ABSTRACT

In this experiment an open-loop dynamic model between tank level and pump speed from set response data was developed. Also, the transient behaviour of proportional-only level control loops were studied. All of the appropriate switches and valves were set as required and the PTC23 console was powered up. Feed tank A was approximately half filled and the feed pump was then switched on. The water supply valve was opened and valve V1 was adjusted until steady state was achieved. The necessary settings were configured on the computer before the controller output underwent an increase of 10%, decrease of 10%, decrease of 10% and another increase of 10% allowing time for steady state to be achieved between each setting. A proportional band of 50% was entered and the setpoint was increased by 25mm and time was allowed for steady state to be achieved. A new controller gain value was computed and using the user specified parameter, θ=0.5 the setpoint was decreased by 25mm and the process variables were permitted to line out. This step was repeated using θ=2.5. Approximately 1L of water was dumped into the tank and the system was allowed to return to steady state. Valve V1 was closed by a few turns and again the system was allowed to return to steady state. Data obtained was saved and the system was shut down. An inversely proportional relationship was observed between pump speed and tank level. An average velocity gain, Kavg of 0.325% increase in level per min was obtained and actual closed loop time constants were 1.0 and 4.4 whereas the theoretical values were 0.5 and 2.5. From the results obtained a proportional level controller will be expected to exhibit offset following step changes in setpoint, pulse disturbances in inlet flowrate and step disturbances in inlet flowrate.

APPARATUS

Figure 1. Apparatus used in the experiment.

Armfield Ltd. process plant trainer (PCT23-MkII) - 2 feed vessels, a 3 stage indirect plate heat exchanger, a holding tube arrangement and a hot water vessel.

Personal computer Jug Water Peristaltic pump

PROCEDURE1. The following switches were set as follows:

All function switches to 'MANUAL' All control potentiometers to minimum (fully counter clockwise) Valve control switch for SOL1 to 'Divert' Valve control switch for SOL2 to 'FEED A' Valve control switch for SOL3 to 'STOP' Valve control switch for SOL4 to 'FILL A' Valve control switch for SOL5 to 'STOP'

2. The PCT23 console was powered up. The 3 circuit breakers and the RCCB on the rear end was checked to ensure that they were in the up position. The computer was then turned on.

3. It was ensured that the flow control valve V1 and the pressure reducing valve PRV1 were fully opened (and that valves V2, V3, V4 and V5 were closed).

4. The water supply valve mounted on the south wall of the Reactions and Control laboratory was gradually opened. The makeup water was allowed to flow into feed tank A until it was approximately half-full. The supply valve was then closed.

5. The PCT23 icon on the Windows desktop was double-clicked and experiment B - "1 loop (level L1 to pump N1)" was set to load. Experimenter was then familiarized with the basic features of the Armsoft package, especially the mimic diagram, graph and table functions available on the toolbar.

6. The flexible tubing was loaded into peristaltic pump N1 and the pump head was clamped onto the tubing. The feed pump was switched on and the feed pump function switch was set to "USB I/O".

7. The mimic diagram was opened and a value of 40 was entered in the "N1" box.

8. The water supply valve was gradually opened until a slow stream of makeup water began to flow into the feed tank. Valve V1 was adjusted until the inflow balanced the effluent flowrate so that the vessel level was constant at approximately 50% of scale.

9. The following were selected: "View", "graph" then "Configure the graph data". The variables "Run 1 Tank A Level L1 (mm)" and "Run @ Setpoint Term (Loop 1) (mm)" was plotted on the primary y-axis and "Run 1 Feed Pump Speed (N1) (%)" on the secondary y-axis. The range of the primary axis was set to 0-250mm and that of the secondary axis to 0-100%. The data

sampling for a sample interval of 2 seconds was configured and the data collection was commenced by clicking the green "Go" icon.

10. The controller output was increased from 40% to 50% and the water level was allowed to fall by 25mm (10% of scale).

11. The controller output was then returned to 40%.

12. Controller output was decreased by 10% and the level was allowed to rise by 25mm.

13. The controller output was increased by 10%.

14. The current value of L1 in the "set point" field was entered by Left-clicking on the PID 1 box on the mimic diagram. (This was done to prevent the controller from "bumping" the process when it was switched from manual to automatic.) A Proportional-only controller was configured by entering a proportional band of 50%, and integral time of 0 seconds and a derivative time of 0 seconds. "Apply" was then selected and the controller was switched to automatic. The system was allowed to run at this operating point for a few minutes, then the set point was increased by 25mm and "OK" was selected. The process was allowed to move to the new steady state.

15. The results of step 10 and 12 was used to derive an estimate of the overall velocity gain, K. with engineering units (% increase in level per minute)/ (% increase in controller output). A new value for the controller gain Kc was then computed by means of the IMC tuning rule (Rivera et al., 1986):

Kc = 1

θ∨K∨¿¿

The user-specified parameter θ was interpreted as the desired closed-loop time constant (in minutes). PID 1 box was reopened and the corresponding proportional band was entered. The level set point was then decreased by 25mm, "OK" was clicked and the process variables were permitted to line out.

