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Question 4 A process stream is heated so that its premixed components achieve a uniform composition, as shown in Figure 4. Temperature control is important to ensure that the mixture is within the temperature range between 140 to 160 °F; too high temperature will decompose the product, whereas a low temperature results in incomplete mixing. The tank is heated by saturated steam condensing inside the heating coil. Steam TC Tsp. °F Feed F, ft/min T₁ °F Condensate miny. T. °F V. It F, ft/min T. °F Figure 5. Heated mixing tank system. The simulated step response of the temperature in the tank after a step change in the feed flowrate at time = 2 minutes is given in Figure 5. Estimating from the same simulation, the transfer function that relates the temperature in the tank to the flow of saturated steam, Fst, is T' 10e-25 °F Fst 5s + 1 ft³/min The temperature sensor has been calibrated to have a range from 135 to 165°F, with negligible dynamics compared to the process. The control valve is linear, and allow a maximum of 30ft³/min to flow through, with a time constant , of 1.0 min. (a) Draw the detailed block diagram for this feedback control system. Find all transfer functions for the block diagram. Please use the matching symbols labelled for the variables as in the diagram and the description given. DO NOT use the generic symbols given in the
textbook. Show your working on the graph in Figure 5 and include it in your solution. Label all signal and variable lines in the diagram and put in the proper transfer function in the blocks, with the correct units. (10 marks) (b) Derive the closed loop transfer function for this control system and give the transfer functions for each of the servo and regulatory modes. Show ALL working. (4 marks) (c) If a proportional controller is used, analyse the stability range for the controller. (5 marks) (d) Calculate the tuning parameters for P controller using Ziegler Nichols online tuning method. Given the information on the process that you have, recommend, and strongly justify (at least 2 to 3 reasons) the best controller modes that will be suitable for the process, knowing that the temperature of the mixture has a slow response time and is sensitive to extreme heat and temperature of the vessel must fall within the recommended range. Please also justify any controller mode that is not suitable for the process. (6 marks) Temperature (°F) 1 0 -1 -2 m 4 on -7 -8 to 10 15 Time (min) 20 25 Figure 5. Temperature response after a step change in feed flow rate, F. at 2 minutes. 30