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EXPERIMENT 5B: PROCESS CONTROL – LEVEL CONTROL TQ

CE20225 Chemical Engineering Skills & Practice 2

Abstract The response of a system to different control systems was investigated in the experiment. The control system used include on/off controller, a proportional-integral-derivative (PID) controller and manual controller which is also known as uncontrolled system. The experiment was carried out with a rig consisting a tank of water where the water level in a process vessel tank was used a PV to be controlled. The aim of the experiment was to control the water level in the process vessel tank by using the different control systems which were mentioned earlier. The on/off controller alternates between 2 different output which was completely switched on or completely switched off. A PID controller continuously minimize the calculated error value which is the difference between the PV and SP over time by the adjusting the MV. The combination of the parameters which showed the most efficient system was when the KC=20, I=2 and D=2. The uncontrolled system was investigated as well. The time constant was calculated with Equation 7 which was 106s. This corresponds to the time taken for the system to respond to the output. It is essential to determine to the time constant as any delay in response would affect the system. Overall, the experiment was successful. However, results could have been improved if a larger range of MV was used. Introduction and Theory A process control is often used to ensure the operation of a plant is efficient and safe. With a control system, an unexpected disturbance that affect the controlled variable can be eliminated and monitored (Nolan, 2019). In industry, a variety of control systems are required as there are a range of process parameters to be controlled in a system. There are two main control systems which are the opened and closed loop control systems. Closed loop system is also known as a feedback control system where the control action depends on the output (Rouse and Haughn, 2017). The control action adjusts automatically when a difference between the set point (SP) and the process variable (PV) is identified. A SP would be fixed in a process where the control system alters the manipulated variable (MV) at the desired condition to minimize the error over time. The output of an opened loop control system does not influence its control action (Bissell, 2017). The opened loop system requires manual adjustment. Consequently, it is less reliable since the system will be affected if no adjustment is made to an error identified. The simplest type of feedback control is on/off control which is also referred as hysteresis control. The control simply involves driving the manipulated variable (MV) from completely close to open according to the position of the PV relative to the set point SP. An example of on/off control is the temperature control of a domestic heating system. The heating system switches on when the thermostat temperature is below the SP and switches off when the thermostat temperature is above the SP. One of the popular feedback control loops includes the proportional-integralderivative (PID) controller. This is because the controller can calculate the MV which depends on the combinations of the correcting terms which includes proportional correcting term output, integral correcting term output and derivative correcting term output (Chevalier et al., 2019). This is shown clearly in Equation 1. 𝑀𝑉(𝑡) = 𝑃𝑜𝑢𝑡 + 𝐼𝑜𝑢𝑡 + 𝐷𝑜𝑢𝑡

Eq(1)

Where Pout , 𝐼𝑜𝑢𝑡 and Dout represent the proportional, integral and derivative correcting outputs respectively. Pout , 𝐼 𝑜𝑢𝑡 and Dout can be calculated with Equation 2, Equation 3 and Equation 4 respectively. 𝑃𝑜𝑢𝑡 = 𝐾𝑐 𝜀(𝑡)

Eq(2)

Where 𝜀(𝑡) represents the time required for the system to respond to an error between the SP and the PV while 𝐾𝑐 represents the proportional controller gain. From Equation 2, the response time decreases when KC increases. However, with only proportional control, an offset always exists in such control as well. Therefore, the PI controller (Equation 3) was used to eliminate the offset.

𝑰𝒐𝒖𝒕 =

𝟏 𝒕 ∫ 𝜺(𝒕)𝒅𝒕 𝝉𝒊 𝟎

Eq(3)

Where 𝜏𝑖 is the time constant. The time constant of a process describes the speed with which the measured PV responds to the changes in the output of controller (Liptak, 2005). The time constant of a liquid-level rig can be determined experimentally by the formula shown in Table 2 (Results and Calculation). The common problem in both controls is if the gain is too large, the output may exceed the set point. Thus, the PID controller (Equation 4) is used to decrease the duration of the offset removal. This is vital in systems which have large time delays. 𝒅

𝑫𝒐𝒖𝒕 = 𝑲𝒅 𝒅𝒕 𝜺(𝒕)

Eq(4)

Where 𝐾𝑑 is the derivative controller gain. The aim of this experiment is to control the liquid level with the use and programming of a feedback control system. The liquid level act as the PV to be controlled. The experiment was carried out with a different control system each time which includes on/off control, uncontrolled system, proportional (P) control, proportional-integral (PI) control and proportional-integral-derivative (PID) control. Thus, it is important to understand the basic principles of the equipment and the operation of different systems such as uncontrolled system and controlled system. Method The CE117 Process Trainer rig and the CE2000 software were the main apparatus. The file ‘exp43.ict’ was loaded under the CE2000 software in the computer. The loop bypass valve was closed while the air vent was opened fully. The process vessel drain was opened to approximately 45°.

