CHEM ENG 3036: Unit Operation Laboratory

Level Control (CON1)

Preliminary ReportSupervisor: Mathew Penna

Group 3Aakriti Bhandari (Leader)

Anton CuguraFabian Ivancic

Aim

The aim of this experiment is to investigate the closed-loop response under proportionalcontrol of a non-self-regulating first order systems. In addition, this experiment also aimsto determine the system parameters such as: transmitter gain (Km), valve gain (Kv) andtank capacitance (C). Open-loop response of the level control system will also be studiedto determine to what extend the given system is non-self-regulating. The final offsetsfrom Servo and Regulator operations will also be compared using proportional control.

Background

Control systems are required in non-self-regulating process to supress the effects of distur-bances, ensure stability and to optimise performance. Alternative self-regulating proccesscan be implemented instead of controlling a non-self-regulating process, but this isn’talways possible and in most cases will cause a large financial burden. Control systemsmay only cost 3-10% of the capital cost but will produce huge returns in the long term.They are also environmentally safe, will reduce consumption of resources and hazards tooperators. Good control systems have the ability to optimise the performance of a processby a great deal.

Theoretical Notes

Depending on a system response to disturbances such as changes in inflow, outflow or pres-sure, it can be classified into ‘self-regulating’ and ’non-self-regulating’. Self-regulatingprocesses have the ability to obtain a steady state regardless of disturbances whereas,non-self-regulating systems cannot. A non-self-regulating process must be controlled us-ing control systems. An open loop system does not self-regulate after a step change inthe input. So, it has to be controlled using feedback, feedforward or inferential controlsystems. This experiment will utilize a feedback control system to regulate a non-self-regulating open loop. The aim of this control system is to control the controlled variable,such as the measured output by changing the manipulated variable(MV) for any changein the initial input(PV). Thus the system now is a closed loop system.

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Open-loop responseThis experiment will utilize a pressurised tank with outlet pneumatic control valve, suchas the one shown Figure 1:

Figure 1: Pressurised tank with pneumatic control valve

A simple material balance for such a process can be written as:

Cdh

dt= q − qo(p) (1)

Where∂qo∂t

= Kv (2)

Equation 1 in terms of deviation variables:

Cdh′

dt= q′ − q′o(p) (3)

Equation 1 and 2 can now be transferred into Laplace domain:

H(s) =1

CsQ̄(s)− 1

CsQ̄o(s) (4)

Control valve:Q̄o(s) = KvP̄ (s) (5)

The block diagram below represents the above open loop system:

Combining equations 4 and 5, the overall transfer function is:

H(s) =1

CsQ̄(s)− Kv

CsP̄ (s) (6)

Case 1: For a step change in the inflow, constant outflow:

Say, there is a step change in inflow of: ∆q Such that: Q̄(s) =∆q

sAnd outflow constant Q̄o(s) = 0

(7)

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Figure 2: Block diagram representing an open loop for a pressurised tank

Substitute Equation 7 into 6 and inverse Laplace the equation to obtain:

h = hss +∆q

Ct (8)

From the equation above, we can see that the tank level will increase or decrease linearly.

A decrease in inflow will attain a slope of:∆q

C< 0

An increase in inflow will attain a slope of:∆q

C> 0

(9)

This system is a pure integrator and will never reach a maximum or a minimum. So it isnon-self-regulating.

Case 2: For a step change in the valve position, constant inflow:

Say, there is a step change in valve position of: ∆p Such that: P̄ (s) =∆p

sAnd inflow constant Q̄(s) = 0

(10)

Substitue Equation 7 into 6 and inverse Laplace the equation to obtain:

h = hss −Kv∆p

Ct (11)

As there is a negative relationship between the height of the tank and the valve opening,the tank level will decrease linearly with time if the valve is open and the tank level willincrease linearly with time if the valve is closed.

