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CHEMICAL ENGINEERING LABORATORY II
1.0 TITLE OF EXPERIMENT: Temperature Process Control.
2.0 OBJECTIVES OF EXPERIMENT
The objective of this experiment is to demonstrate and understand the characteristic
of proportional (P), proportional integral (PI) and proportional-integral-derivative
(PID) controller in a temperature control loop. Besides that, the objective of this
experiment is also to observe the different types of temperature responses to P, PI,
and PID controller.
3.0 INTRODUCTION
Temperature process control is a process of where the temperature of the fluid is
changed in order to be measured, as the heat energy in or out of the space is adjusted
to achieve a desired average or optimum temperature. The temperature control
system consists of a heat exchanger, a sensor, a controller and a control panel. The
controller is used for maintaining the temperature measuring the process variable at a
particular set. In this experiment, a circulation pump transfers water within a closed
circuit in order to allow water to experience heat exchange between the hot and cold
water. The water flow is controlled by an actuator, taking place automatically should
any deviation occurs from the set point with the supply of compressed air.
A proportionalintegralderivative controller (PID controller) is a control
loop feedback mechanism, which is able to minimize errors of the values by
adjusting the process control inputs. The output of a PID controller is a linear
combination of P, I, and D modes of control. The proportional controller, or P
controller, is a linear type of feedback control system and is more complex than an
on-off control system, but simpler than a proportional-integral-derivative (PID)
control system. However, the P-only controller still has some amount of offset away
from the set point. Therefore, with the addition of an extra controlling system, the
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integral controller, forming the proportional-integral (PI) control. The integral action
will attempt to avoid or minimize the offset created in the proportional control by
bringing the output closer to the set point. PID control system is a linear combination
of P, I and the derivative (D) which permits an increase in the proportional gain,
offsetting the decrease error from the integral controlling. The derivative action
reduces the period of cycling, yet producing the same speed of response as with the
proportional action but without offsets.
PI controller offers a balance of complexity and capability that makes them
popular in many process control applications due to the integral action that enables
PI controllers to eliminate offsets.
4.0 MATERIALS AND EQUIPMENT
Figure 4.1: Schematic Diagram of Temperature Control Unit / Trainer.
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5.0 RESULTS AND CALCULATIONS
Experiment 1: Closed Loop Proportional (P) Control
Variable= P Value
Constant = I Value (600 s) and D Value (0 s)
Table 5.1: Load Change (PB = 5)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:10:11 45.0 45.0 12.4
23/03/2011 14:10:13 45.1 45.0 11.8
23/03/2011 14:10:43 43.2 45.0 49.7
23/03/2011 14:11:13 43.1 45.0 50.1
23/03/2011 14:11:43 45.1 45.0 10.623/03/2011 14:12:13 45.1 45.0 11.4