Air Vent

Process Vessel Drain

Loop Bypass Valve

Pump 2 Figure 1: Diagram of TQ CE117 Process Trainer system with labelled parts CE117 Mimic Panel was connected with external wires as Figure (Appendix) . Pump 2 was switched to ‘external’. By varying KC to 1, pump voltage to 5V and the SP to 6V on the software, the relay was switch on at 0.5V with hysteresis of 1V. The process was carried out while the results were recorded in the software. the software was used to record the level, the valve voltage and the SP for at least 3 cycles when the level stabilized. The software was then stopped. The steps were repeated with a KC of 2 and 4. The file ‘exp4-2.ict’ was loaded. The process vessel drain was fully opened now. CE117 Mimic Panel was connected with external wires According to Figure 2 (Appendix). The SP was adjusted to 6V and valve voltage to 10V. The PID controller was set to Proportional Integral control which included P=5 , I=0 and D=0. The results were recorded once again until the level stabilized. The datas were exported before the process was repeated by varying the P value to 10 and 20. It was

decided that P=20 gave the best control. To investigate the I value, the process was repeated by varying I value to 0.5, 1 and 2 and keeping P=20 and D=0. With the results obtained, the chosen optimum I value was 2. To find the optimum D, the process was repeated with different D values (0.5, 1 and 2) while the P value and I value remain the same which is 20 and 2 respectively. Finally, an uncontrolled system was run by loading the file ‘exp4-1.ict’. The connections of the wires were rearranged according to Figure (Appendix). The pump 2 voltage was adjusted to 5.2V and valve voltage to 10V. The software was run, and the results were plotted. The system was left for 10 minutes to allow the level to stabilize before recording the height of the water in the process vessel as Level A. The data was recorded as usual by using the software. The pump voltage was increased by 0.5V. Once the level stabilized, the second height was recorded as Level B. The software was stopped while the results were exported before switching off the system. Results and Calculations Figure 2 shows the results from using on/off controller with a SP of 6V and different KC values (1, 2 and 4). By investigating the P, PI and PID controllers, the graph in Figure 3, Figure 4 and Figure 5 were plotted respectively. Figure 3 was to investigate the proportional control. In Figure 2 and Figure 3, as KC increases, the closer the output is to the set point. From Figure 3, the proportional control leaves an offset error in the final steady-state condition. 8 7

Level (V)

6

5 4

Set Point K_C =1

3 2

K_C= 2

1 0

K_C= 4 0

50

100

150

Time (s)

Figure 2: A graph of the level in the process vessel against time for each KC value 7 6

Level (V)

5 4

Set Point

3

K_C= 5

2

K_C= 10

1

K_C= 20

0 0

50

100

150

200

Time (s)

Figure 3: A graph of the level in the process vessel against time for each P value A PI controller was used in Figure 4 to find the optimum integral gain value (I). From Figure 3, it is obvious that the KC value of 20 has the smallest error. Thus, the KC was set at 20 while varying I to produce Figure 4.

6.6

6.4

Level (V)

6.2 6 Set point

5.8 I= 0.5 5.6

I= 1.0

5.4

I= 2.0

5.2 5 0

20

40

60

80

100

120

140

Time (s)

Figure 4: A graph of the level in the process vessel as time progresses for each I value with KC=20

Level (V)

Figure 5 was plotted based on the results of a PID controller with varying derivative times (D) and I set to 2 and KC set to 20. 6.4 6.35 6.3 6.25 6.2 6.15 6.1 6.05 6 5.95 5.9

Set Point D= 0.5 D= 1.0 D= 2.0

10

30

50

70

90

110

130

150

Time (s)

Figure 5: A graph of the level in the process vessel as time progresses for each D value with P=20 and I=2 The data from the uncontrolled system was recorded in Table 1. Table 1: Flow rate and height for Level A and Level B Level A B

Flow Rate, q (V) Flow Rate, q (L/min) Flow Rate, q (m3/s) 3.6 3.6 6.00E-05 3.8 3.8 6.33E-05 Difference (∆) 3.33E-06

Liquid Level , h (m) 0.116 0.136 0.020

With the data from the uncontrolled system, the process time constant (𝜏) can be determined with Equation 5, Equation 6 and Equation 7 as shown in Table 2. Table 2: Formula and values for the calculation of the process time constant Formula A (m2)

𝜋 ∗ 𝑟2

Value Eq(5)

0.0177

R (s/m2)

∆h/∆q

Eq(6)

6.01E+03

𝜏 (s)

A*R

Eq(7)

1.06E+02

According to Table 1, the graph of the level in the process against time was plotted as shown in Figure 5. 7 6

Level (V)

5

4

Level A

3 Level B

2

Pump Input

1 0 0

200

400

600

800

1000

1200

Time (s)

