Continuous Fermenter Control

Simulates a model of a continuous fermenter. Constant volume reactor where single, rate limiting substrate yields biomass growth and product formation.

Since version 1.
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Reference: Henson, M. A. and D. E. Seborg. (1997.) Nonlinear
           Process Control, Prentice-Hall. pp. 203-204.
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See also:    RHSFermenter, MuFermenter, TimeGUI, Plot2D
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Model parameters
State
The control sampling period and the simulation integration time step
Number of sim steps
Plotting arrays
Run the simulation
Plot Results

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%   Copyright (c) 2013 Princeton Satellite Systems, Inc.
%   All rights reserved.
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Model parameters

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d.yXS   = 0.4;      % Cell-mass yield parameter (g/g)
d.beta  = 0.2;      % Yeild parameter (1/hr)
d.pM    = 50;       % Constant parameter (g/L)
d.kI    = 22;       % Constant parameter (g/L)
d.d     = 0.202;    % Dilution rate (1/hr)
d.alpha = 2.2;      % Yield parameter (g/g)
d.muM   = 0.48;     % Maximum specific growth rate (1/hr)
d.kM    = 1.2;      % Constant parameter (g/L)
d.sF    = 20;       % Feed substrate concentration (g/L)

State

[X;S;P] X = biomass concentration S = substrate concentration P = product concentration ---------------------------

x           = [6;5;19.14];
t           = 0;

The control sampling period and the simulation integration time step

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dT          = 1;

Number of sim steps

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nSim        = 100;
tEnd        = nSim*dT;

Plotting arrays

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tPlot      = zeros(1,nSim);
xPlot      = zeros(3,nSim);

Run the simulation

See RHSFermenter.m which gives a model of a constant volume reactor in which a single, rate limiting substrate promotes biomass growth and product formation. -------------------------------------------------------------------------

for k = 1:nSim
  x           = RK4( 'RHSFermenter', x, dT, t, d );
  t           = t + dT;
  tPlot(k)    = t;
  xPlot(:,k)  = x;
end

Plot Results

Open loop response is given. ----------------------------

Plot2D( tPlot, xPlot,'Time (hr)',['X';'S';'P'],'Fermenter States')

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