23/03/2011 14:12:43 45.0 45.0 13.3
23/03/2011 14:13:13 44.9 45.0 14.4
23/03/2011 14:13:43 45.0 45.0 12.4
23/03/2011 14:14:13 44.9 45.0 14.3
Figure 5.1: Load Change (PB = 5)
Table 5.2: Set Point Change (PB = 5)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 17:12:58 44.9 45.0 28.7
23/03/2011 17:13:00 44.9 45.0 27.9
23/03/2011 17:13:30 47.3 50.0 79.623/03/2011 17:14:00 47.8 50.0 70.7
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23/03/2011 17:14:30 47.6 50.0 75.4
23/03/2011 17:15:00 47.7 50.0 71.7
23/03/2011 17:15:30 47.8 50.0 71.1
23/03/2011 17:16:00 47.2 50.0 83.9
23/03/2011 17:16:30 47.5 50.0 76.9
23/03/2011 17:17:00 47.7 50.0 73.523/03/2011 17:17:30 47.8 50.0 72.7
23/03/2011 17:18:00 47.9 50.0 69.5
23/03/2011 17:18:30 47.3 50.0 82.4
23/03/2011 17:19:00 47.4 50.0 81.6
23/03/2011 17:19:30 47.5 50.0 78.4
23/03/2011 17:20:00 47.7 50.0 75.4
23/03/2011 17:20:30 47.9 50.0 71.7
23/03/2011 17:21:00 47.2 50.0 85.8
23/03/2011 17:21:30 47.4 50.0 80.9
Figure 5.2: Set Point Change (PB = 5)
Table 5.3: Load Change (PB = 20)
Date Time TT01 (C) Set Point (C) Output (%)23/03/2011 14:02:09 45.1 45.0 13.1
23/03/2011 14:02:39 43.6 45.0 20.5
23/03/2011 14:03:09 41.4 45.0 31.9
23/03/2011 14:03:39 44.0 45.0 19.1
23/03/2011 14:04:09 45.1 45.0 13.5
23/03/2011 14:04:39 45.2 45.0 12.9
23/03/2011 14:05:09 45.0 45.0 14.1
23/03/2011 14:05:39 45.0 45.0 14.0
23/03/2011 14:06:09 45.0 45.0 13.8
23/03/2011 14:06:39 44.9 45.0 14.2
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Figure 5.3: Load Change (PB = 20)
Table 5.4: Set Point Change (PB = 20)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 16:55:30 44.7 45.0 28.1
23/03/2011 16:55:32 44.7 45.0 28.1
23/03/2011 16:56:02 46.4 50.0 44.5
23/03/2011 16:56:32 46.6 50.0 43.6
23/03/2011 16:57:02 46.4 50.0 44.7
23/03/2011 16:57:32 46.1 50.0 46.6
23/03/2011 16:58:02 46.4 50.0 45.1
23/03/2011 16:58:32 46.5 50.0 44.7
23/03/2011 16:59:02 46.6 50.0 44.4
23/03/2011 16:59:32 46.7 50.0 43.9
23/03/2011 17:00:02 46.0 50.0 47.1
23/03/2011 17:00:32 46.3 50.0 46.0
23/03/2011 17:01:02 46.4 50.0 45.5
23/03/2011 17:01:32 46.5 50.0 45.0
23/03/2011 17:02:02 46.7 50.0 44.4
23/03/2011 17:02:32 46.0 50.0 47.8
23/03/2011 17:03:02 46.3 50.0 46.523/03/2011 17:03:32 46.5 50.0 45.6
23/03/2011 17:04:02 46.6 50.0 45.3
23/03/2011 17:04:32 46.1 50.0 47.5
23/03/2011 17:05:02 46.3 50.0 46.9
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Figure 5.4: Set Point Change (PB = 20)
Table 5.5: Load Change (PB = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 13:26:15 44.9 45.0 15.1
23/03/2011 13:26:45 45.3 45.0 14.8
23/03/2011 13:27:15 45.2 45.0 14.8
23/03/2011 13:27:45 43.8 45.0 16.3
23/03/2011 13:28:15 39.8 45.0 20.3
23/03/2011 13:28:45 45.0 45.0 15.1
23/03/2011 13:29:15 44.9 45.0 15.2
23/03/2011 13:29:45 45.2 45.0 14.9
23/03/2011 13:30:15 45.0 45.0 15.1
23/03/2011 13:30:45 45.3 45.0 14.8
23/03/2011 13:31:15 45.5 45.0 14.5
23/03/2011 13:31:45 45.2 45.0 14.8
23/03/2011 13:32:15 45.3 45.0 14.8
23/03/2011 13:32:45 45.5 45.0 14.5
23/03/2011 13:33:15 45.2 45.0 14.8
Figure 5.5: Load Change (PB = 100)
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Table 5.6: Set Point Change (PB = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 13:38:47 45.2 45.0 14.8
23/03/2011 13:39:17 45.1 45.0 14.9
23/03/2011 13:39:47 44.9 45.0 15.1