Figure 6: A graph of the level in the process vessel as time progresses with an increase in pump voltage Discussion The response of the system with on/off controller is shown in Figure 2. The SP was 6V which is also the level where the oscillations of the PV happen. The oscillations of each KC value did not change in trend. The maximum and minimum peak of KC value remains approximately the same. This has proven that the on/off controller is a feedback controller that alternates only between two states which are completely switched on or switched off. When the PV goes below the SP, the valve closes completely to fill up the vessel and when the PV goes above the SP, the valve opens fully to drain the excess water. As the Kc increases, the smaller the amplitude between the SP and the peak. Hence, when KC is 4, it has the smallest deviation which makes it nearest to the SP. Therefore, the larger the KC, the smaller the error. From Figure 2, the time taken for one cycle is around 75s when KC is 1, whereas the time taken for one cycle is around 45s when KC is 4. This has proven that the larger the KC, the lesser time required for the system to respond to an error as mentioned earlier in Introduction. The results of using a proportional control is displayed in Figure 3. As KC increases, the closer the PV is to the set point, the smaller the error. Figure 3 also showed that the P control leaves an offset error in the final steady-state condition which is a major disadvantage of using a proportional control (Cooper, 2020). The results of using a PI controller was shown in Figure 4.The offset error in the final steady-state condition of a pure P controller (Figure 3) was eliminated since the integral term accelerates the process towards the SP by adding a control effect due to the past accumulated error value. However, the PV overshoot the SP which was 6V. This is because the integral term responds to accumulated past errors. From Figure 4, the larger the I value, the nearer it is to the SP which means the smaller the error. The area under each curve shows the integral sum of error. As time progresses, the integral sum of the error decreases. This has proven the theory shown in Equation 3 (Introduction) that the accumulated error decreases as time progresses. Thus, the optimum I value to use in the PID controller is 2. By increasing the derivative time, control system reacts more aggressively to changes in the error term. Hence, the speed of the overall control system response increased. Figure 8 was produced based on the responses to a PID controller. The KC was set to 20 and the I was set to 2 while varying the D. The curves with D of 1 and 2 respectively have very similar results whereas the curve with D value of 0.5 has the

largest deviation from the SP. When the D value is 0.5, the time taken for the oscillation to level off is the longest. Figure 6 was based on the investigation of uncontrolled system where manual adjustment was required to change the pump voltage from 5.2V to 5.7V. When the pump voltage was 5.2V, the liquid level was recorded as Level A (0.116m) only when the level stabilized. The pump voltage was manually increased to 5.7V, therefore, increasing the flowrate as well. The liquid level was recorded as Level B which was a height of 0.136m. The difference in height was 0.02m which was a 17% difference. The time constant was calculated by using Equation 7. Time constant was calculated to describe the speed with which the PV responds to the output (Liptak, 2005). It is important to get the exact timing correct as delayed responses may negatively impact the controller’s performance. The results shown in Figure 2 and Figure 3 could have been improved with a wider range of KC whereas Figure 4 could have been improved with a wider range of I used. More combinations of PID control could have been investigated as well. The height of the water in the tank was read by eye. To improve accuracy of the reading, a pressure transmitter could have been used to measure the water level. Conclusion From this experiment, it can be concluded that the output of an on/off controller is either maximum or minimum which depends on the value of the PV. The output is maximum if the PV exceeds the SP; the output is minimum if the PV is below the SP. The response time of the system decreases when the KC increases. A PID controller continuously minimize the calculated error value which is the difference between the PV and SP over time by the adjusting the MV. The system responded differently by tuning the P gain, I gain and D. A major weakness of P control is that an offset error is produced in the final steady-state condition. Thus, the PI control is needed to eliminate the offset error. With a large I gain, the error in the system will be small. The most efficient combinations of the parameters were P=20, I=2 and D=2. The uncontrolled system was tested as well. The calculated time constant was 106s. The shorter the time required, the more efficient is the system is. The uncontrolled system was less reliable since manual adjustment was required compared to the controlled system where the adjustment happens automatically. The experiment was successful since the response of different control systems were obtained. However, the accuracy of the results could have been improved by using a larger range of the MV. References Nolan, D. (2019). Handbook of fire and explosion protection engineering principles. 4th ed. Gulf Professional Publishing, pp.1-32. Bissell, C. (2017). Control Engineering. Milton, UNITED KINGDOM: Routledge. Rouse, M. and Haughn, M., 2017. What is closed loop control system?. [online] Tech Target. Available from: https://whatis.techtarget.com/definition/closed-loop-control-system [Accessed 11 Oct. 2019]. Liptak, B., 2005. Instrument engineers' handbook volume two. 4th ed. Hoboken: Taylor and Francis, pp.1660-1675. Chevalier, M., Gómez-Schiavon, M., Ng, A. and El-Samad, H. (2019). Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules. Cell Systems, 9(4), pp.338353.e10. Cooper, D., 2019. Integral Action and PI Control – Control Guru. [online] Controlguru.com. Available from: https://controlguru.com/integral-action-and-pi-control/ [Accessed 19 Feb. 2020].

Appendix

Figure 7: CE117 Mimic Panel set up for Part A

Figure 8: CE117 Mimic Panel set up for Part B

Figure 9: CE117 Mimic Panel set up for Part C...