MCEN 4043: System Dynamics Control System Design Project

Liquid Level Control System Using a Solenoid Valve Sarah LeVine, Kyle Manhart, Torie Monzon 6 December 2010

INTRODUCTION A liquid level system using water as the medium was constructed to demonstrate a functioning proportional control system. The system consisted of two 5 gallon buckets, with a solenoid valve to control the input flow from Tank 1 to Tank 2, an orifice to drain the water from Tank 2, and four load cell weight sensors underneath Tank 2 to calculate the height of the liquid in the tank. A photo of the setup is shown in Figure 1, and shown schematically in Figure 2.

Actuator (solenoid valve)

Tank 1

Q in

Tank 2

Q out (orifice) Sensor (4 load cells) Figure 1. Setup of liquid level system.

Figure 2. Schematic of Liquid Level System.

Tank 2 was drained constantly through an orifice created by a partially open valve so QIN would be greater than QOUT for input flow rates above roughly 50% of the maximum. Tank 1 provided a reservoir for the input flow, and was refilled between measurements. Sudden changes in the level of Tank 1 resulted in a sudden change in pressure on the solenoid valve, which would result in a sudden jump in flow rate. The solenoid valve operated by opening when a DC

voltage of 24V was applied across its terminals, otherwise it remained closed. To control flow rate through the valve, a 10Hz duty cycle varied the amount of time it saw 24V and remained open. Using a LabVIEW program, the duty cycle of the solenoid valve controlled the flow rate into Tank 2 depending on the desired height of the tank. The level of the water ranged from 3.5 to 7 inches.

SETUP The solenoid valve was powered by 24V from a voltage supply and amplified with a transistor. The circuit for the solenoid valve is shown in Figure 3.

Figure 3. Schematic of Solenoid-Transistor Circuit.

Tank 2 was positioned on four load cells connected to the DAQ SCXI-1122 channel 1 and were imported to a LabVIEW program using a DAQ Assistant. The load cells had four wires, two inputs and two outputs. The + output (yellow wire) was connected to the + CH1 input on the DAQ board and the - output (white wire) was connected to the – CH1 output on the DAQ board. The + input (red wire) was connected to the + 5 V from the power supply and the – input (black wire) was connected to ground on the power supply. Figure 4 shows a schematic of the load cells, which were connected in parallel in order to output a single voltage signal.

Figure 4. Schematic of Load Cell Wiring.

The load cells had a voltage output corresponding to an increase in weight, and were calibrated by subtracting a voltage offset and multiplying the signal by a calibration factor to correspond to the weight of the system at different liquid level heights. The tank was measured filled at half inch intervals with a calibrated weight scale, then measured again at the same intervals with all four load cells. Average load cell voltage offset and calibration values were used for a midpoint value of 5 inches. The tank was approximated as a cylinder with constant cross sectional area. Three 2 liter bottles filled with water were placed in the tank to reduce the area of the fluid in order to get a faster change in height, and the total range of the system was restricted to the straight sections of the 2 liter bottles, resulting in a total range of

3.5 to 7 inches for the system. Weight was divided by the density of water at standard temperature and pressure to determine volume of the tank, and the height of Tank 2 was computed by dividing the volume by its cross sectional area. The area of Tank 2 was determined by subtracting the area of the three bottles from the area of the green bucket. Two preliminary LabVIEW programs were written to test the solenoid valve actuator and load cell sensors independently. Refer to Figures 5 and 6.

Figure 5. LabVIEW Program to control duty cycle of the solenoid valve actuator.

Figure 6. LabVIEW Program to input and calibrate data from the load cells.

Once the actuator and sensors were successfully controlled, their programs were combined and rewired with a PID control shown in figure 7.

Figure 7. LabVIEW water level control program with PID controller.

