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Industrial Control Systems - Pneumatic Systems

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Industrial Control Systems - Pneumatic Systems

  1. 1. Industrial Control Behzad Samadi Department of Electrical Engineering Amirkabir University of Technology Winter 2009 Tehran, Iran Behzad Samadi (Amirkabir University) Industrial Control 1 / 17
  2. 2. Pneumatic Systems Electrical Analogy Type of System Electrical Pneumatic T-Variable i, current q, mass flow A-Variable v, voltage p, pressure Dissipator resistor orifice Storage (A-Type) capacitor air tank Storage (T-Type) inductor long pipe Unidirectional diode check valve Behzad Samadi (Amirkabir University) Industrial Control 2 / 17
  3. 3. Pneumatic Systems Electrical Analogy Type of System Electrical Pneumatic T-Variable i, current q, mass flow A-Variable v, voltage p, pressure Dissipator resistor orifice Storage (A-Type) capacitor air tank Storage (T-Type) inductor long pipe Unidirectional diode check valve High pressure pneumatic systems are very nonlinear due to the compression of air. In this course, low pressure pneumatic systems and linear models around the operating point are considered. [Macia and Thaler, 2004, Ljung and Glad, 1994] Behzad Samadi (Amirkabir University) Industrial Control 2 / 17
  4. 4. Pneumatic Dissipator Hagen - Poiseuille Law ∆p = 8µL πr4 q = Rf q ∆p = pressure drop q = mass flow rate µ = dynamics viscosity L = length of the pipe r = radius Behzad Samadi (Amirkabir University) Industrial Control 3 / 17
  5. 5. Pneumatic Dissipator Hagen - Poiseuille Law ∆p = 8µL πr4 q = Rf q ∆p = pressure drop q = mass flow rate µ = dynamics viscosity L = length of the pipe r = radius Hagen (1839) - Poiseuille (1838-1840) Law corresponds to Ohm’s law for electrical circuits (v = ρ L Ai = Ri) Describes slow viscous incompressible flow through a constant circular cross-section Behzad Samadi (Amirkabir University) Industrial Control 3 / 17
  6. 6. Pneumatic Dissipator Computation of the value of the gas flow resistance may be quite time consuming. [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 4 / 17
  7. 7. Pneumatic Dissipator Computation of the value of the gas flow resistance may be quite time consuming. It can however be easily determined from the plot of ∆p versus q. Rf = d(∆p) dq [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 4 / 17
  8. 8. Pneumatic Capacitor q p Capacitance Cf = dm dp Cf = capacitance m = mass of gas inside the tank p = gas pressure Behzad Samadi (Amirkabir University) Industrial Control 5 / 17
  9. 9. Pneumatic Capacitor Ideal Gas Law pV T = nR p =gas pressure V =volume of the gas T =absolute temperature n =number of moles of gas R =universal gas constant Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
  10. 10. Pneumatic Capacitor Ideal Gas Law pV T = nR p =gas pressure V =volume of the gas T =absolute temperature n =number of moles of gas R =universal gas constant m =nM = pV RT M M =molar mass Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
  11. 11. Pneumatic Capacitor Ideal Gas Law pV T = nR p =gas pressure V =volume of the gas T =absolute temperature n =number of moles of gas R =universal gas constant m =nM = pV RT M M =molar mass Pneumatic Capacitor Cf = dm dp = V R M T Isothermal change is assumed. Behzad Samadi (Amirkabir University) Industrial Control 6 / 17
  12. 12. Simple Air Tank Air Tank Compressed Air Orifice p in p out Behzad Samadi (Amirkabir University) Industrial Control 7 / 17
  13. 13. Simple Air Tank Air Tank Compressed Air Orifice p in p out pin =Rf Cf dpout dt + pout pin =input pressure pout =air tank pressure Rf =orifice resistance Cf =air tank capacity Behzad Samadi (Amirkabir University) Industrial Control 7 / 17
  14. 14. Pneumatic Nozzle-flapper Amplifier [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 8 / 17
  15. 15. Pneumatic Relay In this course, it is assumed that Pneumatic Relay is a linear gain. [Love, 2007] Behzad Samadi (Amirkabir University) Industrial Control 9 / 17
  16. 16. Check Valve Pneumatic diode [Parr, 1999] Behzad Samadi (Amirkabir University) Industrial Control 10 / 17
  17. 17. Bellows Bellows actuator [Parr, 1999] Behzad Samadi (Amirkabir University) Industrial Control 11 / 17
  18. 18. Bellows Bellows actuator Bellows feedback [Parr, 1999] Behzad Samadi (Amirkabir University) Industrial Control 11 / 17
  19. 19. Pneumatic Proportional Controller [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 12 / 17
  20. 20. Pneumatic Proportional Controller pb = K1x [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  21. 21. Pneumatic Proportional Controller pb = K1x pb = K2z [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  22. 22. Pneumatic Proportional Controller pb = K1x pb = K2z pc = K3z [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  23. 23. Pneumatic Proportional Controller pb = K1x pb = K2z pc = K3z pc = K1K3 K2 x = Kx [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  24. 24. Pneumatic Proportional Controller pb = K1x pb = K2z pc = K3z pc = K1K3 K2 x = Kx x = b a+b e − a a+b y [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  25. 25. Pneumatic Proportional Controller pb = K1x pb = K2z pc = K3z pc = K1K3 K2 x = Kx x = b a+b e − a a+b y Apc = Ksy [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 13 / 17
  26. 26. Pneumatic PD Controller [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 14 / 17
  27. 27. Pneumatic PI Controller [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 15 / 17
  28. 28. Pneumatic PID Controller [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 16 / 17
  29. 29. I/P Converter [Parr, 1999] Behzad Samadi (Amirkabir University) Industrial Control 17 / 17
  30. 30. Ljung, L. and Glad, T. (1994). Modeling of Dynamic Systems. Prentice Hall PTR, 1 edition. Love, J. (2007). Process Automation Handbook: A Guide to Theory and Practice. Springer, 1 edition. Macia, N. F. and Thaler, G. J. (2004). Modeling and Control of Dynamic Systems. Delmar Learning. Ogata, K. (1997). Modern Control Engineering. Prentice Hall, 3 edition. Parr, A. (1999). Hydraulics and Pneumatics: A Technicians and Engineers Guide. Butterworth-Heinemann, 2 edition. Behzad Samadi (Amirkabir University) Industrial Control 17 / 17

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