% Example est ch13ex13.m
% program to illustrate nonlinear model based estimatin
% programmed by B. Joseph Washington University April 1993
%
% This program requires the nonlinear least squares program from the
% Optimization Toolbox
% It also requires a function file called est82f.m which
% evaluates the errors to be minimized
%
% First let us provide values for the measurements
% Variable definitions
x=zeros(10,1);xm=zeros(9,1);
% Enter initial guesses for the variables to be estimated
x(1)=357 ;  % x(1)=t1 temperature in first tank
x(2)=460 ;  % x(2)=t2 temperature in second tank
x(3)=20 ;  % x(3)=f0 flow into first tank
x(4)=20;   % x(4)=f1 flow into second tank
x(5)=20 ;  % x(5)=f2 flow out of second tank
x(6)=60  ; % x(6)=c0 concentration of feed into first tank
x(7)=20;   % x(7)=v1 volume of first tank
x(8)=10 ;  % x(8)=v2 volume of second tank
x(9)=30 ;  % x(9)=c1 concentration in first tank
x(10)=10;   % x(10)=c2 concentration in second tank
% Now enter the measurements on the process
% These are stored in xm and passed to the function that
% evaluated the residuals
xm(1)=350.; % measured value of t1  deg R
xm(2)=450 ; % measured value of t2  deg R
xm(3)=20.5; % measured value of f0  cuft/hr
xm(4)=20.;  % measured value of f1  cuft/hr
xm(5)=20.1; % measured value of f2  cuft/hr
xm(6)=60.1; % measured value of c0  lbmol/cuft
xm(7)=20.5; % measured value of v1 cuft
xm(8)=10.1; % measured value of v2 cuft
xm(9)=30.1; % measured value of c1 lbmol/cuft
options=[];grad=[];% We are not going to use these options hence set to null
% The following call solves the nonlinear least squares problem
% The call requires the Optimization Toolbox
xr=leastsq('ch13ex13a',x,options,grad,xm);
f=ch13ex13a(x,xm);
fr=ch13ex13a(xr,xm);
[x xr]
pause % hit any key
[f fr]
norm(x-xr)^2