23/03/2011 13:40:17 45.9 50.0 19.223/03/2011 13:40:47 45.5 50.0 19.6
23/03/2011 13:41:17 45.7 50.0 19.4
23/03/2011 13:41:47 45.9 50.0 19.2
23/03/2011 13:42:17 45.6 50.0 19.5
23/03/2011 13:42:47 45.5 50.0 19.7
23/03/2011 13:43:17 46.2 50.0 19.0
23/03/2011 13:43:47 46.0 50.0 19.2
23/03/2011 13:44:17 45.7 50.0 19.5
23/03/2011 13:44:47 46.0 50.0 19.3
23/03/2011 13:45:17 45.9 50.0 19.323/03/2011 13:45:47 45.7 50.0 19.6
23/03/2011 13:46:17 46.0 50.0 19.3
23/03/2011 13:46:47 45.9 50.0 19.4
23/03/2011 13:47:17 45.5 50.0 19.8
23/03/2011 13:47:47 45.8 50.0 19.5
23/03/2011 13:48:17 45.9 50.0 19.5
23/03/2011 13:48:47 45.5 50.0 19.9
23/03/2011 13:49:17 46.0 50.0 19.5
23/03/2011 13:49:47 45.9 50.0 19.5
23/03/2011 13:50:17 45.9 50.0 19.6
23/03/2011 13:50:47 46.2 50.0 19.3
23/03/2011 13:51:17 45.9 50.0 19.6
23/03/2011 13:51:47 45.9 50.0 19.6
23/03/2011 13:52:17 46.2 50.0 19.4
23/03/2011 13:52:47 45.8 50.0 19.7
Figure 5.6: Set Point Change (PB = 100)
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Table 5.7: Mean Temperatures, Settling Time for Different PB Values
PB value
Mean Temperature (C) Settling Time (s)
Load ChangeSet Point
ChangeLoad Change
Set Point
Change
5 45.0 47.6 71 127
20() 45.0 46.3 67 41100 45.2 46.0 467 1
Experiment 2: Closed Loop Proportional-Integral (PI) Control
Variable= I Value
Constant = P Value (20 s) and D Value (0 s)
Table 5.8: Load Change (I = 1)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:33:41 45.0 45.0 13.7
23/03/2011 14:33:43 45.0 45.0 13.6
23/03/2011 14:34:13 42.6 45.0 46.3
23/03/2011 14:34:43 47.3 45.0 17.4
23/03/2011 14:35:13 45.3 45.0 12.6
23/03/2011 14:35:43 45.1 45.0 11.1
23/03/2011 14:36:13 44.9 45.0 12.5
23/03/2011 14:36:43 44.9 45.0 14.8
23/03/2011 14:37:13 45.1 45.0 12.8
23/03/2011 14:37:43 44.9 45.0 13.3
23/03/2011 14:38:13 44.9 45.0 15.2
Figure 5.7: Load Change (I = 1)
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Table 5.9: Set Point Change (I = 1)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 16:37:29 45.1 45.0 28.1
23/03/2011 16:37:31 45.0 45.0 28.2
23/03/2011 16:38:01 46.9 50.0 92.4
23/03/2011 16:38:31 47.4 50.0 100.023/03/2011 16:39:01 47.7 50.0 100.0
23/03/2011 16:39:31 47.7 50.0 100.0
23/03/2011 16:40:01 48.0 50.0 100.0
23/03/2011 16:40:31 48.1 50.0 100.0
23/03/2011 16:41:01 47.5 50.0 100.0
23/03/2011 16:41:31 47.4 50.0 100.0
23/03/2011 16:42:01 47.7 50.0 100.0
23/03/2011 16:42:31 47.8 50.0 100.0
23/03/2011 16:43:01 47.9 50.0 100.0
23/03/2011 16:43:31 48.0 50.0 100.023/03/2011 16:44:01 47.3 50.0 100.0
23/03/2011 16:44:31 47.5 50.0 100.0
23/03/2011 16:45:01 47.7 50.0 100.0
23/03/2011 16:45:31 47.8 50.0 100.0
23/03/2011 16:46:01 48.0 50.0 100.0
23/03/2011 16:46:31 47.6 50.0 100.0
23/03/2011 16:47:01 47.6 50.0 100.0
23/03/2011 16:47:31 47.7 50.0 100.0
23/03/2011 16:48:01 47.9 50.0 100.0
Figure 5.8: Set Point Change (i = 1)
Table 5.10: Load Change (I = 10)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:27:14 45.0 45.0 12.7
23/03/2011 14:27:16 45.0 45.0 12.8
23/03/2011 14:27:46 44.9 45.0 13.5
23/03/2011 14:28:16 45.3 45.0 11.7
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23/03/2011 14:28:46 45.4 45.0 10.5
23/03/2011 14:29:16 45.1 45.0 11.7
23/03/2011 14:29:46 44.9 45.0 12.8
23/03/2011 14:30:16 45.2 45.0 11.3
23/03/2011 14:30:46 45.3 45.0 10.6
23/03/2011 14:31:16 44.9 45.0 12.2
Figure 5.9: Load Change (I = 10)
