% Example ID2.2 Estimating parameters of a first order model
% 
% Copyright 1996, Babu Joseph, Washington University in St. Louis
% clc;echo on;
% This program computes the parameters using a linear least squares approach
%
% the data give is as follows
% ( It is  step response of a first order process with gain 1 and tau=5)
%
% 	Input	Output
%	1	0
%	1	.18
%	1	.33
%	1 	.45
%	1	.55
%	1	.67
%
% First set up the matrices
A=[	0 	1
	-.181	1
	-.33	1
	-.45	1
	-.67	1];
%
b=[	.18
	.33
	.45
	.55
	.67];
%
% The model is given by
x=A\b;
% The model coefficients are
a1=x(1)
b1=x(2)
% The error is the model is given by
Sum_of_Squares=norm(b-A*x)^2