MICHIGAN STATE UNIVERSITY COLLEGE OF ENGINEERING
Heat Exchanger Control
Experiment
CHE 432: Process Control
Jeff Adkins, Stephen Lindeman, Samantha Oudeh, Julie Wilt, and Isaac Wolf
11/19/2013
Executive Summary
The main goal of this lab was to experimentally characterize and implement a process control
strategy for a heat exchanger system. The temperature of water entering a cold water reservoir was the
measured output variable. The hot water inlet flow rate was the manipulated variable. The first step
taken was to determine the maximum and minimum outlet temperature of the cold water outlet. After
this was completed, the system was characterized by using an open loop configuration and performing
bump tests by manipulating the hot water inlet flow rate. The process gain, time constant, and dead
time were found by fitting the data to a first order plus time delay (FOPDT) model. These were then
used with the Cohen-Coon tuning rule to calculate the parameters that were used for closed loop
control.
Three sets of tuning parameters were tested by changing the set point and adding a system
disturbance. The parameters found from the Cohen-Coon tuning rule were used for the initial run. The
first run resulted in a stable system that reached the desired set point. For the second set of tuning
parameters, the process gain (Kc) was increased to make the system more aggressive. The second run
resulted in a faster response to the set point and disturbance changes while remaining stable. The third
set of tuning parameters used the same process gain as the second set, but also decreased the integral
time constant term. These were determined to be the best set of parameters tested, and resulted in the
lowest peak time and rise time after a change in the set point. However, this tuning set increased the
settling time by 6.7% for a disturbance response when compared to the second tuning set.
The best set of tuning parameters was chosen based on which set resulted in the least integral
error during testing. This was analyzed by calculating the integral squared area error (ISAE) and the
integral squared time area error (ISTAE). The third set of parameters had the lowest calculated ISAE and
ISTAE, which means that it had the smallest total deviation from the set point over time. It was
determined that the third set of parameters resulted in the best system control because it gave the
fastest system response, and also showed the least deviation from the set point.
Introduction
Process controls is important to maintain a specific set point of a system without having to
manually change the process variables. There are many ways to define a control scheme, including the
use of tuning rules. In this experiment, a system is analyzed and fit with tuning rules in order to gauge
the effect on system controller response and stability.
The system in this experiment is comprised of a heater, a heat exchanger, a condenser, and a
reservoir tank. The system can be found in Figure 1. The blue lines correspond to flow of the cold water
and the red lines correspond to flow of the hot water. The flow rate of the hot water is the controlled
variable, while the temperature of the cold water exiting the system is the measured output variable.
The cold water stream is cooled by the air heat exchanger where the temperature is measured by a
thermocouple. The cold water stream then enters a reservoir where it is recycled to the system.
Figure 1. Process Flow Diagram for Heat Exchanger Control System
This heat exchanger system is applicable to other industrial processes. In process plants it is
important to keep a reservoir temperature uniform. For example, condensate and steam systems can
be controlled similarly to this process.
The system is manipulated using a pre-installed computer program. This software allows for 1)
tuning parameters to be altered and 2) system changes to be observed. This program also allows
experimental data to be exported for further analysis. In this heat exchanger experiment, the control
system is characterized by performing bump tests, changing the set point, and introducing a system
disturbance. This will result in a greater understanding of system dynamics and effective controller
schemes for the heat exchanger.
Results
To begin the experiment, the maximum and minimum outlet temperatures were found by
observing the system response at valve positions of 0% and 100% (the valve position percentage
corresponds to the fraction that the valve is open). The maximum outlet temperature was found to be
52.2 OC and the minimum temperature was found to be 36.3 OC.
To characterize the system in the open loop, a valve position was chosen to be 40%. Bump tests
were performed by changing the valve position to 50% and allowing the system to reach steady state.
The valve position was then changed to 30% and the system was again allowed to reach steady state.
The process gain, time constant, and process dead time were found for the open loop system by fitting a
first order plus time delay (FOPTD). The results for these parameters can be found in Table 1, below. See
the Appendix for the complete determination of the FOPTD fit.
Table 1. Open Loop System Characteristics
Parameter
Process Gain (KP)
Value
0.04
Unit
C/%
Time Constant (τP)
14
seconds
Process Dead Time (ϴP)
9.5
seconds
O
Tuning parameters were found using the Cohen-Coon tuning rules found in week 8-9 of the
lecture slides (Table 2). Inputs for tuning rules were inserted into the control scheme and tested for
accuracy. Although parameters with higher degree of accuracy were found, the controller program only
accepted integer values. Therefore, values were rounded to the nearest integer. The controller gain was
entered in terms of proportional band. For sample calculations on the Cohen-Coon parameters and
proportional band, see the Appendix.