Table 5.11: Set Point Change (I = 10)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 16:24:17 45.2 45.0 28.423/03/2011 16:24:32 45.3 45.0 28.0
23/03/2011 16:25:02 47.0 50.0 48.6
23/03/2011 16:25:32 46.6 50.0 55.5
23/03/2011 16:26:02 47.1 50.0 57.8
23/03/2011 16:26:32 47.3 50.0 61.0
23/03/2011 16:27:02 47.6 50.0 63.4
23/03/2011 16:27:32 47.7 50.0 66.1
23/03/2011 16:28:02 47.1 50.0 72.9
23/03/2011 16:28:32 47.3 50.0 76.7
23/03/2011 16:29:02 47.5 50.0 79.5
23/03/2011 16:29:32 47.6 50.0 82.5
23/03/2011 16:30:02 47.8 50.0 85.1
23/03/2011 16:30:32 48.0 50.0 87.4
23/03/2011 16:31:02 48.0 50.0 90.1
23/03/2011 16:31:32 47.5 50.0 96.2
23/03/2011 16:32:02 47.3 50.0 100.0
23/03/2011 16:32:32 47.6 50.0 100.0
23/03/2011 16:33:02 47.7 50.0 100.0
23/03/2011 16:33:32 48.0 50.0 100.0
23/03/2011 16:34:02 48.0 50.0 100.0
23/03/2011 16:34:32 48.1 50.0 100.023/03/2011 16:35:02 47.9 50.0 100.0
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Figure 5.10: Set Point Change (I = 10)
Table 5.12: Load Change (I = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:19:49 44.8 45.0 13.1
23/03/2011 14:19:55 44.8 45.0 13.2
23/03/2011 14:20:25 41.4 45.0 30.5
23/03/2011 14:20:55 44.9 45.0 13.2
23/03/2011 14:21:25 45.1 45.0 12.0
23/03/2011 14:21:55 44.9 45.0 13.1
23/03/2011 14:22:25 45.1 45.0 12.3
23/03/2011 14:22:55 45.2 45.0 11.723/03/2011 14:23:25 45.1 45.0 12.3
23/03/2011 14:23:55 44.9 45.0 13.4
Figure 5.11: Load Change (I = 100)
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Table 5.13: Set Point Change (I = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 16:11:12 44.8 45.0 28.0
23/03/2011 16:11:14 44.8 45.0 28.0
23/03/2011 16:11:44 46.8 50.0 100.0
23/03/2011 16:12:14 47.8 50.0 100.023/03/2011 16:12:44 47.8 50.0 100.0
23/03/2011 16:13:14 48.0 50.0 100.0
23/03/2011 16:13:44 48.1 50.0 100.0
23/03/2011 16:14:14 47.8 50.0 100.0
23/03/2011 16:14:44 47.3 50.0 100.0
23/03/2011 16:15:14 47.6 50.0 100.0
23/03/2011 16:15:44 47.7 50.0 100.0
23/03/2011 16:16:14 47.9 50.0 100.0
23/03/2011 16:16:44 48.1 50.0 100.0
23/03/2011 16:17:14 48.1 50.0 100.023/03/2011 16:17:44 47.2 50.0 100.0
23/03/2011 16:18:14 47.5 50.0 100.0
23/03/2011 16:18:44 47.7 50.0 100.0
23/03/2011 16:19:14 47.8 50.0 100.0
23/03/2011 16:19:44 48.0 50.0 100.0
Figure 5.12: Set Point Change (I = 100)
Table 5.14: Mean Temperatures and Settling Time for Different I Values
I value
Mean Temperature (C) Settling Time (s)
Load ChangeSet Point
ChangeLoad Change
Set Point
Change
1() 45.0 47.7 36 14010 45.2 47.8 42 630
100 45.1 47.8 73 300
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Experiment 3: Closed Loop Proportional-Integral-Derivative (PID) Control
Variable= D Value
Constant = P Value (20 s) and I Value (1 s)
Table 5.15: Load Change (D = 1)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:41:26 45.4 45.0 13.4
23/03/2011 14:41:29 45.4 45.0 13.6
23/03/2011 14:41:59 44.3 45.0 30.1
23/03/2011 14:42:29 43.0 45.0 20.9
23/03/2011 14:42:59 44.2 45.0 23.7
23/03/2011 14:43:29 44.4 45.0 23.6
23/03/2011 14:43:59 44.5 45.0 24.8
23/03/2011 14:44:29 44.3 45.0 26.0
23/03/2011 14:44:59 44.5 45.0 25.923/03/2011 14:45:29 44.6 45.0 26.1
23/03/2011 14:45:59 44.4 45.0 28.8
23/03/2011 14:46:29 44.5 45.0 27.5
23/03/2011 14:46:59 44.7 45.0 27.6
Figure 5.13: Load Change (D = 1)