Experimenting with the PID values produced results supporting the use of a single proportional gain, discussed in the results. Additionally, utilizing the actuator control VI in the above produced long timing delays. The control was therefore redesigned without the integrator and derivative controls, and the Wait blocks were adjusted to be more synchronous to reduce time delay. Calibration curves for voltage-height were used to zero and calibrate the load cells and were found to have an offset voltage of 0.2596V and a calibration factor of 204.8 Inches/Volt. Additional calibration data used for the LabVIEW control program and Simulink model can be found in the appendix. The system was reworked with a case structure to determine if the error was negative, zero or positive. If negative, a gain of zero was implemented producing a zero duty cycle and the solenoid would not open since the water level was at or above the specified height, allowing Tank 2 to drain. When the difference was greater than zero the duty cycle varied from 80% to 100%, utilizing a gain of 5% per inch of height difference. The final LabVIEW control is shown below in Figures 8 and 9.

Figure 8. LabVIEW water level control program with proportional controller and more robust time delays.

Figure 9. LabVIEW control front panel.

BILL OF MATERIALS Materials and their sources used in this project are summarized inthe Bill of Materials shown in Table 1. Table 1. Bill of Materials

Part Water Tank Load Cells Solenoid Valve Transistor Orifice Tubing Containment Tank 2 Liter Bottles Wood Stools

Vendor ITLL – Mike Elliot ITLL – Darren McSweeney ITLL – Nick Stites ITLL ITLL Astrophysics Research Lab McGuckin Hardware ITLL ITLL

Price Borrowed Borrowed Borrowed Borrowed Borrowed Borrowed $15.00 Found / Reused free Fabricated from scrap materials

Quantity 2 4 1 1 2 2 1 3 2

ANALYSIS A first order transfer function of the two-tank liquid level system is developed below. A is the average cross sectional surface area of the bucket, R is the resistance of the out flow orifice, g is gravity, H is height, and qV is volumetric flow rate of QOUT.

̇ ( ) ( ) ( )(

( ) ( ) )

( ) ( ) ( )

( ) ( ) The area used for calculations is the average area of the level system range, 5 inches. DBucket is bucket diameter and D2 Liter is 2 liter bottle diameters.

R is estimated utilizing the following formula and varied within 1% since resistance is typically determined empirically. L is the valve length, μ is the kinematic viscosity, ρ is the water density, DValve is the orifice valve diameter. The orifice valve was only partially open and was considered to have a wetted diameter equivalent to 1/4 DValve. (

Eqn. (1)

)

Substituting A and R produces the following first order transfer function.

( ) ( )

Eqn. (2)

A model of the system response was built in MATLAB’s Simulink extension using equation 2 and the proportional gains taken from the LabVIEW code for the solenoid control values, shown in Figure 10. With all other values known, the resistance of the outflow orifice could then be determined empirically by matching the Simulink model with the results of the physical system after an initial guess given by Equation 1.

Figure 10. Simulink Block Diagram.

RESULTS The system functioned properly and responded as predicted. Due to the small flow rate relative to the cross sectional area of the system, the input flow was restricted to a range of 80% to 100% in order to overcome the outflow and arrive at the desired height. Figure 11 shows the response of this system to a 1-inch height increase, which took 400 seconds to reach and maintain the steady state.

Figure 12. Fill from 5 inches to 6 inches with flow rate ranging from 80-100%

Figure 12 shows the response of the system when the flow rate was allowed to range between 0% and 100%, it took 1800 seconds to reach 98% of the steady state. It was unable to arrive at the desired height using only a proportional controller because the system reached an input flow rate equal to or less than the outlet flow rate. Although an integral control would allow the system to reach its steady state at this range of flow rates, the system response of the former system was 600% faster. For this reason integral control was deemed unnecessary and the flow was restricted to an 80% minimum in the final system design.

Figure 13. Fill from 5 inches to 6 inches with flow rate ranging from 0-100%.