For both Cases, there is a constant rate of rise or fall in the tank levels, which is dictatedby the tank capacitance, C. C can be calculated using equations 11 or 8 and both shouldgive the same answer(usually equal to the area of tank). As stated before, no final valuewill be attained, so both cases are non-self-regulating, pure integrator.

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Closed-loop responseFigure 3 shows the pressurised tank with a control system that can control the height andthe flow of the output using level and flow controller respectively.

Figure 3: Pressurised tank with pneumatic control valve and control system in place

General block diagram for a closed loop is shown in Figure 4:

Figure 4: Block diagram representing a general closed loop

The closed loop block diagram for the pressurised tank used in this experiment is shownin Figure 5

Figure 5: Block diagram representing a closed loop for a pressurised tank

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From Figure 5,Q̄o(s) = KvKc[H̄sp(s)− H̄(s)Km] (12)

From Equation 4, the open loop response of the process is:

H(s) =1

CsQ̄(s)− 1

CsQ̄o(s) (13)

The overall transfer function in Laplace domain from Equations 12 and 13 is now:

H̄(s) =1Cs

1− 1CsKvKcKm

Q̄−1CsKvKcKm

1− 1CsKvKcKm

H̄sp (14)

The response from a closed-loop system can be evaluated using two modes, Servo andRegulator.

Servo ResponseServo responses are used to evaluate the effect of a change in set point with steadydisturbance (D = Dss).

In this experiment, Q̄(s) = 0 for a set point change of H̄sp(s) =∆r

s(15)

Substituting Equation 15 into 14 and applying inverse Laplace Transformation and forτ = C

−KvKcKmgives Equation 16:

h′(t) =∆r

Km(1− e

−tτ ) (16)

As t→∞, h′ → ∆rKm

So the final change in level is equal to the change in set point which indicates a zeroerror and no offset.

Regulator ResponseRegulator responses are used to evaluate the effect of disturbances with no change in theset point (R = Rss).

In this experiment, H̄sp(s) = 0 for a step change in the inflow of ∆q : Q̄(s) =∆q

s(17)

Substituting Equation 17 into 14 and applying inverse Laplace Transformation gives Equa-tion 18:

h′(t) =∆q

−KvKcKm(1− e

−tτ ) (18)

As t→∞, h′ → ∆q−KvKcKm

This indicates that the final value deviates from the initial set point, leading to a off-set. As offset = old set point - final value

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Experimental

This section contains the experimental arrangement, equipment and utilities required,start up and shut down procedure and the experimental procedure.

Experimental Arrangement

Figure 6: Experimental setup for CON1

Figure 7: P&ID diagram for the setup shown in Figure 6

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Equipment and their brief use in this experiment

1. Cylindrical tank with inside diameter of 15.2cm, pressurised at ≈7psi with air tocontain water at various levels

2. Rotameter x2 to measure the flow rate of water in and out of the system.

3. Pneumatic control valve(air to close valve) to control the outlet flow rate ofwater.

4. Fischer & Porter 53MC1100 PID controller to adjust the outlet flow rate ofwater through the pneumatic valve and also to change the set point tank level.

5. Water control valve to manually control the inflow of water.

6. Headspace pressure regulating control valve to manually control the vesselpressure.

7. Level trasmitter to measure the differential pressure, tank level and to send signalto the controller.

8. Ruler to measure the change in water level in the tank.

9. Stopwatch to keep a record to time elapsed.

Utilities

1. Water from mains

2. Compressed air, at 600 kPa

Start-up ProcedureNB: Do not operate the brass gate valve shown in Figure 6.

1. Make sure that the compressor is on. The pressure gauge on the western wall ofthe laboratory should be indicating ≈600 psi. If not, contact technical staff forassistance.

