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بسم الله الرحمن الرحيم Advanced Control Lecture two

بسم الله الرحمن الرحيم Advanced Control Lecture two. 1- A modeling procedure ( Marlin, Chapter 3 ) 2- Empirical modeling ( Smith & Corripio , Chapter 7 ) 3- Control valve: Action, characteristics and capacity ( Smith & Corripio , Chapter 5 ).

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بسم الله الرحمن الرحيم Advanced Control Lecture two

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  1. بسم الله الرحمن الرحيمAdvanced ControlLecture two 1- A modeling procedure (Marlin, Chapter 3) 2- Empirical modeling (Smith & Corripio, Chapter 7) 3- Control valve: Action, characteristics and capacity (Smith & Corripio, Chapter 5) Lecturer: M. A. Fanaei Ferdowsi University of Mashhad

  2. We can tune the controller only after the process steady-state and dynamic characteristics are known. Types of model 01_5 Modeling (relation between inputs and outputs of process) • White box (first principles) n black box (empirical) • Linear n non-linear • Static n dynamic • Distributed n lumped • Time domain n frequency domain • Continuous n discrete For further reading refer to :Roffel & Beltlem, “Process dynamics and control”, Wiley, 2006

  3. A modeling procedure • 1. Define goals • Specific design decisions • Numerical values • Functional relationships • Required accuracy • 2.Prepare information • Sketch process and identify system • Identify variables of interest • State assumptions and data • 3.Formulate model • Conservation balances • Constitutive equations • Rationalize • Check degrees of freedom • Dimensionless form • 4.Determine Solution • Analytical • Numerical • 5. Analyze results • Check results for correctness • Limiting and approximate answers • Accuracy of numerical method • Interpret results • Plot solution • Characteristic behavior • Relate results to data and assumptions • Evaluate sensitivity • 6. Validate model • Select key values for validation • Compare with experimental results • Compare with results from more complex model

  4. F F CAo V CA Example 1. Isothermal CSTR • Define Goals • Dynamic response of a CSTR to a step in the inlet concentration. • The reactant concentration should never go above 0.85 mole/m3 • When the concentration reaches 0.83 mole/m3, would a person have enough time to respond? What would a correct response be? • The system is the liquid in the tank (as shown in Fig.). • The important variable is the reactant concentration in the reactor. Prepare Information

  5. F F CAo V CA Example 1. Isothermal CSTR Prepare Information … • Assumptions • Well-mixed vessel • Constant density • Constant flow in • Constant temperature • Data • F = 0.085 m3/min , V = 2.1 m3 • (CAo)initial = 0.925 mole/m3 ,DCAo = 0.925 mole/m3 • The reaction rate is rA = -kCA , with k = 0.04 min-1

  6. F F CAo V CA Example 1. Isothermal CSTR Formulate Model • Material balance: • Rationalize : • Degrees-of-freedom: One equation, one variable(CA), two external • variables (F and CAo) and two parameters (V and k). • Therefore the DOF is zero, and the model is exactly specified.

  7. F F CAo V CA Example 1. Isothermal CSTR Analytical Solution

  8. Example 1. Isothermal CSTR

  9. Empirical Modeling (Step Testing) Step Change Record Process Sensor/ Transmitter Final Control Element m(t), % c(t) , % Process Gain:

  10. FOPDT Model Fit 1 :

  11. FOPDT Model Fit 2 :

  12. FOPDT Model Fit 3 :

  13. Control Valve m(t) vp(t) Cv(t) f(t) Control Valve Action Control Valve Characteristics Control valve Capacity

  14. Control Valve • Control Valve Action is selected based on safety consideration • Fail-Closed (FC) or Air-to-Open (AO) : • Fail-Open (FO) or Air-to-Close (AC) : τv : Time constant of valve actuator (3-6 sec for pneumatic actuator) The gain of FC (AO) valve is positive The gain of FO (AC) is negative

  15. Control Valve • Control Valve Characteristics • Linear • Quick-opening • Equal percentage Rangeability parameter (50 or 100)

  16. Control Valve Control Valve Characteristics : How we must select the correct valve characteristics (Linear or Equal percentage) The correct selection requires a detailed analysis of the installed characteristics • As a rule of thump: • Choose a linear valve if at design conditions the valve is taking more than half of the total pressure drop (Δpv > 0.5 Δpo ). • Choose an equal percentage valve if at design conditions the valve is taking less than half of the total pressure drop (Δpv < 0.5 Δpo). • Equal percentage valves are probably the most common ones.

  17. Control Valve Control Valve Capacity The control valve capacity is : The flow in U.S. gallons per minute (gpm) of water that flows through a valve at a pressure drop of 1 psi across the valve Liquid Flow: Where: f(t) = volume flow rate (gpm) Δpv = presuure drop across the valve (psi) Gf = specicific gravity

  18. Control Valve Control Valve Capacity • Gas Flow • Subcritical flow: • Critical flow: • Where: • fs (t) = Gas volume flow at standard conditions,14.7 psia & 60 oF (scfh) • Cf = Critical flow factor (0.6 – 0.95 , typically 0.9) • p1 = Pressure at valve inlet (psia), T = Tempreture at valve inlet (oR) • G = Gas specific gravity

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