FUTURE WORK There are several improvements that could be made to the system design. Response time would decrease significantly with a smaller ratio of surface area to flow rate. This could be achieved with a narrower Tank 2, a larger input valve, or both a narrower tank and larger valve. Since valves are more costly than tanks, a narrower tank such as a graduated cylinder would be the best improvement. Graduated cylinders also have the added advantage of measurement lines for more accurate height measurement. Tank 1 should remain large in order to keep the change in pressure on the solenoid valve as low as possible as it empties into Tank 2.

CONCLUSION A liquid level system has a slow response time relative to other types of control systems. The response time of the system created in this study was on the order of hundreds of seconds, and varied depending on the desired height change due to differences in pressure on QOUT with changing height if the liquid in Tank 2. Because of this slow response, an effective control system design utilizes a simple proportional controller. Faster and more accurate response times can be obtained by substantially changing the physical system and including a PID controller.

APPENDIX Raw data and plots used for Load Cell calibration.

Height (in) Weight (lbs) Voltage (V) Calibration Factor (lb/V) 7 28.95 57.1 6.5 28.05 56 6 27.25 0.288868 54.2 5.5 26.3 0.286423 52.7 5 25.6 0.283977 51.5 4.5 24.8 0.281531 50.1 4 23.95 0.279086 48.8 3.5 23.15 0.27664 48.2 3 22.4 0.274195 46 2.5 21.6 0.271749 44.5 4.95 Height (in) Weight (lbs) Area (in^2) Density (lb/in^3) Volume (in^3) g (in/s^2) row (lb/in^3) P (psi) 7 28.95 69.08 0.036 804.1666667 386.4 0.036 97.3728 6.5 28.05 69.08 0.036 779.1666667 386.4 0.036 90.4176 6 27.25 69.08 0.036 756.9444444 386.4 0.036 83.4624 5.5 26.3 69.08 0.036 730.5555556 386.4 0.036 76.5072 5 25.6 69.08 0.036 711.1111111 386.4 0.036 69.552 4.5 24.8 69.08 0.036 688.8888889 386.4 0.036 62.5968 4 23.95 69.08 0.036 665.2777778 386.4 0.036 55.6416 3.5 23.15 69.08 0.036 643.0555556 386.4 0.036 48.6864 3 22.4 69.08 0.036 622.2222222 386.4 0.036 41.7312 2.5 21.6 69.08 0.036 600 386.4 0.036 34.776 Q_out Height (in) time (s) Weight (lfb) row (lb/in^3) mass (lbm) 7 180 0.776 0.036 21.55555556 5 180 0.389 0.036 10.80555556 3 120 0.269 0.036 7.472222222

rate (lbm/s) 0.119753 0.060031 0.062269

Q_in v.s duty cycle 0.7

y = 0.0121x - 0.5512 R² = 0.9819

Q in (in^3/s)

0.6 0.5 0.4 0.3 0.2 0.1 0 0

20

40

60

80

100

120

Duty Cycle (%)

Load cell Voltage vs. Height

Voltage (V)

0.29 0.285

y = 0.0049x + 0.2595 R² = 1

0.28 0.275 0.27 0

1

2

3

4

5

6

7

Height (In)

y = 13.91x R² = 1

Pressure v.s Height 120

Pressure

100 80 60 40 20 0 0

1

2

3

4 Height (In)

5

6

7

8

Q_out

y = 0.0299x - 0.0893 R² = 1

0.14 Q out (In^3/s)

0.12 0.1 0.08 0.06 0.04

0.02 0 0

1

2

3

4

5

6

7

8

Height (In)

Weight vs. Height

y = 1.6248x + 17.487 R² = 0.9995

35

Weight (LBf)

30

25 20 15 10 5 0 0

1

2

3

4

5

6

7

8

Height (In)

Volume vs. Height Volume (In^3)

1000

y = 45.135x + 485.75 R² = 0.9995

800 600 400 200 0 0

1

2

3

4 Height (In)

5

6

7

8