# Process Dynamics And Control

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nd EnergyIncompressible flowConstant hold-upConstant mean pressure16

Process Modeling Under constant hold-up and constant density Mass balance equation Total Mass Mass In Mass Out Constant volume17

Process Modeling Under constant hold-up and constant mean pressurechanges Energy Balance leads to an enthalpy balance Inlet Enthalpy Outlet Enthalpy Heat flow to the system Work done on system Total enthalpy in the system18

Process ModelingAfter substitution,withfixed and assuming constantDivide by Heat input from a hot (or cold source) at temperaturewhereis a heat-transfer coefficientis the effective area for heat transfer19

Process Modeling Modeling heat input Heat input is proportional to the difference in temperature20

Process ModelingAssume F is fixed then the ODE is linear, use LaplaceTransformswhereis the tank residence time (or time constant)Isolating and solving forgives21

Process ModelingIf F changes with time then the differential equation does nothave a closed form solution.Productsandequation nonlinear.makes this differentialSolution will need numerical integration.22

Process Modeling Gravity tankFohObjectives: height of liquid in tankFundamental quantity: Mass, momentumAssumptions: FLOutlet flow is driven by head of liquid in the tankIncompressible flowPlug flow in outlet pipeTurbulent flow23

Process ModelingFrom mass balance and Newton’s law,A system of simultaneous ordinary differential equations resultsLinear or nonlinear?24

Solution of ODEs Mechanistic modeling results in (sets of) nonlinear ordinarydifferential equations Solution requires numerical integration To get solution, we must first: specify all constants specify all initial conditions specify types of perturbations of the input variablesFor the heated stirred tank, specify specify specify25

Input Specifications Study of control system dynamics Observe the time response of a process output inresponse to input changes Focus on specific inputs1. Step input signals2. Ramp input signals3. Pulse and impulse signals4. Sinusoidal signals5. Random (noisy) signals26

Common Input Signals1. Step Input Signal: a sustained instantaneous changee.g. Unit step input introduced at time 127

Common Input Signals2. Ramp Input: A sustained constant rate of changee.g. Ramp input at time t 128

Common Input Signals3. Pulse: An instantaneous temporary changee.g. Fast pulse (unit impulse) at t 129

Common Input Signals3. Pulses:e.g. Rectangular Pulse30

Common Input Signals4. Sinusoidal input, e.g.31

Common Input Signals5. Random Input, e.g. white noise32

Process Modeling For control applications: Modeling objectives is to describe process dynamics based on the laws of conservation of mass, energy and momentum The balance equation 1.Mass Balance 2.Energy Balance 3.Momentum Balance (Newton’s Law) Rate of Accumulation of fundamental quantity Flow In Flow Out Rate of Production - File Size: 1MBPage Count: 32Explore furtherPDF Download Process Dynamics Modeling And Control Freewww.nwcbooks.comProcess Dynamics and Control - PDF Free Downloadepdf.pubUnderstanding Process Dynamics And Control PDF Download .www.fuadherbal.netA Short Introduction to Process Dynamics and Controlwww.users.abo.fiProcess Dynamics And Control Lecture Notesrims.ruforum.orgRecommended to you b

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