Table 5.16: Set Point Change (D = 1)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 14:57:49 44.8 45.0 31.7
23/03/2011 14:57:50 44.8 45.0 31.6
23/03/2011 14:58:20 46.4 50.0 49.4
23/03/2011 14:58:50 47.0 50.0 53.6
23/03/2011 14:59:20 47.2 50.0 56.8
23/03/2011 14:59:50 47.2 50.0 62.0
23/03/2011 15:00:20 47.1 50.0 65.6
23/03/2011 15:00:50 47.4 50.0 68.7
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23/03/2011 15:01:20 47.7 50.0 70.8
23/03/2011 15:01:50 47.9 50.0 73.0
23/03/2011 15:02:20 47.8 50.0 77.7
23/03/2011 15:02:50 47.2 50.0 84.0
23/03/2011 15:03:20 47.5 50.0 85.7
23/03/2011 15:03:50 47.6 50.0 89.323/03/2011 15:04:20 47.8 50.0 91.6
23/03/2011 15:04:50 48.0 50.0 93.6
23/03/2011 15:05:20 47.7 50.0 99.7
23/03/2011 15:05:50 47.4 50.0 100.0
23/03/2011 15:06:20 47.7 50.0 100.0
23/03/2011 15:06:50 47.8 50.0 100.0
23/03/2011 15:07:20 47.9 50.0 100.0
23/03/2011 15:07:50 48.1 50.0 100.0
23/03/2011 15:08:20 48.0 50.0 100.0
23/03/2011 15:08:50 47.2 50.0 100.023/03/2011 15:09:20 47.6 50.0 100.0
23/03/2011 15:09:50 47.7 50.0 100.0
23/03/2011 15:10:20 47.8 50.0 100.0
Figure 5.14: Set Point Change (D = 1)
Table 5.17: Load Change (D = 10)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 15:15:43 44.9 45.0 31.8
23/03/2011 15:15:46 44.9 45.0 30.1
23/03/2011 15:16:16 43.7 45.0 53.7
23/03/2011 15:16:46 45.2 45.0 19.0
23/03/2011 15:17:16 45.5 45.0 23.4
23/03/2011 15:17:46 45.6 45.0 26.8
23/03/2011 15:18:16 45.7 45.0 26.2
23/03/2011 15:18:46 45.8 45.0 24.4
23/03/2011 15:19:16 45.8 45.0 26.323/03/2011 15:19:46 45.6 45.0 25.8
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23/03/2011 15:20:16 45.8 45.0 22.7
23/03/2011 15:20:46 45.7 45.0 23.3
23/03/2011 15:21:16 45.6 45.0 23.0
23/03/2011 15:21:46 45.6 45.0 20.5
23/03/2011 15:22:16 45.6 45.0 19.0
23/03/2011 15:22:46 45.4 45.0 22.223/03/2011 15:23:16 45.3 45.0 19.9
Figure 5.15: Load Change (D = 10)
Table 5.18: Set Point Change (D = 10)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 15:33:09 45.0 45.0 30.0
23/03/2011 15:33:11 45.2 45.0 24.8
23/03/2011 15:33:41 46.6 50.0 28.5
23/03/2011 15:34:11 47.0 50.0 36.1
23/03/2011 15:34:41 47.6 50.0 38.3
23/03/2011 15:35:11 48.1 50.0 40.2
23/03/2011 15:35:41 48.0 50.0 52.0
23/03/2011 15:36:11 48.3 50.0 49.5
23/03/2011 15:36:41 48.6 50.0 48.3
23/03/2011 15:37:11 48.6 50.0 55.9
23/03/2011 15:37:41 48.4 50.0 58.723/03/2011 15:38:11 48.7 50.0 56.4
23/03/2011 15:38:41 49.0 50.0 56.8
23/03/2011 15:39:11 48.7 50.0 67.8
23/03/2011 15:39:41 48.6 50.0 63.5
23/03/2011 15:40:11 48.9 50.0 62.9
23/03/2011 15:40:41 49.0 50.0 64.4
23/03/2011 15:41:11 49.0 50.0 69.9
23/03/2011 15:41:41 48.5 50.0 79.1
23/03/2011 15:42:11 48.9 50.0 70.1
23/03/2011 15:42:41 49.1 50.0 70.523/03/2011 15:43:11 49.3 50.0 71.1
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Figure 5.16: Set Point Change (D = 10)
Table 5.19: Load Change (D = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 15:48:45 45.2 45.0 22.4
23/03/2011 15:48:47 45.2 45.0 22.2
23/03/2011 15:49:17 43.8 45.0 64.8
23/03/2011 15:49:47 45.0 45.0 30.6
23/03/2011 15:50:17 45.1 45.0 28.6
23/03/2011 15:50:47 45.2 45.0 28.2
23/03/2011 15:51:17 45.1 45.0 33.0
23/03/2011 15:51:47 45.2 45.0 31.423/03/2011 15:52:17 45.3 45.0 30.4
23/03/2011 15:52:47 45.4 45.0 28.1
23/03/2011 15:53:17 45.3 45.0 32.6
23/03/2011 15:53:47 45.3 45.0 32.5
Figure 5.17: Load Change (D = 100)