16. Step 15 was then repeated for a different value of θ.

17. Approximately 1 litre of water was dumped into the tank and the system was allowed to return to steady-state operation.

18. Valve V1 was closed by a few turns but the inlet flow was not shut off completely. Steady-state was achieved and the data collection then ended.

19. Results were saved ("File", "Save As") in Formula One and Excel formats and these files were copied to a diskette. The makeup water valve was closed and the controller was switched to manual, controller output was set to 0% (system was exited.)

20. All controls on the console were set to minimum/OFF and all function switches to MANUAL. The console and computer were turned off. The clamps on the peristaltic pump head was released to prevent distortion of the flexible tubing.

RESULTS/ CALCULATIONS

09:33:5809:39:3409:45:1009:50:4609:56:2210:01:580

20

40

60

80

100

120

140

160

0.00

10.00

20.00

30.00

40.00

50.00

60.00

water levelpump speed

sample time

water level (mm) pump speed (%)

Figure 2. Open loop data collected in steps 3(x) through 3(xiii).

Velocity Gain, K =

Final Process Variable−Initial ProcessVariableInitial ProcessVariable

∗100

Percentagec h ange∈Controller Outputtime

From step 10 in the procedure:

Final height = 102mm

Initial Height = 127mm

Percentage change in controller output = 40 - 50

Time = 8.2mins

K1 =

(102−127)127

∗100

40−508.2

K1 = 0.240% increase in level per min

From step 12 in the procedure:

Final height = 135mm

Initial Height = 110mm

Percentage change in controller output = 31-41

Time = 12.9-7.35mins

K2=

135−110110

∗100

31−4112.9−7.35

K2=0.409% increase in level per min

Kavg = K1+K 2

2

= 0.240+0.409

2

= 0.325% increase in level per min

When the dynamics of the sensor/ transmitter and final control element are negligible, the open-loop response of the measured % level (PV) to changes in controller output (CO) can be modelled as

d P V ' (t)dt

= K CO' (t)

given that:

PV'(t) = PV(t) - PVss

CO'(t) = CO(t) - COss = m

where m is the percentage increase in CO(t) when t=0

d P V ' (t)dt

= Km

Separating Variables and integrating both sides:

∫dPV'(t) = ∫Km dt

PV'(t) = Km(t) + c

where c is a constant

Since the system was initially at steady state:

PV'(0) = Km(0) + c

c = 0

PV'(t) = Km(t)

recall: PV'(t) = PV(t) - PVss

PV(t) = Km(t) + PVss

Therefore, for step changes in setpoint under IMC proportional control, the transient response of the measured level follows a first-order linear differential equation with time constant θ.

10:07:1410:18:4410:30:1410:41:4410:53:1411:04:4411:16:140

20

40

60

80

100

120

140

160

180

0.00

20.00

40.00

60.00

80.00

100.00

120.00

tank levelset pointpump speed

Sample time

leve

l and

setp

oint

val

ues

pum

p sp

eed

(%)

Figure 3. Closed loop data recorded in steps 3(xiv)-(xviii).

Controller gain, Kc = 1

θ∨K∨¿¿

Theoretical values of θ = 0.5 and 2.5

when θ = 0.5

Kc1 = 1

0.5∨0.325∨¿¿ = 6.15

Proportional Band = 100K c

= 1006.15 =

16.26

when θ = 2.5

Kc2 = 1

2.5∨0.325∨¿¿ = 1.23

Proportional band = 1001.23 = 81.30

SAMPLE CALCULATIONS:

Actual value of θ1:

Initial tank level, L1 = 168mm

Initial time, T1 = 10:20:02

Final tank level, L2 = 140mm

Final time, T2 = 10:27:46

L1 + 0.632 (L1 - L2) = 168 + 0.632(140-168)

= 150.30mm

150.30mm occurs at T3 = 10:21:02

Actual value of θ1 = T3 - T1

= 10:21:02 - 10:20:02

= 1.0 min

Table 1. Actual and theoretical values of the closed loop time constant.

Closed loop time constant, θActual Value Theoretical value

1.0 0.54.4 2.5

DISCUSSION

There are many applications of level control in the chemical industry, an application of such would be a hot water tank where water is removed, perhaps for washing down, and the level needs to be restored ready for the next wash cycle.