2. Check that the compressed air shut-off valve is open. (Located above to the rightof the equipment on a cable tray).

3. Ensure the controller is on and is in manual mode.

4. Close water control valve (location: shown in Figure 6).

5. Slowly open the mains water valve, if not open already.

6. Ensure the headspace shut-up valve is closed.

7. Open the headspace pressure regulating control valve, adjusting pressure to ≈ 7 psi.

8. Verify that air is releasing from the pressure relief valve at approx 7 psi, contactsupervisor if it is not.

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9. Open the bleed valve on low pressure air side of the level transmitter until all air ispurged.

10. If the tank is empty, fully close the pneumatic control valve, set OUT at 100 % spanusing the controller (Figure 8. Then open the water control valve (Figure 6) untilthe tank level can be observed at the bottom on the sight tube.

11. Direct the bleed valve on the water (high pressure) side of the level transmitter intoa bucket open it momentarily, ensuring that there is no air in the line.

Figure 8: Display of the controller buttons

Experimental ProcedureThis section is divided into three subsections: A: Determining gain(transmitter and valve),B: Open loop response and C: Closed loop response (Servo and Regulator)

Part ADetermining transmitter gain

1. Set the controller to manual mode, should follow on from start-up

2. Refer to the PV column display and the sight tube to check the level in the tank.

(a) If the tank is full: press the button (decrease OUT) to open the pneumaticcontrol valve and wait until the level is visible at the top of the sight tube.

(b) If the tank is near empty: repeat step 10 from the start-up procedure.

3. Ensure that the tank maintains a steady level by closing the pneumatic control valveand water control valve.

4. Press Disp 500 and record PV % span indicated on the controller and measure thetank level using a ruler.

5. Add or release water in increments and record at each new water level(repeat step4) until the entire height range has been covered.

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Determining the valve gain

1. Open the water control valve at an arbitrary tank level so a low reading is shownby the inlet rotameter

2. Attain a balance of the inflow and the outflow (steady state). This can be done byclosing or opening the pneumatic control valve as required.

3. Record the steady state flow rate and OUT % span and also PV % span

4. Increase the inflow rate (by opening water control valve) a small amount and thenopen the pneumatic control valve to reach the system to a steady-state at roughlythe same tank level and record the SS flow rate and OUT % span.

5. Repeat step 4 until the inflow is at its maximum

6. Repeat steps 1-5 for other tank levels.

Part B: Open loop response

1. Attain SS at an arbitary flow rate and tank level.

2. Record the flow rate, PV % span and OUT % span.

3. Quickly change the inflow rate to a new level and start the stopwatch(timer).

4. Record the new inflow rate and PV % span at relatively small time intervals (5-10seconds) until the tank is nearly full or empty.

5. Avoid overfilling/emptying of the tank by changing the inflow rate back to its pre-vious setting.

6. Repeat steps 3-6 for a number of different inflow step-change.

7. Repeat steps 3-6 for a number of different OUT %span (valve position) step changes.

Part C: Closed loop response

1. Attain SS at an arbitary flow rate and tank level.

2. Record the flow rate, PV % span and OUT % span.

3. Set PID controller parameter:

(a) set Tr to zero (press CO, then Tr, enter zero, press enter)

(b) set Td to zero (press CO, then Tdr, enter zero, press enter)

4. Set MR to the OUT % span corresponding to the current inflow rate: from Part B,press CO, then 511, enter OUT % span, press enter.

5. Set SP to the current PV by pressing CO 511 PV Enter on the inside panel

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6. Set the controller to automatic mode and wait for the system to stabilize.

Regulator response

7. Quickly change the inflow rate to a new level. Start the stop watch.

8. Record this new new inflow rate and the PV % span at small time intervals (5-10seconds) until the system stabalizes to a new steady-state.

9. Record the final offset (PV deviation from the intial steady-state in %span)

10. Press CO 501 PV Enter on the inside panel to set SP to the current PV

11. Set MR to the OUT %span that corresponds to the new inflow and wait for thesystem to re-stablize

12. Repeat steps 7-11 for a number of different inflow step changes.

Servo response

13. Press CO 501# Enter on the inside panel to step-change SP and start the stopwatch.

14. Record PV %span at small time intervals (5-10 seconds) until the system settles toa new steady-state.

15. Record/note the change on SP

16. Record the final offset (PV deviation from the final Set Point(SP) in %span)

17. Set SP to the current PV by Press CO 501# Enter on the inside panel, if requiredand wait for the system to restabilize.

