UTC Engineering 3280L Spray Paint Booth Pressure Control System Yellow team: Caroline Brune, Chris Legenski
Table of Contents I. Introduction... 4 Figure 1: Schematic Diagram of the Dunlap Plant Spray-Paint Booths... 4 II. Background and Theory... 5 Figure 2: Block Diagram of Paint Booth System... 5 A. Component 1: Variations in Measured Quantities... 5 B. Component 2: Transient Responses of the System... 5 Figure 3: Step Input... 6 Figure 4: Step Response... 6 Equation 1: Student T s Statistics using 95% confidence Interval... 6 Figure 5: Student s T... 7 III. Procedure... 8 A. Component 1: Variations in Measured Quantities... 8 Procedure 1: Constant Pressure with both Dampers Open... 8 B. Component 2: Transient Responses of the System... 8 Procedure 2: Step Response with both Dampers Open... 8 IV. Results... 10 A. Component 1: Variations in Measured Quantities... 10 Graph 1: Steady State Operating Curve... 10 B. Component 2: Transient Responses of the System... 10 Graph 2: Flow System Gain... 11 Graph 3: Flow System Dead Time... 12 Graph 4: Flow System First Order Time Constant... 13 V. Discussion... 14 A. Component 1: Variations in Measurement Quantities... 14 B. Component 2: Transient Responses of the System... 14 VI. Conclusion and Recommendations... 15 A. Component 1: Variations in Measurement Quantities... 15 B. Component 2: Transient Responses of the System... 15 VII. Appendices... 16 A. Component 1: Variations in Measurement Quantities... 16 1-30-2013 Page 2
Figure 6: Component 1 Data... 16 B. Component 2: Transient Responses of the System... 17 Graph 4: Step Response Data Obtain Example... 17 Figure 7: Component 2 Data... 18 1-30-2013 Page 3
I. Introduction Green Engineering s plant, located in Dunlap, Tennessee, contains a series of equipment in the process of engine assembly. The housings contained in these engines are first spray painted in three rooms, each pressurized to control the exhaust which emits to the atmosphere by passing through a filter. The emission must be in accordance with US-EPA, the state of Tennessee, and local Air Pollution Control Agency. A variable-speed pneumatic blower is under feedback control to maintain the desired booth pressure, as illustrated in Figure 1. Figure 1: Schematic Diagram of the Dunlap Plant Spray-Paint Booths Solenoid-operated valves, D-1 and D-2, have been installed to close off pressurizing to booths 2 and 3 when they are not in use. This report details the relationship between the pressure in the rooms and the speed of the blower s motor. 1-30-2013 Page 4
II. Background and Theory The variable speed of the blower operates under pressure feedback control. The system s Manipulated variable, m(t), is a function of time. This input function represents the power sent to the motor and ranges from 0-100%. The Controlled variable or output function, c(t), represents the pressure in the booth in units of centimeters of water; a function of time. Figure 2 illustrates this relationship between input and output of the pressure feedback control system. Figure 2: Block Diagram of Paint Booth System A. Component 1: Variations in Measured Quantities Each experimental measurement contains associated error which can be found using multiple steady-state measurements of the output function. Once multiple data points have been achieved for each experimental output, obtain the mean and standard deviation. The associated error, termed uncertainty, will be twice the value of the standard deviation. Adding and subtracting the uncertainty to the mean provides the true value of the function at a confidence level of 95%. The experiment detailed within this report is executed with both solenoid valves open. B. Component 2: Transient Responses of the System This experiment is designed to find the coefficients for a transient mathematical model for the pressure booth system. These coefficients are found by providing an abrupt, instantaneous change in the system s input, a step change. The system pressure output, in response to the change in input, is termed the step response of the system. To obtain step response data, the system is started at an input greater than zero, called the base line value of m(t). Once the base line reaches steady state, the system is abruptly changed up or down creating a step increase or decrease respectively. This method is illustrated in Figure 3. 1-30-2013 Page 5
Figure 3: Step Input The output is plotted against time to obtain the step response, as demonstrated in Figure 4. Figure 4: Step Response A response curve as shown in Figure 4 conveys the system takes a certain time to respond to the input step. Characteristics of these graphs determine the First-order Plus Dead Time (FOPDT) parameters of the system: steady state gain, response time, and dead time. The associated error in each average is calculated using Student T Statistics as illustrated in Equation 1. Equation 1: Student T s Statistics using 95% confidence Interval»»º» ¹º¹» ¹ººº»/º Where X-max and X-min represent the largest and smallest data point, n is the number of data points, and t is the student s T shown in Figure 5. 1-30-2013 Page 6
Figure 5: Student s T n t t/n 2 6.3 3.1 3 2.9 1.0 4 2.3 0.6 5 2.1 0.4 6 2.0 0.3 10 1.8 0.2 18 1.7 0.09 1-30-2013 Page 7
