 = Ya, a - a = u The relevant transfer functions for the components of the closed-loop system are also given as follows: 91(s), process; @d1(s), disturbance (inlet stream temperature), h(s), thermocouple; 8c (s), feedback controller, go(s), control valve; 9dz (s), disturbance (steam pressure). (a) Develop a block diagram for the closed-loop system showing all the components, and obtain the closed-loop transfer function equation. (b) For the specific situation in which the following transfer function are given: 0.5 = 1 2 = 0.5s + 0.15 9az(s)=1557 = 1 h(s)=00251 + Under PI control with T1 = 0.2, find the range K€ values for which the system remains stable. (c) If a cascade control strategy is to be implemented, how should the second control loop be configured (i.e., what will it manipulate, and what measurement will it accept)? Draw the block diagram for the process under this strategy. If the new controller is specified as a proportional controller with gain Ke2 = 5.0, with the primary controller as givenir part (b), find the range of K€ values for which the cascade control system will be stable. T1 P Set point T 11 TT TC - T& Figure 3: Water heating tank process. Problem 3: For the blending process (Continuing Problem), the transfer functions for this process are given as: F1(s) 2.5s+1'FF(s) 5s+1 The plant transfer function matrix now becomes: e-0.1s e-0.1s 5s+1 = -0.1e O.1e 2.5s+1 2.5s+1_ 1. Perform an interaction analysis using RGA 2. Choose the optimal pair of control and manipulated variables to minimize interactions and compare with the base case discussed in Chapter 15. 3. Design and implement a multi-loop PI controller, with parameters based on ZN tuning for both level and composition loops (take into account that the level controller is the same as designed before since the corresponding transfer functions have not changed). 4. Design and implement a decoupling controller for the process and compare the performance with conventional multi-loop control. Problem 4 The "low-boiler column" in a distillation train used to separate the products of an industrial chemical reactor has the following experimentally determined approximate transfer function model y(s) = g(s)u(s) + ga(s)d(s) Where. -0.012 0.011 -0.00175e-0.1: 0.004s + 1 0.055s + 1 0.00525s + 1 -0.013 0.075 - -0.00012e-0.25: g(s) = 0.00325s + 1 0.015s + 1 0.0141s + 1 -0.0043 0.04 0.000086 S S S -0.0041 0.185 0.0041s + 1 0.37s + 1 ga(s) = -0.001 0.16 0.000225s + 1 0.4s + 1 The variables are defined in terms of deviation variables y1= T36 temperature of tray 36 (C) y2= Bottom Temperature (°C) y3=Reflux receiver level (ft) mi= Reflux Flow Rate (lb/hr) mz= Reboiler Heat Duty (NHDU) m3= Condenser Cooling Water Flowrate (lb/hr)) d1 = Feed Flow Rate d2= Feed Temperature a) Assuming that it has been predetermined that the bottom temperature is to be controlled with the reboiler heat duty, use the RGA to determine how the remaining variables should be paired. b) Using the yi-m3; y2-m2; y3-m1 pairing and using the following controller parameters Loop 1: (T36 loop) Kc=-80; 1/t1=3.5 Loop 2: (Bottom Temperature loop) K.=2.0; 1/t1=6.0 Loop 3: (Reflux level loop) Kc=-500; 1/t1=2.0 Obtain the simulation of the overall column response to a 600 lb/hr step increase in the feed flowrate Now, using the yi-mi; y2-m2; y3-m3 along with the following controller parameters Loop 1: (T36 loop) Kc=-500; 1/tr=1.0 Loop 2: (Bottom Temperature loop) Kc=4.5; l/tr=2.0 Loop 3: (Reflux level loop) Kc=12000; 1/t1=0.8 Obtain the simulation of the overall column response to a 600 lb/hr step increase in the feed flowrate. Compare the results under both the old and new configurations c) Givennow that for economic and environmental reasons the temperature T36 is the most critical of all the low boiler columns variables, and that very tight control is therefore required for this variable, which of the two configurations investigated in part b) is preferable. Discuss your answer in the light of the RGA results obtained in part a) Given that Tray 36 is close to the top of the column and that the reflux receiver is a 3ft diameter cylindrical drum into which empties all the material from the (essentially total) condenser. From a consideration of the physics of the problem, which would you expect to be more effective manipulated variable to use in controlling this temperature: the reflux flow rate or the condenser cooling temperature, Support your answer adequately. Offer an explanation for the results given by the RGA. d) Repeat part b) for a step input disturbance of 5°C in the feed temperature. Once again, comment on which configuration provides tighter control of the critical T36 variable.

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