EE 350
LINEAR SYSTEMS ANALYSIS
Fall 2007
Laboratory #4: Feedback Control
The objectives of the fourth laboratory are as follows.
•
Introduce MATLAB commands relevant to Laplace transform analysis.
•
Show, by experiment, that a closedloop system is more robust at rejecting disturbances than an
openloop system.
MATLAB commands Relevant to Laplace Transform Analysis
1. The MATLAB command
step
calculates the step response of a LTI system. As an example, consider
a secondorder system with unity DC gain,
ζ
=0
.
2,
ω
n
= 1 [rad/sec]:
%
Describe the system in terms of the transfer function
Kdc = 1;
z = 0.2;
wn = 1;
num = [Kdc*wn^2];
den = [1,2*z*wn,wn^2];
% Find the step response (MATLAB automatically plots the response)
step(num,den)
2. When it is necessary to know the response of a system to a more general input, use the
lsim
command.
Simulate the the response of the previous system to the input
u
(
t

10)

u
(
t

40):
% Construct the input f(t)
t = linspace(0,100);
f = [0*ones(1,10),ones(1,30),0*ones(1,60)];
lsim(num,den,f,t)
%plot f on top of response
hold
plot(t,f,’r:’)
3. Another command of interest is
pzmap
, which constructs a polezero map for a given transfer
function:
%
Describe the system in terms of the transfer function
num = [1,3];
den = [1,2,2];
pzmap(num,den)
1