Control Final Exam Model. B..

Final exam model B (Twintich)

Q1 Two liquid stream with flow rates F1 and F2 and temperature T1 and T2 flow through two separate pipes which converge at a mixing junction (see the Fi gure). We want to maintain constant the flow rate F3 and the temperature T 3 of the liquid stream resulting from the mixing of the first two streams. a- Identify the control objectives, disturbances, disturbances, available measurements. Is this a SISO or a MIMO system.  b- Develop a control system that uses only feedback controllers. c- Develop a control system that uses only feedforward controllers. d- Develop two different control systems that uses both feedback and feedforward controllers.

What is a SISO system and what is i s a MIMO system? Give examples for Both .

Q2 a- A jacketed vessel is used to cool a process stream as shown shown in Figure. The The following information is available: i) The volume of liquid in the tank V and the volume of coolant in the jacket VJ remain constant. Volumetric flow rate qF is constant but Qj varies with time. ii) Heat losses from the jacketed vessel are negligible. iii) Both the tank constants and the jacket contents are well mixed and have significant thermal capacitances. iv) The thermal capacitances of the tank wall and the jacket wall are negligible. v) The overall heat transfer coefficient for transfer between the tank liquid and the coolant varies with coolant flow rate: U= KqJ0.8 Where, U = Btu/h ft 2 oF ,

qJ = ft3/h

K = constant

Drive a dynamic model for this system. (state and additional assumptions that you make)

 b- Let F(s) =

 s 2 

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 s 

9 s

2

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3

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.

 s  1

Perform long division and determine the quotient and the remainder c- Find the laplace transform of   f  (t ) 1 2e 2t  

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Q3

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A stirred tank blending process described by Eqs. 1 &2 is operating with w 1= 600 kg/min, w 2=2 kg/min, and x 1 = 0.05. The liquid volume and liquid density are constant, 2 m 3 and 900 kg/m 3, respectively. - Calculate the initial steady state value of the exit composition, x(0). - Calculate the exit composition response to a step increase in inlet concentration x1 from 0.05 to 0.075. Use the initial steady state composition calculated in part (a). - Calculate the approximate exit composition response to a sudden change in w2 from 2kg/min to 1 kg/min. Again use the original steady state value of x(0).

  1      K     X   s    W   s      s  1      s  1 

 X  '  s    V  p dx ' w dt 

  x  '

1

1

w

'

'

1

2

w2'   x '

Q4 a- Pneumatic control valves are to be specified for the applications listed below. State whether an A-O or A-C valve should be specifi ed for the following manipulated variables and give reason (s). a- Steam pressure in a reactor heating coil.  b- Flow rate of reactants into a polymerization reactor. c- Flow of effluent from a wastewater treatment holding tank into a river. d- Flow of cooling water to a distillation condenser.  b- Several linear transmitters have been installed and calibrated as follows: 1- Flow rate: 400 gal/min → 15 psig Pneumatic transmitter  0gal/min → 3 psig 2- Pressure: 30 in Hg → 20 mA Current transmitter 10 in Hg → 4 mA