Spray Boot Pressure Station UTC -ENGR 3280-L Week 10 March 20, 2013 Blue Team. Ethan Tummins Jeff Clowdus Jerry Basham

Transcription

1 Spray Boot Pressure Station UTC -ENGR 3280-L Week 10 March 20, 2013 Blue Team Ethan Tummins Jeff Clowdus Jerry Basham

2 Presentation Overview Spray Booth Pressure Station Overview Steady State Operating Curve (SSOC) Step Response and Modeling Frequency/Relay Response and Modeling Root Locus Modeling Conclusions

3 Spray Booth Pressure Station Diagrams Duct #1 Open, #2 Closed Input % values were varied to obtain output ranges of 5 to 29 cm-h2o

4 SSOC Experiment Input ranges from 33% to 66% used to obtain desired output ranges of 5 to 29 cm-h2o Figure shows Steady State Operating Curveof combined data from team members experiments

5 Step Response Gain, Dead Time and Time Constant calculated from analysis of step response Figure shows step up response analysis example Input, m(t) (%) Gain=K = Δc/Δm = 0.6 cm-h20/% Δc = 11.0 cm-h2o Δm = 20% Δc = 11.0 cm- H2O 63.2%Δc = 9.5 cm-h2o Time (sec) Input Value(%) Output(cm-H20) Time Constant = τ= 0.1sec Dead Timet0 = 0.1 sec Output, c(t) (cm-h2o)

6 Step Response Results Figures show Gain, Dead Time and Time Constant w/ Uncertainty of Step Up and Step Down Experiments 0.7 Gain (cm-h2o/%) Gain, K, (cm-h2o/%) Up Down

7 Time Constant (sec) Up Down Dead Time (sec) Up Down Dead Time, t0, (sec) Time Const., τ, (sec)

8 Step Response FOPDT Modeling Linear First Order Plus Dead Time (FOPDT) Model used to observe dynamic response of system Figure shows example of Step Up Response compared to FOPDT Model Input (%) FOPDT Model Output (cm-h2o) Time (sec)

9 Modeling (Alternate Method) Figure shows Alternate Modeling Method used to obtain same results as FOPDT using trapezoid rule Input, m(t) (%) k= 11.0 cm-h2o k = 11.0 cm- H2O 63.2%k = L (sec) L+τ(sec) Time (sec) A0 = 1.0cm^2 τ= (A0/k)e^1 = 0.1sec A1 = 0.4cm^ Output, c(t) (cm-h2o)

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11 Frequency Response Sine function input Time response output Amplitude ratio and phase lag observed Tables show numerical results used for bode plots

12 Freq. Response Results Amplitude Ratio Model AR Phase Angle Model PA

13 Alt. Method Relay Response 80 Observe time response of output to relay feedback control Figure and table show results of experiment (note: according to Dr. Henry, a negative time constant is incorrect and does not prove time travel like I hoped) Pu1 Pu2 Pu ΔM =40% 60 Input (%) ΔC1=11.0cm-H20 ΔC2=11.5cm-H20 ΔC3 = 11.5cm-H Output (cm-h2o) Input Value(%) 5 30 Output(cm- Kcu = 4.4 ±0.5cm-H2O/%, τ= 0.1 sec, t0 = 0.1sec H20) Time (sec)

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15 Root Locus Modeling Plot proportional only feedback ctrl. system parameters used in FOPDT modeling, K, T, t0 Insert K, T, t0 into Root Locus Excel template (that kind Dr. Henry made for us) to determine Kc Determine responses to step change in set point

16 Root Locus Results IMAGINARY AXIS ROOT LOCUS PLOT REAL AXIS -40

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18 Conclusions Important system values: K, τ, t0, Kcuand Fu K, τ, t0 were obtained from analysis of SSOC graphs, Step and FOPDT Modeling Kcuand Fu were later found using K, τ, t0 in Frequency and Relay experiments and Root Locus Modeling Results are generally limited to 2 significant figures due to the approximate nature of the experiments

19 Final Values Input ranges from 33% to 66% were used to obtain the desired output ranges of 5 to 29 cm-h2o SSOC and Step Response provided a K of 0.6 cm-h20/%, τof 0.1 sec and t0 of 0.1 sec. Frequency Response bode plot provided a Kcuof 38 and an Fu of 1.5Hz Root Locus Modeling provided KCD of degrees and KCU of degrees

20 NO MAS 1 CLAP

21 Background Brief description of system, Diagram, "input" and "output" Brief Review of performance curves (SSOC), Operating range Baseline Input and Output Objective of controller design Previous Work Brief Review of system transfer function (FOPDT or other) (include parameter values) Don't show how to calculate any fit Don't show Excel equations Show only 1 step experiment and the model fit, zoomed in to where it is interesting (Show more if there is some significant reason to) Don't show equations for mean, standard deviation or Student's T Brief Review of Bode plots and results Don't show how to calculate AR and PA Don't show Excel equations Show only 1 sine experiment and the model fit, zoomed in to where it is interesting (Show more if there is some significant reason to) Don't show equations for mean, standard deviation or Student's T Description of feedback control in your system CLTF for your system Modeling Root locus Don't show Excel equations Model & parameters Controller operating lines on the SSOC to illustrate offset for all the Kc values you show on the Root Locus. Final value theorem results for the output function. Results Kcu, Kc for quarter decay, Kc for critical damping, range of Kc for underdamped, range of Kc for overdamped