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Table 5.20: Set Point Change (D = 100)
Date Time TT01 (C) Set Point (C) Output (%)
23/03/2011 15:55:25 45.3 45.0 35.4
23/03/2011 15:55:35 45.3 45.0 35.6
23/03/2011 15:56:05 46.2 50.0 40.4
23/03/2011 15:56:35 46.4 50.0 43.023/03/2011 15:57:05 46.7 50.0 42.5
23/03/2011 15:57:35 47.0 50.0 44.5
23/03/2011 15:58:05 46.6 50.0 63.1
23/03/2011 15:58:35 46.9 50.0 61.2
23/03/2011 15:59:05 47.2 50.0 62.8
23/03/2011 15:59:35 47.3 50.0 64.4
23/03/2011 16:00:05 47.5 50.0 67.7
23/03/2011 16:00:35 47.7 50.0 67.9
23/03/2011 16:01:05 47.3 50.0 87.0
23/03/2011 16:01:35 47.4 50.0 92.623/03/2011 16:02:05 47.5 50.0 93.2
23/03/2011 16:02:35 47.7 50.0 94.8
23/03/2011 16:03:05 47.8 50.0 97.5
23/03/2011 16:03:35 48.0 50.0 97.0
23/03/2011 16:04:05 48.1 50.0 98.9
23/03/2011 16:04:35 47.4 50.0 100.0
23/03/2011 16:05:05 47.4 50.0 100.0
23/03/2011 16:05:35 47.5 50.0 100.0
23/03/2011 16:06:05 47.7 50.0 100.0
23/03/2011 16:06:35 47.8 50.0 100.0
Figure 5.18: Set Point Change (D = 100)
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Table 5.21: Mean Temperatures and Settling Time for Different I Values
D value
Mean Temperature (C) Settling Time (s)
Load ChangeSet Point
ChangeLoad Change
Set Point
Change
1() 44.5 47.7 65 44610 45.7 48.9 208 >750100 45.2 47.7 234 550
Offset Calculation
Taking P=5 in Experiment 1 as sample calculation,
Offset = Mean Value of Operating TemperatureSet Point
= 47.6 C45 C
= 2.6 C
Refer Table 6.1 for complete offset values for all conditions.
Overshoot Calculation
Figure 5.19: Performance characteristics of an underdamped process.
Overshoot is only applicable when the system attempts to make the response of the
controlled variable to a set-point change, which exhibit a prescribed amount of
overshoot and oscillation as it settles at the new operating point.
eh
ts= settling time
tp = time to first peak
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By using Figure 5.2 for reference for calculation,
Overshoot summary,
Table 5.22: Offset value for proportional change only
P Overshoot % Remarks
100 - No overshoot
20 () 17.0212766 -
5 35.71428571 -
Table 5.23: Offset value for proportional change onlyI Overshoot % Remarks
1 - No overshoot, drifting oscillation only
10 - Drifting new set point
100 - No overshoot, drifting oscillation only
Table 5.24: Offset value for proportional change only
D Overshoot % Remarks
1 - Drifting new set point
10 20 -
100 - Drifting new set point
6.0 DISCUSSION
Figure 6.1: Temperature Control System Block Diagram
P
I
D
Temperature
Controller
Error
Detector
Control
Valve
Process
Temperature
Transmitter
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Figure 6.1 indicates the cycle of temperature control system. The temperature
transmitter used to measure the current temperature, . The temperature transmitter
will send an analogue signal to the error detector so that the error detector can
compare the value between the analogue of current temperature,
and the set point
temperature, . The temperature controller will then receive the error from the
Error Detector through the P,I and D. Controller will send an electrical current signal
to the Control Valve and the control valve is used to vary the liquid flow rate. The
liquid flow rate will be controlled by the openings of the control valve.
