MATLAB Closing a Feedback Loop (2.010)

MATLAB Closing a Feedback Loop

MATLAB has many built-in functions to help analyze controls systems:

bode, step, pzmap plotting functions
tf, ss, zpk for creating systems in various ways
tfdata, ssdata, zpddata getting from one system representation to another
margin for getting both Gain and Phase margin (and crossover freq's)

...so it's not suprising you can ALSO create a feedback system automatically:

using feedback.

Obviously, relying too much on MATLAB might get you into trouble once a quiz comes along...

But here's an example MATLAB session using this command.
'Hsys', the system in the RETURN path of the feedback loop, can be any system -- including just a constant (gain value) like '1':
Note the included '0' in the denominator polynomial to get the intended orders for the s's...

ť Gsys=tf([1e-5 1e3 1e9],[2e-2 1e3 5e4 0])

Transfer function:
1e-005 s^2 + 1000 s + 1e009
-----------------------------
0.02 s^3 + 1000 s^2 + 50000 s

ť Hsys=1

Hsys =

1

ť Tsys=feedback(Gsys,Hsys)

Transfer function:
1e-005 s^2 + 1000 s + 1e009
-------------------------------------
0.02 s^3 + 1000 s^2 + 51000 s + 1e009

ť subplot(121); bode(Gsys)
ť subplot(122); bode(Tsys)

Open-loop system Gsys (left) ..... Closed-loop system Tsys (right)

gonzo@mit.edu

2.010 Tutorial #3, 29-Sep-00