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Industrial Control Systems - Thermal Systems

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Industrial Control Systems - Thermal 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 / 7
  2. 2. Thermal Systems Electrical Analogy Type of System Electrical Thermal T-Variable i, current q, heat flow A-Variable v, voltage T, temperature Resistance resistor thermal resistor Storage (A-Type) capacitor thermal capacitor Storage (T-Type) inductor unknown Note that q is in units of power and no T-type thermal energy storage has been identified. [Ogata, 1997] Behzad Samadi (Amirkabir University) Industrial Control 2 / 7
  3. 3. Heat Transfer Conduction: Heat transfer through solid media Behzad Samadi (Amirkabir University) Industrial Control 3 / 7
  4. 4. Heat Transfer Conduction: Heat transfer through solid media T1 − T2 =Rcq Rc = d KA d =thickness of the wall A =area of the wall K =thermal conductivity of the wall’s material [Macia and Thaler, 2004] Behzad Samadi (Amirkabir University) Industrial Control 3 / 7
  5. 5. Heat Transfer Convection: Heat transfer through a fluid (liquid or gas) Behzad Samadi (Amirkabir University) Industrial Control 4 / 7
  6. 6. Heat Transfer Convection: Heat transfer through a fluid (liquid or gas) T1 − T2 =Rhq Rc = d hA d =thickness A =area h =convection coefficient [Macia and Thaler, 2004] Behzad Samadi (Amirkabir University) Industrial Control 4 / 7
  7. 7. Heat Transfer Radiation: Behzad Samadi (Amirkabir University) Industrial Control 5 / 7
  8. 8. Heat Transfer Radiation: q =AεFσ(T4 1 − T4 2 ) A =area of the surface of the object of interest ε =parameter descriptive of the emission of surfaces 1 and 2 σ =Stefan-Boltzman Constant F =geometrical shape factor T1, T2 =absolute temperatures of bodies 1 and 2 [Macia and Thaler, 2004] Behzad Samadi (Amirkabir University) Industrial Control 5 / 7
  9. 9. Heat Transfer Radiation: q =AεFσ(T4 1 − T4 2 ) Rr = 1 AεFσ(T2 1 + T2 2 )(T1 + T2) ⇒ T1 − T2 = Rr q [Macia and Thaler, 2004] Behzad Samadi (Amirkabir University) Industrial Control 6 / 7
  10. 10. Thermal Capacitance q =C dT dt C =mcx C =thermal capacitance of the object m =mass of the object cx =specific heat of material [Macia and Thaler, 2004] Behzad Samadi (Amirkabir University) Industrial Control 7 / 7
  11. 11. 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. Behzad Samadi (Amirkabir University) Industrial Control 7 / 7

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