The system is given by:
G(s) = 1/((s+0.1)(s+3))
I need to convert it to G(z), it's discrete form.
The sample time T is 0.1 seconds.
To convert it they give
G(z) = (1-z^(-1))*Z-transform[G(s)/s]
The Attempt at a Solution
Obviously I started with G(s)/s. That gives you another s term at the bottom.
I then broke it up into partial fractions so that I had.
(10/(3s)) + (0.1145/(s+3)) + (3.45/(s+0.1))
Then I used the table in my book to convert all the s to z values using the following two formulas.
1/s = z/(z-1)
1/(s+a) = z/(z-e^(-aT))
I then multiplied by the (1-z^(-1)) term for my G(z) answer.
When I was done I had a second order polynomial at the top and at the bottom. And all my coefficients were wrong. I did this same question using the c2d (continuous to discrete) function in matlab, and it gave a different answer.
Matlab and my textbook both have the same answer, which is:
z^2 -1.731z + 0.7334