18. Repeat steps 13-17 for a number of different SP step-changes.

19. Repeat both Regulator and Servo response operation for 2 different controller gains.Pb = 100

Kc. (To change Pb: press CO Pb ## Enter)

Shut-down Procedure

1. Set the controller to manual mode

2. Close to pneumatic control valve (increase OUT %span to 100%) and open waterinlet valve to allow tank to reach near full.

3. Close the water inlet valves and the mains water valve

4. Reduce the headspace pressure to zero by closing the headspace pressure regulatingcontrol valve and pulling up on the pressure relief valve ring.

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NOTE

1. Monitor head space pressure- needs to be constant, manually adjustments may berequired

2. Do NOT overfill the tank.

3. If the tank is allowed to drain completely, it must be refilled to the point wherewater level can be seen at the bottom of the sight tube. Then get rid of the air,using appropriate valve.

Nomenclature

Table 1: Nomenclature table

h tank level mC Capacitance L/mhss Steady State tank level mKc Controller gainKm Transmitter gain %span/mKv Pneumatic Control Valve gain L/min/%spanp Transducer pressure %spanq Inlet Flow rate L/minqo Outlet Flow rate L/minr Set point %spane Error (r-hKm) %spans Laplace variable min−1τ Closed-loop time constant mint Time min

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Risk Assessment

Hazard Identification

Table 2: Hazard Identification table

Various Hazards Yes or No?Hazardous substances NoHigh or very low temperature parts NoMoving or high energy parts NoElectrical hazards YesHigh pressure or vacuum YesEmissions or wastes NoErgonomic hazards NoLaser, etc NoSharps NoRemote, isolate or after hour work YesHazardous plant NoExcessive noise NoSpecial emergency procedures NoOther hazards Yes

Risk QuantificationA risk quantifying matrix such as the one shown in Figure 9 is used.

Figure 9: Risk Matrix

Table 3: Hazard Identification table

Hazards Probability Consequence Risk PriorityElectrical Hazards (wet controlpanel/short circuit)

2 1 2 Low

High Pressure or Vacuum (Valves fail-ure or over filling)

4 3 9 Moderate

Remote work (use of lader) 3 1 3 LowOther Hazards(water spill, etc) 2 2 4 Low

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Hazard Mitigation:Steps outlined below should be followed to prevent any of the hazards presented in Table 3:

1. Make sure the work environemnt is clean, tidy and free from any liquid spills

2. Ensure any electrical appliances or control switches are isolated from possible spillls

3. To prevent the pressure relief valve from failing, manually check the pressure reliefvalve. This is described in more detail on page 2 of S.O.P.

4. To prevent pneumatic control valves from failing, check that all the air hoses thatare connected to the valve are sealed and in good condition, prior to the experiment.

5. To prevent the tank from overfilling, check for faulty valves and moderate the setpoints.

6. To prevent any accidents from height, ensure the ladder is on stable ground and isproperly positioned.

7. DO NOT use a chair to check that the compressed air shut off valve is open.

8. To avoid other hazards, make sure all group memebers are familiar with the S.O.Psand correct procedures.

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Data Tables

Part ADetermining Transmitter gain

Table 4: Raw data to determine the transmitter gain

Controller PV (%span) Height of water (as seen in the sight glass)(cm)

Determining Valve gainTank Level 1Steady State flow rate:PV (%span):

Table 5: Raw data to determine the Valve gain (tank level 1)

SS Rotameter tube reading (cm) Controller OUT (%span)

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Tank Level 2Steady State flow rate:PV (%span):