III. Procedure A. Component 1: Variations in Measured Quantities Procedure 1 details the operating conditions in obtaining each data point. The target output ranged from 2-20 cm-h2o. Procedure 1: Constant Pressure with both Dampers Open 1. Access UTC laboratories on the web, pressure station with constant input 2. Fill in name, location, and email 3. Detail length of operation, selected input value 4. Select the time for dampers #1 and #2 to be open 5. Click run experiment 6. Export the data to excel once experiment is complete 7. Plot booth pressure vs. time and locate the steady state time segment 8. Obtain the average and standard deviation of the steady state power output data 9. Repeat steps 2-8 with different input values 10. Plot booth pressure vs. input power for each calculated average 11. Add error bars for each average calculated from two times each standard deviation 12. This graph represents the steady-state operating curve for the system operating at both dampers open B. Component 2: Transient Responses of the System Procedure 2: Step Response with both Dampers Open 1. Access UTC laboratories on the web, pressure system with step input 2. Fill in name, location, and email 3. Detail input, step input, duration of first input, and total length of operation 4. Select time for dampers #1 and #2 to be open 5. Click run experiment 6. Export the data to excel upon completion of experiment 7. Plot booth pressure vs. time (Figure 4) to locate the steady state base output and step output 8. Calculate the average pressure for both outputs at each respective steady state 9. Divide change in output by change in input to obtain gain 10. Insert a line tangent to the steepest slope of the output step response 11. Dead time is determined by the distance between the input base line s initial step to the line configured in step 10 12. Insert a vertical line where dead time horizontal line intersects the sloped line from step 10 1-30-2013 Page 8
13. First order time constant is the distance between the dead time to step 12 s vertical line 14. Repeat steps 2-13 for three step ups and three step downs 15. The uncertainty of each data point is calculated using Student T statistics with 95% confidence interval (Equation 1 and Figure 5) 1-30-2013 Page 9
IV. Results A. Component 1: Variations in Measured Quantities Graph 1 demonstrates averages and associated error in the output range of 1.5 19 cm-h2o. Reported averages and uncertainties are located in Appendix A. Graph 1: Steady State Operating Curve 22 20 18 16 Steady-State Operating Curve Booth Pressure (cm-h2o) 14 12 10 8 6 4 2 0 30 35 40 45 50 55 60 65 Input Power (%) B. Component 2: Transient Responses of the System Graphs 2-4 represent the FODPT constants measured in low, medium, and high ranges with each range containing step up and down with associated error bars. The values and error are also located in Appendix B. 1-30-2013 Page 10
Graph 2: Flow System Gain Flow System Gain High-down High-up Miid-Down Mid-up Lower Down Lower-Up 0.0 0.2 0.4 0.6 Cm-H2O/% 1-30-2013 Page 11
Graph 3: Flow System Dead Time Flow System Dead Time High-down High-up Miid-Down Mid-up Lower Down Lower-Up 0.0 0.1 0.2 0.3 Seconds 1-30-2013 Page 12
Graph 4: Flow System First Order Time Constant Flow System First Order Time Constant High-down High-up Miid-Down Mid-up Lower Down Lower-Up 0.0 0.1 0.2 0.3 0.4 Seconds 1-30-2013 Page 13
V. Discussion A. Component 1: Variations in Measurement Quantities Associated error increased as the input power percentage increased. The uncertainty at 20cm- H2O output was more than double the uncertainty at 2cm-H2O. This information shows that as the system is operated at higher input percentages, associated error increases. B. Component 2: Transient Responses of the System The measured gain resulted in a tendency to decrease as input increased. Downward steps were larger in each range then their respected upward steps. The measured dead time proved larger as input increased, with downward steps greater than double their respected upward steps. The first order time constant achieved the most consistent data and slightly decreased as input increased. The downward steps in the first order time constants are larger than each respected range upward step. 1-30-2013 Page 14
VI. Conclusion and Recommendations A. Component 1: Variations in Measurement Quantities When high booth pressures are required, associated error is much greater. This must be accounted for by inputting a slightly higher input percentage so that legal air pollution is maintained. B. Component 2: Transient Responses of the System Downward step responses are larger than upward step responses. As input power percentage increases, gain and dead time also increase while the first order time constant only slightly decreased. 1-30-2013 Page 15
VII. Appendices A. Component 1: Variations in Measurement Quantities Figure 6: Component 1 Data Input (%) Average Output (cm-h2o) Standard Uncertainty Deviation 32 2 0.5 0.9 34 4 0.5 1.0 36 5 0.6 1.1 38 6 0.6 1.2 40 7 0.7 1.3 42 7 0.9 1.7 45 9 0.9 1.8 48 11 1.0 1.9 49 11 0.9 1.8 50 12 1.0 2.0 52 13 1.0 2.0 52 12 0.8 1.6 54 14 1.1 2.3 55 14 1.0 1.9 55 14 1.0 1.9 58 16 1.2 2.5 60 18 1.2 2.3 63 19 1.2 2.3 1-30-2013 Page 16
B. Component 2: Transient Responses of the System Graph 4 demonstrates an experimental graph to obtain the FOPDT constants Graph 4: Step Response Data Obtain Example 8 Upward Response Step Example 7 6 Output (cm-h20) 5 4 3 2 1 0 14 14.1 14.214.3 14.4 14.5 14.6 14.714.8 14.9 15 15.115.2 15.3 15.415.5 15.615.7 15.815.9 16 Time (s) 1-30-2013 Page 17
Figure 7 represents the average and uncertainty obtained for each range s upward and downward step. Figure 7: Component 2 Data Range K Uncertainty Low-Up 0.35 0.01 Low-Down 0.48 0.03 Mid-Up 0.38 0.06 Mid-Down 0.56 0.01 Hi-Up 0.59 0.01 Hi-Down 0.62 0.03 Range Dead Time Uncertainty Low-Up 0.07 0.05 Low-Down 0.20 0.10 Mid-Up 0.07 0.10 Mid-Down 0.20 0.10 Hi-Up 0.04 0.02 Hi-Down 0.08 0.05 Range Tau Uncertainty Low-Up 0.12 0.05 Low-Down 0.23 0.07 Mid-Up 0.12 0.07 Mid-Down 0.23 0.10 Hi-Up 0.17 0.05 Hi-Down 0.22 0.05 1-30-2013 Page 18