Some advantages of including liquid inventories in the design of a chemical plant are:

1. They allow plant operation to continue when some flows are temporarily disabled.

2. They ensure liquid flow to a pump - if the vessel were to empty, liquid flow would be interrupted to the pump which may result in damage of the pump (if it remains in operation without flow)

3. Allows the plant to operate more efficiently - they can be placed between a disturbance source and a sensitive unit to reduce variation in stream properties and flow rate in input flows. (the disturbance magnitude is significantly decreased)

Some disadvantages of including liquid inventories in the design of a chemical plant are:

1. They can be costly to the company- cost of vessels, land or building space and maintenance

2. Cost of material inventory - money invested in feed stock rather than distributed as profit

3. Potential quality degradation from storing material

4. Reduces safety - the net effect of any accident can be much worse when a large inventory of flammable or hazardous material is involved.

In order to accomplish the objectives of the experiment ( to develop an open-loop dynamic model between tank level and pump speed from step response data and to study the transient behaviour of proportional-only level control loops) steady state is required. Steady state can be defined as a process which doesn't change with time, in this case: inlet flow = outlet flow. In order to achieve this, the level controller was configured for direct action. Direct action means that the process variable would vary directly proportional to the controller output (i.e. the tank level would be directly proportional to the pump speed). Hence, during the experiment direct action was used as opposed to reverse action. This allowed the pump speed to increase (remove water from the tank at a faster rate) as the tank level was increased, therefore, achieving steady state.

The IMC tuning rule was used to (Rivera et al., 1986) was used to compute a new value

for the controller gain, Kc. This rule states that Kc = 1

θ∨K∨¿¿ . It can be observed from this

equation that the controller gain is inversely proportional to the tuning parameter, θ. Hence, an increase in θ would result in a decrease in the controller gain. The controller gain is then used to find the proportional band from the following equation:

Proportional band = 100K c

Now, relating the tuning parameter to the proportional band gives a proportional relationship whereas an increase in θ would lead to an increase in the proportional band. An increase in θ upon the closed-loop response of the controlled level and manipulated flow rate would therefore lead to a large proportional band which gives a longer time period for the tank level to approach the set point.

With reference to figure 2, an offset can be observed for step changes in the setpoint (decreasing the tank level by 25mm). The offset observed was approximately 4mm. For pulse

disturbances in inlet flowrate, when 1L of water was dumped into the tank, an offset of 3mm is observed. This is shown in figure 2 around the 11:06:42 sample time where it can be observed that set point and tank level lines do not meet. Also, with respect to figure 2, for step disturbances in inlet flow rate (step 18 in the procedure), an offset of 12mm is observed. Hence, from these results, a proportional level controller would be expected to exhibit offset following:

- step changed in set point- pulse disturbances in inlet flowrate- step disturbances in inlet flowrate

With reference to table 1, the actual closed loop time constants were found to be 1.0 and 4.4 whereas the theoretical values were 0.5 and 2.5 respectively. Overall, the actual values are larger than the theoretical values, therefore, it can be deduced that a longer time was taken for the water level to decrease by 63.2% of the overall decrease.

Even though an offset was shown in the results, the equipment used was appropriate for the illustration of the relevant engineering principles. The offset in readings may have been as a result of the equipment not being calibrated. Also, the actual tank level had a ±10mm difference from the tank level noted by the computer. A recommendation for this experiment would be to perform regular maintenance on the equipment as well as to ensure the equipment is properly calibrated.

SOURCES OF ERROR:

Parallax error when reading the tank level Incorrect calculations Incorrect data may have been inputted into the computer Equipment was not calibrated resulting in inaccurate results.

PRECAUTIONS:

Water levels were read at eye level to the meniscus Calculations were done twice to ensure the correct value was found

CONCLUSIONS

An inversely proportional relationship is observed between pump speed and tank level An open loop dynamic model between tank level and pump speed from step response

data was developed. An average velocity gain, Kavg of 0.325% increase in level per min was obtained A proportional level controller will be expected to exhibit offset following step changes

in setpoint, pulse disturbances in inlet flowrate and step disturbances in inlet flowrate. Actual closed loop time constants were 1.0 and 4.4 whereas the theoretical values were

0.5 and 2.5 implying that a longer time was taken for the water level to decrease by 63.2% of the overall decrease.

RECOMMENDATIONS

Equipment should be regularly cleaned and maintained Equipment should be calibrated Internet should be provided in the lab so that the results can be emailed to the students. A longer time period should be allowed to ensure the process has attained steady state.

REFERENCES

Level and Flow Control Applications. (2014). Retrieved from Spirax Sarco: http://www.spiraxsarco.com/resources/steam-engineering-tutorials/control-applications/level-and-flow-control-applications.asp

Marlin, T. (1995). Process Control: Designing Processes and Control Systems for Dynamic Performance. McGraw-Hill, New York.

Rivera, D.E., M. Morari and S. Skogestad (1986). "Internal Model Control. 4. PID controller design". Ind. Eng. Chem. Process Des. & Dev., 25, 252-265

Laboratory Manual: CHNG 2009/2010. Chemical Engineering Laboratory (2014-2015)

APPENDIX

See attached CD for results.