# Control Systems Question. Need to convert a plant from G(s) to G(z) (discrete).

• xiN

## Homework Statement

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.

## Homework Equations

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:

0.00452z +0.004076
---------------------
z^2 -1.731z + 0.7334

I don't know if bumps are allowed, but any help with this problem would be much appreciated. I'm really stumped.