Type 1 Systems Examples
Let's say that we have a system that looks like this:
where G(s) is:
1
-----------------
s (s + 2)(s + 3)
Let's look at the closed-loop response for this system when we use different inputs:
Step Input
num = 1;
den = conv([1 2],[1 3]);
den = conv(den,[1 0]);
[clnum,clden] = cloop(num,den);
step(clnum,clden)
Our steady-state error is zero.
Ramp Input
num = 1;
den = conv([1 2],[1 3]);
den = conv(den,[1 0]);
[clnum,clden] = cloop(num,den);
t = 0:0.1:100;
u = t;
[y,x] = lsim(clnum,clden,u,t);
plot(t,y,t,u)
xlabel('Time(secs)')
ylabel('Amplitude')
title('Input-purple, Output-yellow')
Our steady-state error is a constant.
Parabolic Input
num = 1;
den = conv([1 2],[1 3]);
den = conv(den,[1 0]);
[clnum,clden] = cloop(num,den);
t = 0:0.1:150;
u = 0.5*t.*t;
[y,x] = lsim(clnum,clden,u,t);
plot(t,y,t,u)
xlabel('Time(secs)')
ylabel('Amplitude')
title('Input-purple, Output-yellow')
Our steady-state error is infinity (the error continually increases as time goes to infinity).
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8/28/96 LJO
