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

2. Yellow Team
Jimy George
Jeff Lawrence
Taylor Murphy
Jennifer Potter

3. Outline
Flow System Background
SOPDT System Theory
Model Results

4. Outline Proportional Controller Comparison of FOPDT & SOPDT results
Conclusion

5. Flow System Setup

6. Block Diagram

7. Laplace Domain
R(s)
C(s)

8. Time Domain

9. Modeling Observations

10. Parameters involved

11. Modeling Observations Recap

12. Negative Feedback Loop

13. Closed Loop Transfer Function

14. Characteristic Equation

15. Characteristic Equation
For

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

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

18. Corresponding Frequency Experiment

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

20. Comparison of fu

21. Comparison of Kc

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