bioreactcstf.m

Matlab在化学工程中的应用

function BioReactCSTF
% 生化反应器稳态模拟和动态模拟
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2002/04/22 $

clear all
clc
global D mumax Y km xf2 k1

% parameter values
D = 0.3;
mumax = 0.53;
Y = 0.4;
km = 0.12;
xf2 = 4.0;
k1 = 0.4545;

% 求解稳态方程
x0 = [1 1];
x = fsolve(@BioReactorModel_SS,x0)
fprintf('\n\t稳态时生物量和底物的浓度分别是%.3f和%.3f',x(1),x(2))

% 求解动态方程
tspan = [0 30];
x0 = [1 1];
[t,x] = ode45(@BioReactorModel_Dyn,tspan, x0);

% 浓度动态变化图
plot(t,x(:,1),'b-',t,x(:,2),'k--')
xlabel('time (s)')
ylabel('x')
legend('biomass','substrate')


% ------------------------------------------------------------------
function f = BioReactorModel_SS(x)
% Steady-state biochemical reactor model
%
% 变量variables：
% x(1) = biomass
% x(2) = substrate
% 参数parameters：
% D = dilution rate (F/V, time^-1)
% Y = yield (biomass/substrate)
% mu = specific growth rate
% mumax = parameter
% km = parameter
% k1 = parameter
% xf2 = substrate feed concentration

global D mumax Y km xf2 k1
% Substrate Inhibition expression for specific growth rate
mu = mumax*x(2)/(km+x(2)+k1*x(2)*x(2));

% dynamic equations
f = [(mu-D)*x(1); D*(xf2 -x(2)) - mu*x(1)/Y ];

% ------------------------------------------------------------------
function dxdt = BioReactorModel_Dyn(t,x)
% Dynamic model of biochemical reactor
%
% 状态变量state variables：
% x(1) = biomass
% x(2) = substrate
% 参数Parameters：
% D = dilution rate (F/V, time^-1)
% Y = yield (biomass/substrate)
% mu = specific growth rate
% mumax = parameter
% km = parameter
% k1 = parameter
% xf2 = substrate feed concentration

global D mumax Y km xf2 k1

% Substrate Inhibition expression for specific growth rate
mu = mumax*x(2)/(km+x(2)+k1*x(2)*x(2));

% dynamic equations
dxdt = [(mu-D)*x(1); D*(xf2 -x(2)) - mu*x(1)/Y ];