FLOW RATE CONTROL SYSTEM SECOND ORDER PLUS DEAD TIME MODEL April 20, 2006 U.T.C Engineering 329

Yellow Team Jimy George Jeff Lawrence Taylor Murphy Jennifer Potter

Outline Flow System Background SOPDT System Theory Model Results

Outline Proportional Controller Comparison of FOPDT & SOPDT results Conclusion

Flow System Setup

Block Diagram

Laplace Domain R(s) C(s)

Time Domain

Modeling Observations

Parameters involved

Modeling Observations Recap

Negative Feedback Loop

Closed Loop Transfer Function

Characteristic Equation

Characteristic Equation For

Solving CE for Kc Direct Substitution Set s = iωU Set like terms equal to zero Imaginary part: [0.0079 ωU3-(0.6 +0.048Kcu) ωU]i=0i

Direct Substitution (cont’d) Real part: 0.24Kcu - 0.12 ωU2 + 1 = 0 ωU = 5 => fu = 0.8 Kcu = 8.3 %/(lb/min)

Corresponding Frequency Experiment

Observations Phase Angle = -1800 Amplitude Ratio = 0.12 Kcu calculated = 8.3

Comparison of fu

Comparison of Kc

Conclusion Kc = 8.3 %/(lb/min) SOPDT more accurate than FOPDT Always scope for improved results