% Function file for example est8.2
% This evaluates the residuals in the nonlinear equations
% for nonlinear least squares
%
function f=fun(x,xm) ;
f=zeros(13,1);
% EXtract variables from vector x
t1=x(1);   % Temperature of tank 1
t2=x(2);   % Temperature of tank 2
f0=x(3);   % Flow into tank 1
f1=x(4);   % Flow into tank 2
f2=x(5);   % Flow out of tank 2
c0=x(6);   % Concentration of reactant in feed
v1=x(7);   % Volume of tank 1
v2=x(8);   % Volume of tank 2
c1=x(9);   % Concentration of reactant in tank 1
c2=x(10);  % Concentration of reactant in tank 2
%
% Enter measuements from plant
t1m=xm(1);   % Measured value of temperature in tank 1
t2m=xm(2);   % Measured value of temperature in tank 2
f0m=xm(3);   % Measured value of flow into tank 1
f1m=xm(4);   % Measured value of flow into tank 2
f2m=xm(5) ;  % Measured value of flow out of tank 2
c0m=xm(6);   % Measured value of feed concentration
v1m=xm(7);   % Measured value of volume in tank 1
v2m=xm(8);   % Measured value of volume in tank 2
c1m=xm(9);   % Measured value of concentration in tank 1
%
%
k1=2400*(exp(-4000/t1)); % Rate of reaction in tank 1
k2=2400*(exp(-4000/t2)); % Rate of reaction in tank 2
%
% Next calculate the residuals for least squares
%
f(1)=(f0-f1);                  % Residual in total balance tank 1
f(2)=(f1-f2);                  % Residual in toatl mass balance tank 2
f(3)=f0*c0-f1*c1-k1*c1^2*v1; % Residual in comp balance tank 1
f(4)=f1*c1-f2*c2-k2*c2^2*v2; % Residual in comp balance tank 2
%
% These are residuals in  measurement equations
%
f(5)=(t1-t1m);
f(6)=(t2-t2m);
f(7)=f0-f0m;
f(8)=f1-f1m;
f(9)=f2-f2m;
f(10)=c0-c0m;
f(11)=c1-c1m;
f(12)=v1-v1m;
f(13)=v2-v2m;