Table 2. Closed Loop Tuning Parameters
Tuning Parameter
Controller Gain (KC)
Proportional Band (PB)
Value
55.37
Unit
C/%
O
--
Integral Time Constant (τI)
11
19
seconds
Derivative Time Constant (τD)
3
seconds
A set point test (Figure 2) was performed with the initial tuning rules where the set point was
changed from 47oC to 49oC. After the system stabilized, it was then disturbed by shutting off the cold
water supply pump for 10 seconds (Figure 3). The system response was plotted for both the set point
change and disturbance.
Reservoir Temperature (°C)
50
49.5
49
48.5
48
47.5
47
PV
46.5
SP
46
600
800
1000
1200
Time (s)
Reservoir Temperature (°C)
Figure 2. Set Point Test for Tuning Parameter 1
54
52
50
48
46
44
PV
42
SP
40
1384
1434
1484
1534
Time (s)
Figure 3. Disturbance Test for Tuning Parameter 1
The tuning rules were then modified in a series of runs to determine the most accurate set of tuning
rules. See Table 3 for a summary of runs performed. Plots for all additional sets can be found in the
Appendix.
Table 3. Summary of Tuning Parameter Sets
Tuning Set
1
2
3
Proportional Band
11
8
8
Integral Time Constant (s)
19
19
13
Derivative Time Constant (s)
3
3
3
Discussion
To analyze the overall performance of each tuning set, calculations were done to analyze the
overall error in each response. The first error calculation was the integral squared area error (ISAE). The
ISAE was calculated by finding the area bounded by the set point and process value. The second error
calculation was the integral squared time area error (ISTAE) where the overall error is time dependent;
therefore, error is weighted heavier after longer periods of time. Both error evaluations show that the
3rd tuning set showed a response closest to the set point as seen in Table 4, below.
In addition to the error analysis, the system rise time, peak time, and peak overshoot ratios
were found for each run. These helped measure the response time and the aggressiveness of the
response. As seen in Table 4 below, the rise time and peak time decreased with more aggressive tuning
parameters.
Increasing the controller gain makes the controller more aggressive in its attempt to return the
outlet temperature to the set point. By increasing KC, it is expected that the peak overshoot ratio
increases. The results in Table 4, below show that both tuning sets 1 and 2 have the same peak
overshoot despite an increase in KC. This is likely due to the temperature reading limitations. The
temperature reports to the nearest 0.1OC; therefore, the difference may not have been large enough to
show a change in the reported overshoot.
Table 4. Summary of Set Point Tests
Tuning Set
ISAE (°C2s)
ISTAE (°C2s2)
Rise Time (s)
Peak Time(s)
Peak Overshoot Ratio
1
2
3
103
81
77
10,766
1,687
1,424
78
67
45
122
107
83
0.15
0.15
0.15
A similar analysis was performed on the disturbance tests for each run. An error analysis showed
trends similar to the set point test where the 3rd tuning set resulted in the least error as shown in Table
5 below. In addition, the settling time was calculated by determining where the response remained
within 0.1OC of the set point. The results showed that though tuning set 3 had the least error it had a
longer settling time than tuning set 2.
The disturbance was theoretically equivalent for each tuning set; however, differences are likely
due to human error. The disturbance was introduced to the system by unplugging the cold water pump
for 10 seconds. There is a lag time associated with unplugging the pump and plugging it back in that may
have contributed to error.
Table 5. Summary of Disturbance Tests
Tuning Set
ISAE (°C2s)
ISTAE (°C2s2)
Settling Time (s)
1
52
4,403
98
2
75
1,074
60
3
46
774
64
Due to time constraints, runs could not be extended long enough for multiple oscillations to
occur; therefore, a decay ratio for each run was not found for tuning sets 2 and 3. For tuning set 1, the
decay ratio was found to be 1. It is likely that this is due to the same discrepancy in temperature reading
limitations as described above.
The heat exchanger system had physical components that limited the effectiveness of tuning
procedures. One of the physical constraints is the heat transfer in the heat exchanger. It can be assumed
that there is not perfect heat exchange in the system due to resistances such as fouling, pipe
conductivity, and heat exchanger area. The resistance to heat exchange can cause limitations in the
output temperature of the cold stream.
