Consider the transfer functions Hs 14s2 2s 1 Dz 14z2 2z

Consider the transfer functions H(s) = 1/4s^2 + 2s + 1 D(z) = 1/4z^2 + 2z + 1 Determine their Tustin and FE equivalents for T = 1 (DT and CT respectively).

Solution

We can find the Tustin equivalents using matlab as follows:

>> H=tf(1, [4 2 1])

H =

1
---------------
4 s^2 + 2 s + 1

Continuous-time transfer function.

>> Hd=c2d(H, 1, \'tustin\')

Hd =

0.04762 z^2 + 0.09524 z + 0.04762
---------------------------------
z^2 - 1.429 z + 0.619

Sample time: 1 seconds
Discrete-time transfer function.

(2) Tustin equivalent of DT function:

>> HD=tf(1, [4 2 1], 1)

HD =

1
---------------
4 z^2 + 2 z + 1

Sample time: 1 seconds
Discrete-time transfer function.

>> HC=d2c(HD,\'tustin\')

HC =

0.3333 s^2 - 1.333 s + 1.333
----------------------------
s^2 + 4 s + 9.333

Continuous-time transfer function.