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function KineticsEst1_int

% ¶¯Á¦Ñ§·½³ÌΪrA=dCA/dt=-k1*CA^2+k2*CB*CC
clear all;
clc
global CAm CBm CCm
t=[0 10 30 60 90 150 210 270 330];
CAm=[10 9 8 7 6 5 4 3 2];
CBm=[0 0.5 1.5 2 2.5 3 3.5 4 4.5]
CCm = [ÓÐÎÊÌ⣬²»ÁÐÁË];

% ·ÇÏßÐÔÄâºÏ
beta0=[0.0000053 10];
tspan = [0 10 30 60 90 150 210 270 330];
CA0 = 9.672;
CB0 = 0;
CC0 = 0;
[beta,resnorm,resid,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@OptObjFunc,beta0,[0 0],[],[],tspan,[CA0 CB0 CC0])
ci = nlparci(beta,resid,jacobian)

% ÄâºÏЧ¹ûͼ(ʵÑéÓëÄâºÏµÄ±È½Ï)
[t4plot CA4plot] = ode45(@KineticsEqs,[tspan(1)  tspan(end)],[CA0 CB0 CC0],[],beta);
plot(tspan,CAm,'bo',t4plot,CA4plot,'k-')
legend('Exp','Model')
xlabel('ʱ¼ät, min')
ylabel('Ũ¶ÈC_A, mol/L')

%²Ð²î¹ØÓÚÄâºÏÖµµÄ²Ð²îͼ
[t Y]=ode45(@KineticsEqs,tspan,CA0,[],beta);
Figure, plot(CAc,resid, '*')
xlabel('Ũ¶ÈÄâºÏÖµ(mol/L)'), ylabel('²Ð²îR(mol/L)'), refline(0,0)

% ²ÎÊý±æÊ¶½á¹û
fprintf('Estimated Parameters:\n'),
fprintf('\tk1 = %.4f ¡À %.4f\n',beta(1),ci(1,2)-beta(1))
fprintf('\tk2 = %.4f ¡À %.4f\n',beta(2),ci(2,2)-beta(2))
% ------------------------------------------------------------------
function f = OptObjFunc(beta,tspan,CA0,CAm)
global CAm CBm CCm
[t Y] = ode45(@KineticsEqs,tspan,CA0,[],beta);
if length(t)==length(tspan)
    f = Y - [CAm CBm CCm];
else
    f=100000;
end
% ------------------------------------------------------------------
function dy = KineticsEqs(t,Y,beta)    Õâ¸öµØ·½Ò»Ö±¿´²»¶®Àý×ÓΪʲôÕâô±à
CA=Y(1);
CB=Y(2);
CC=Y(3);
dCAdt = -beta(1)*CA^2 +beta(2)*CB*CC;            % k1= beta(1), k2= beta(2)
dCBdt = beta(1)*CA*CB-beta(2)*CC;
dCCdt = beta(2)*CC;
dy=[dCAdt;dCBdt;dCCdt];
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[ Last edited by jesschen on 2009-6-19 at 18:19 ]
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