Hi Peter,
I'm back again. I have been working away at control theory and am happy with my understanding.
I used Matlab to convert my laplace transform to a z transform.
0.00375 X= --------------------- (s+0.15)*(s+0.25)Which converts it to
0.000438*z + 0.000410 -------------------------- z^2-1.81*z+0.818then the difference equation is got by dividing the num and dem them by the highest order z
0.000438 + 0.000410z^-1-----------------------------
1-1.81*z^-1+0.818*z^-2therefore
x(n)-1.81*x(n-1)+0.818*x(n-2) = 0.000438*u(n)+0.0004104*u(n-1)
therefore
x(n) = 1.81*x(n-1)-0.818*x(n-2) +0.000438*u(n)+0.0004104*u(n-1)
Which is a little different to your result of
x(n) = 1.81*x(n-1)-.819*x(n-2)+.0004387*u(n-1)+.0004104*x(n-2)
Have I got lost somewhere again?