# Finding Zero-Pole Gain Form Of Tranfer Functions From State-Space Model In MatLab®

There are various kinds of commands in Matlab® to convert the transfer functions into another form. One of these commands is the ‘ss2zp()’ command. You can calculate the zero-pole gain form of transfer functions with the state-space forms of them with the ‘ss2zp()’ command in Matlab®.

Here we explain how to do this kind of thing in Matlab® with a very basic example below. Try the codes below in your Matlab® software.

## How To Use The ‘ss2zp()’ Command In MatLab®?

For example, you have a state-space model of a transfer function like this;

[x1; x2] = [0 1; -3 -4]*[x1(t); x2(t)] + [0; 1]*u(t);

y(t) = [10 0][x1(t), x2(t)] + 0*u(t);

You need to properly define this state-space form to find the zero-pole gain form of the transfer function.

``````>> x = [0 1; -3 -4];
y = [0;1];
z = [10 0];
t = 0;
[a, b, c] = ss2zp(x,y,z,t)

a =

0×1 empty double column vector

b =

-1
-3

c =

10

>> ``````

As you see in the example above, we defined all the vectors and matrices in the state-space model respectively. ‘x’, ‘y’, ‘z’, and ‘t’ are these matrices and vectors respectively. We typed these vectors and matrices inside the parentheses of the ‘ss2zp()’ command respectively.

And we assigned the ‘ss2zp()’ command to three result variables which are ‘a’, ‘b’, and ‘c’.

As you see in the result at the command window, ‘c’ is the numerator of the zero-pole gain form transfer function and ‘b’ includes the roots of the denominator’s roots. The transfer function is like this;

TF = 10/((s+1)(s+3));

## Conclusion

As you see above, it is very simple to calculate the zero-pole gain form of transfer fuınctions from the state-space model it in Matlab® with the ‘ss2zp()’ command.

Do not forget to leave your comments and questions below about the use of the ‘ss2zp()’ command in Matlab® below.

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