PROC 2090 – PROCESS CONTROL AND SIMULATION
Assignment: Modelling and Design of Feedback Controllers with
SIMULINK (20 marks)
(maximum TWO students per group)
Note: Assignment submission material must include BOTH
(i) written solutions (calculations, graphs etc) in PDF format
(ii) simulink files
Check for due dates (according to computer groups) in Canvas.
Assignment to be submitted in Canvas (include written solutions and
Simulink files), written solutions can be scanned and uploaded.
Problem 1: Cooling system (12 marks)
Consider the well mixed, jacketed cooling system shown below. It is proposed
that the cooling water flow rate Fw will be used to control the outlet stream
temperature T2 against fluctuations in the inlet temperature T1.
Cooling system design and operating conditions:
Jacket heat transfer coefficient: U = 1.225×106 J/hr.m2.C
Area of jacket/tank interface: A = 31 m2
Steady-state flow rate: F = 2.83 m3/hr
Fluid density: r = 993 kg/m3
Fluid heat capacity: Cp = 4190 J/kg C
Volume of fluid in tank: V = 18.2 m3
Volume of fluid in jacket: Vj = 2 m3
Jacket inlet temperature: Tw = 20 C
Steady-state inlet temperature: T1 = 82 C
Steady-state outlet temperature: T2 = 38 C (set point)
Additional information:
Transmitter gain = 1
Valve gain = 1
You may assume that the flow rate F, inlet jacket temperature Tw, fluid volumes
in the tank and the jacket, the fluid and heat exchanger properties are all
constant, but T1, T2, and Fw may change.
Questions:
a) Identify the system parameters and variables (along with variable types
for open- and closed-loop operation). Derive the open-loop transfer
functions that relate changes in T2 to T1, T2 to T, T to Fw, and T to T2,
each with all other variables fixed. Calculate the values of the time
constants and gains. Use these transfer functions to determine the openloop
transfer functions that relate changes in T2 to T1 and T2 to Fw when
T can vary. (4 marks)
b) Sketch the open- and closed-loop block diagrams, and the
instrumentation diagram for the process (transmitter, controller, control
valve) (2 marks)
c) Draw the Simulink model for the control scheme. Use Simulink to
determine the PI and PID tuning parameters using the closed-loop tuning
method (5 marks)
d) Test the PI and PID controllers using the following disturbance: ΔT1 = –5
oC. Comment on which control scheme performs better and why (1
mark)
Problem 2: Heat exchanger (8 marks)
Consider the heat exchanger below, where the inflow rate of acetone is used to
control the outflow temperature of decane.
At steady state, acetone enters at 120°C, heating up the incoming decane
stream from 80°C to 95°C. The outlet temperature of decane stream is
maintained by manipulation of the acetone inlet valve. At steady state operation,
the flow rate of decane is 390 kmol/hr.
To determine the system dynamics, two separate process reaction curve tests
(PRCTs) were performed. In the first PRCT, the decane flow rate was suddenly
decreased to 250 kmol/hr, and outlet decane temperature was recorded in the
table below. For the second PRCT, the acetone valve was suddenly opened
from 20 to 30 % and the outlet decane temperature was recorded in the table
below.
Additional Information:
The valve and transmitter gains are both 1 with negligible dead time and time
constant
TC TT
DECANE IN
ACETONE IN
ACETONE OUT
DECANE OUT
Questions:
a) Identify the control, disturbance and manipulated variables and use the
FOPDT method to estimate the transfer functions for the input variables
(3 marks)
b) Use these transfer functions to tune the control scheme above as PI and
PID controller (1 mark)
c) Draw a block diagram of the process and develop a Simulink model to
test the PI and PID controllers (3 marks)
d) Comment on which controller works best and why (1 mark)
Outlet Decane Temperature Responses to Step Tests
Decane 390 to 250 kmol/hr Acetone Valve 20% to 30%
Time (min) Decane Temp Time (min) Decane Temp
0 90.916 0 85.258
0.3 90.916 0.3 85.258
0.6 90.916 0.6 85.9871
0.9 92.2342 0.9 87.1483
1.2 93.4804 1.2 88.3826
1.5 94.6042 1.5 89.5295
1.8 95.5946 1.8 90.5287
2.1 96.4604 2.1 91.3793
2.4 97.2085 2.4 92.0932
2.7 97.8498 2.7 92.6878
3 98.4003 3 93.1855
3.3 98.8711 3.3 93.5976
3.6 99.2718 3.6 93.9385
3.9 99.6125 3.9 94.2203
4.2 99.9024 4.2 94.4535
4.5 100.149 4.5 94.6464
4.8 100.36 4.8 94.8059
5.1 100.539 5.1 94.938
5.4 100.692 5.4 95.0472
5.7 100.823 5.7 95.1376
6 100.934 6 95.2124
6.3 101.03 6.3 95.2742
6.6 101.111 6.6 95.3253
6.9 101.181 6.9 95.3676
7.2 101.241 7.2 95.4022
7.5 101.292 7.5 95.4309
7.8 101.335 7.8 95.4546
8.1 101.372 8.1 95.4742
8.4 101.404 8.4 95.4903