Table 6: Raw data to determine the Valve gain (tank level 1)

SS Rotameter tube reading (cm) Controller OUT (%span)

Tank Level 3Steady State flow rate:PV (%span):

Table 7: Raw data to determine the Valve gain (tank level 1)

SS Rotameter tube reading (cm) Controller OUT (%span)

Note: Controller OUT represents valve diaphragm pressure

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Part B: Open-loop responseSteady State rotameter tube reading (cm):SS PV (%span):SS OUT (%span):Inflow rate 1 (new):

Table 8: Raw data to determine the Open-loop response (inflow rate 1)

Time(s) PV (%span)

Inflow rate 2 (new):

Table 9: Raw data to determine the Open-loop response (inflow rate 2)

Time(s) PV (%span)

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Inflow rate 3 (new):

Table 10: Raw data to determine the Open-loop response (inflow rate 3)

Time(s) PV (%span)

Inflow rate 4 (new):

Table 11: Raw data to determine the Open-loop response (inflow rate 4)

Time(s) PV (%span)

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Inflow rate 5 (new):

Table 12: Raw data to determine the Open-loop response (inflow rate 5)

Time(s) PV (%span)

Inflow rate 6 (new):

Table 13: Raw data to determine the Open-loop response (inflow rate 6)

Time(s) PV (%span)

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New output 1 OUT(%span):

Table 14: Raw data to determine the Open-loop response (output 1)

Time(s) PV (%span)

New output 2 OUT(%span):

Table 15: Raw data to determine the Open-loop response (output 2)

Time(s) PV (%span)

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New output 3 OUT(%span):

Table 16: Raw data to determine the Open-loop response (output 3)

Time(s) PV (%span)

New output 4 OUT(%span):

Table 17: Raw data to determine the Open-loop response (output 4)

Time(s) PV (%span)

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New output 5 OUT(%span):

Table 18: Raw data to determine the Open-loop response (output 5)

Time(s) PV (%span)

New output 6 OUT(%span):

Table 19: Raw data to determine the Open-loop response (output 6)

Time(s) PV (%span)

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Part C: Closed-loop responseRegulator responseController gain: Proportional band: Steady State rotameter tube reading (cm):SS PV (%span):SS OUT (%span):

Inflow rate 1 (new):

Table 20: Raw data to determine the Closed-loop response (inflow rate 1)

Time(s) PV (%span)

Inflow rate 2 (new):

Table 21: Raw data to determine the Closed-loop response (inflow rate 2)

Time(s) PV (%span)

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Inflow rate 3 (new):

Table 22: Raw data to determine the Closed-loop response (inflow rate 3)

Time(s) PV (%span)

Inflow rate 4 (new):

Table 23: Raw data to determine the Closed-loop response (inflow rate 4)

Time(s) PV (%span)

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Inflow rate 5 (new):

Table 24: Raw data to determine the Closed-loop response (inflow rate 5)

Time(s) PV (%span)

Inflow rate 6 (new):

Table 25: Raw data to determine the Closed-loop response (inflow rate 6)

Time(s) PV (%span)

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Servo responseSS PV (%span):New Set Point 1:

Table 26: Raw data to determine the Closed-loop response (Servo, SP: 1)

Time(s) PV (%span)

New Set Point 2:

Table 27: Raw data to determine the Closed-loop response (Servo, SP: 2)

Time(s) PV (%span)

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New Set Point 3:

Table 28: Raw data to determine the Closed-loop response (Servo, SP: 3)

Time(s) PV (%span)

New Set Point 4:

Table 29: Raw data to determine the Closed-loop response (Servo, SP: 4)

Time(s) PV (%span)

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New Set Point 5:

Table 30: Raw data to determine the Closed-loop response (Servo, SP: 5)

Time(s) PV (%span)

New Set Point 6:

Table 31: Raw data to determine the Closed-loop response (Servo, SP: 6)

Time(s) PV (%span)

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