kineticsest1_int.m

《实用化工计算机模拟：MATLAB在化学工程中的应用 》这本书光盘里的程序~

function KineticsEst1_int
% 动力学参数辨识: 用积分法进行反应速率分析得到速率常数k和反应级数n
% Analysis of kinetic rate data by using the integral method
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center,
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2003/07/27 $
%
% Reaction of the type -- rate = kCA^order
% order - reaction order
% rate -- reaction rate vector
% CA -- concentration vector for reactant A
% T -- vector of reaction time
% N -- number of data points
% k- reacion rate constant

clear all
clc

global CAm
t = [0 20  40  60  120  180  300];
CAm = [10  8  6  5  3  2  1]';

% 非线性拟合
beta0 = [0.0053 1.39];
tspan = [0 20  40  60  120  180  300];
CA0 = 10;
[beta,resnorm,resid,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@OptObjFunc,beta0,[],[],[],tspan,CA0,CAm)
ci = nlparci(beta,resid,jacobian)

% 拟合效果图(实验与拟合的比较)
[t4plot CA4plot] = ode45(@KineticsEqs,[tspan(1)  tspan(end)],CA0,[],beta);
plot(t,CAm,'bo',t4plot,CA4plot,'k-')
legend('Exp','Model')
xlabel('时间t, s')
ylabel('浓度C_A, mol/L')

% 残差关于拟合值的残差图
[t CAc] = ode45(@KineticsEqs,tspan,CA0,[],beta);
figure
plot(CAc,resid,'*')
xlabel('浓度拟合值（mol/L）')
ylabel('残差R (mol/L)')
refline(0,0)

% 参数辨识结果
fprintf('Estimated Parameters:\n')
fprintf('\tk = %.4f ± %.4f\n',beta(1),ci(1,2)-beta(1))
fprintf('\tn = %.2f ± %.2f\n',beta(2),ci(2,2)-beta(2))

% ------------------------------------------------------------------
function f = OptObjFunc(beta,tspan,CA0,CAm)
[t CAc] = ode45(@KineticsEqs,tspan,CA0,[],beta);
f = CAc - CAm;

% ------------------------------------------------------------------
function dCAdt = KineticsEqs(t,CA,beta)
dCAdt = -beta(1)*CA^beta(2);            % k = beta(1), n = beta(2)