An additional physical constraint was the relatively small volume of cool water available in the
reservoir. The air-cooled heat exchanger was unable to lower the effluent water temperature back to
the original value. As each run of the experiment progressed, the water temperature in the reservoir
gradually increased. Due to recycling of the cold water from the reservoir, the outlet temperature was
slightly more difficult to control than if the cold water was always fed at a constant temperature to the
process. To alleviate this constraint, reservoir water was changed out after each run. This change-out
could not be exact, since the water was retrieved from a faucet. To decrease human error, the same
person re-filled the reservoir each time so that change-out would be consistent.
A more efficient air-cooled exchanger would improve the process and eliminate the gradual
temperature increase. However, with the current equipment and as stated above, the reservoir water
had to be changed frequently to avoid higher temperature readings. If the inlet temperature varied
extensively within an experimental run, the determined tuning parameters would not accurately
characterize the system.
It is likely that a cascade control system would improve the control scheme for the heat
exchanger system. The cascade system would work by adding a second loop with a flow indicator and
additional control of the valve position of the hot stream. This system would respond to disturbances in
flow rate of the hot stream such as a pump failure or fluctuations in flow rate.
Conclusions
From the data shown above, the 3rd tuning set was determined to be the best control scheme. In
this tuning set, the proportional band was set at 8, the integral time constant was 13 and the derivative
time constant was 3. These parameters were stepped from an initial guess using Cohen-Coon tuning
rules. From trends seen in this experiment, more aggressive tuning parameters provide less overall
error. With further experimentation, proportional band could be increased and integral time could be
decreased further to provide even better tuning parameters in the bounds of system stability.
Appendix and Sample Calculations
Figure 1A. Tuning Parameter Determination
𝛼 = 𝑡𝑃𝑉 𝑠𝑡𝑎𝑟𝑡 − 𝑡𝐶𝑂 𝑠𝑡𝑒𝑝 = 197 − 187.5 = 9.5 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝜏 = 𝑡63.2 − 𝑡𝑃𝑉 𝑠𝑡𝑎𝑟𝑡 = 211 − 197 = 14 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝐾=
0.1 <
∆𝑃𝑉 50.6 − 49.8
°𝐶
=
= 0.04
∆𝐶𝑂
50 − 30
%
𝛼 9.5
=
= 0.68 < 1 → Cohen − Coon is valid
𝜏 14
1
𝜏
4
1 𝛼
𝐾𝑐 = 𝐾 ∗ (𝛼) ∗ [3 + 4 ( 𝜏 )]
(1)
1
14
4 1 9.5
∗ ( ) ∗ [ + ( )] = 55.37
0.04 9.5
3 4 14
𝛼
𝜏
𝛼
13+8∗( )
𝜏
32+6∗( )
𝜏𝐼 = 𝛼 ∗ [
]
(2)
9.5
32 + 6 ∗ ( 14 )
9.5 ∗ [
] = 18.59 ≅ 19
9.5
13 + 8 ∗ ( )
14
𝜏𝐷 = 𝛼 ∗ [
9.5 ∗ [
𝐾𝐶 = 55.37 ∗
4
𝛼
𝜏
11+2∗( )
4
9.5
11 + 2 ∗ ( 14 )
]
(3)
] = 3.08 ≅ 3
∆𝑃𝑉
52.2 − 36.3
= 55.37 ∗
= 8.80
∆𝐶𝑂
100 − 0
𝑃𝐵 =
𝑃𝐵 =
100
𝐾𝑐
100
= 11.36 ≅ 11
8.80
(4)
49.5
49
48.5
48
47.5
47
PV
46.5
SP
46
500
550
600
650
700
750
Time (s)
Figure 2A. Set Point Test for Tuning Parameter 2
Reservoir Temperature (oC)
Reservoir Temperature (oC)
50
54
52
50
48
46
44
PV
42
SP
40
779
829
879
929
Time (s)
Figure 3A. Disturbance Test for Tuning Parameter 2
49.5
49
48.5
48
47.5
47
PV
46.5
SP
46
300
350
400
450
500
550
Time (s)
Figure 4A. Set Point Test for Tuning Parameter 3
54
Reservoir Temperature (°C)
Reservoir Temperature (°C)
50
52
50
48
46
44
PV
42
SP
40
585
635
685
735
Time (s)
Figure 5A. Disturbance Test for Tuning Parameter 3