Temperature control utilizes a feedback loop that begins with a system's
measured temperature. A temperature sensor - typically a thermocouple, RTD or
thermistor - measures a process's real-time temperature and feeds the reading back to
a controller. The controller compares the measured temperature to the set point
temperature and actuates devices like heaters or valves to bring the temperature to
the desired set point. The three most common methods of control are proportional
(P), proportional-integral (PI) and proportional-integral-derivative (PID). For this
experiment we had two parts to be done, that are load change and set point change.
This both, are actually the disturbance of the process. The disturbances are the
change of the flow rate in between and also the set point change (temperature
change). When there is disturbance, there will be some fluctuating in the current
value of temperature. The current value of temperature supposed to be nearest to the
set point, but due to the disturbance the value will shoot up. To come back to the set
point value, the output (the opener of valve) will be increased automatically to have a
current value of temperature near to the set point.
For the load change experiment, the cold water flow rate is changed from 5
LPM to 10 LPM and back to 5 LPM. The increased in the amount of cold water
entering the heat exchanger will cause the reduction of water outlet temperature. This
introduced disturbance will cause the system to respond and try to return the cold
water outlet temperature to the set point by controlling the electro-pneumatic
proportional valve (adjusting the opening of hot water inlet). For the set point change
experiment, the set point is increased from 45 C to 50 C. This increase in set point
will cause the system to try to give response so that the process value (temperature)
matches the new set point.
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For proportional control, the controller output is proportional to the error
signal. A disadvantage of proportional-only control is that a steady-state error or
offset occurs after a set-point change or a sustained disturbance. In principle, offset
can be eliminated by manually resetting either the set-point or bias value after an
offset occurs. However, this approach is inconvenient because operator intervention
is required and the new value of set point must usually be found by trial and error.
Integral control action provides automatic reset of set point. It is widely used
because it provides an important practical advantage, the elimination of offset. When
integral action is used, controller output changes automatically until it attains the
value required to make the steady state error zero. Proportional-integral controller
provides immediate corrective action as soon as an error is detected without the
problem of offset. One disadvantage of using integral actions is that it tends to
produce oscillatory response of the controlled variable and reduces the stability of
the feedback control system. A limited amount of oscillation can be tolerated
because it is often associated with a faster response. The undesirable effects of too
much integral action can be avoided by proper tuning of the controller or by
including derivative action which tends to counteract the destabilizing effects.
Derivative control action is to anticipate the future behavior of the error
signal by considering its rate of change. While for proportional control, it reacts to a
deviation in temperature only, making no distinction as to the time period over which
the deviation develops. Integral control action is also ineffective for a sudden change
in temperature because corrective action occurs when the deviation persists for a
long period. Derivative control action also tends to improve the dynamic response of
the controlled variable by decreasing the process settling time, the time it takes the
process to reach steady state.
In conclusion, when there is a step change in a disturbance variable occurs,
proportional control speeds up the process response and reduces the offset. The
addition of integral control action eliminates offset but tends to make the response
more oscillatory. Adding derivative action reduced both the degree of oscillation and
the response time.
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Table 6.1: Comparison between Different Values of P, I and D.
Controller
Mode
Proportional Proportional-Integral Proportional-Integral-Derivative
P=100 P=20 P=5 I=100 I=10 I=1 D=1 D=10 D=100
Operating
Value46 46.3 47.6 47.8 47.8 47.7 47.7 48.9 46.45
Offsets 1 1.3 2.6 2.8 2.8 2.7 2.8 2.7 2.7
Response
Time
Almost Immediate
Response
Behavior
Moderate
Oscillation
Little
Oscillation
Large
Oscillation
Moderate
Oscillation
Large
Oscillation
Little
Oscillation
Little
Oscillation
Moderate
Oscillation
Large
Oscillation
Selection
Table 6.2: Comparison between P, PI and PID of Controller Mode.
Controller Mode Proportional Proportional-Integral Proportional-Integral-Derivative
Operating Value 46.63 47.77 48.1
Offsets 1.63 2.77 3.1
Response Time Almost Immediate
Response
Behavior Little Oscillation Moderate Oscillation Large Oscillation
Selection
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From the graphs and results, it can be clearly seen that the set point change
takes longer to settle and creates more cycle (oscillation) for the system to reach
steady state compared to load change.
Theoretically, the sensitivity of controller will increase as Kc increases. In
other words, when Kc increases, the controller is very sensitive and results in larger
response and more overshoot when the controller is making correction to the
disturbances in the system.
where,
PB proportional band or P-value
Kc controller gain
According to Equation 1, the P-value is inversely proportional to the
controller gain, Kc. At large P-value, the controller become less sensitive as Kc is
small. This theory applies in this experiment as the larger the P-value, the smaller the
overshoot.
Besides that, we also observed that the offset value decreases as the P-value
decreases. This phenomenon can be explained with Equations 2 and 3.
where
KOL open loop gain
Kv valve gain
Kp process gain
Km steady state gain
ffe
where,Mis the set point
From Equation 2, KOL is proportional to Kc. In Equation 1, we showed that P-value is
inversely proportional to Kc. Therefore, when P-value decreases, the Kc and KOL
increases. When KOL increases, the offset decreases. So, when P-value decreases, the
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offset decreases. A large Kc is not always desirable as it will tend to cause
oscillations.
Integral control action is widely used because it provides an important
practical advantage, the elimination of offset. When integral action is used, controller
output changes automatically until it attains the value required to make the steady
state error zero. Therefore, in this experiment, the offset value cannot be compared in
terms of integral time value as this mode of control eliminates the problem of offset.
Response time for all the three mode of control is almost immediate
whenever there is a disturbance to the system as can be seen in the results and graph.
This is because all three mode of control (P, PI and PID) include the proportional
control, where it provides immediate corrective action as soon as an error is detected.
While for the response behavior, we can see that the oscillation occur the
most in PID control mode, followed by PI and lastly P control as the addition of D-
value tends to amplify noise. This noise amplification increases as the D-value
becomes larger. A larger D-value also causes the system to exhibit larger and longer
oscillations.
Underdamped systems frequently overshoot their target value initially. This
initial surge is known as the "overshoot value". The ratio of the amount of overshoot
to the target steady-state value of the system is known as the percent overshoot.
Percent overshoot represents an overcompensation of the system, and can output
dangerously large output signals that can damage a system. Percent overshoot is
typically denoted with the term OS. No percentage overshoot is most preferable.
Based on our calculations, the proportional integral there is no overshoot percentage.
When proportional, the control process gives an overshoot percentage when P=20
and P=5. The value of P=100 there is no overshoot percentage. For proportional
integral derivate, when D=10 there is overshoot percentage. During this mode, the
settling time for set point change is very high. So we can conclude that due the
higher value of settling point, there will be an overshoot percentage. Another
situation, during the proportional mode when P=100 the settling time is just 1 s.Tha he lwe eling pin we bained hee i n any eh.
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Overall the proportional mode gives a lower operating value. And when as
the P values increases the operating value decreases and it requires less settling time
for the temperature to reach its steady temperature (nearest to its set point).
Theoretically, PID gives the best control system. However, in this
experiment, it shows that the inclusion of D gives longer settling time and higher
oscillation than PI control. Overall, by comparing all the response (operating value,
offset, overshoot, settling time, response time and response behavior), we conclude
that the best choice (a symbol of is located near all the response factors) of control
mode is PI with the setting of P = 20 and I =1 where all the factors are within the
acceptable range.
One of the recommendations is that the value of D should not be so high,
because the settling time required for the process to achieve steady state is very high.
So it require us to stay longer, hence the results we obtain might not be so accurate.
Apart from that, the pressure should be constant throughout the process and there
should be an alarm to alert us when there is no pressure being supplied. This is
because, during the experiment, the compressor may not working all of sudden, and
we are not being notified for this incident. Due to the un-working compressor, the
settling time for the process value to achieve a steady state is higher.
7.0 CONCLUSIONIn conclusion, proportional mode gives a lower operating value. The operating value
is inversely proportional with the P value. In this experiment, we found out PI
controller is the best choice with P = 20 and I = 1, in which the mean temperatures
f lad change and e pin change ae 45.0C and 47.7C, respectively.
8.0 REFERENCES
Seborg, D. E., Edgar, T. F., & Mellichamp, D. A. (2004). Process dynamics and
control (2nd Edition). New Jersey: John Wiley & Sons.
Julabo (2010). Temperature Control Solutions, Retrieved March 20, 2011 fromwww.julabo.de
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