Type 0 Systems Examples

Let's say that we have a system that looks like this:

where G(s) is:

```1
---------------
(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]);
sys = tf(num,den);
sys_cl = feedback(sys,1);
[y,t] = step(sys_cl);
u = ones(size(t));
plot(t,y,'y',t,u,'g')
axis([0,3,0,1.1])
```

Our steady-state error is a constant.

## Ramp Input

```num = 1;
den = conv([1 2],[1 3]);
sys = tf(num,den);
sys_cl = feedback(sys,1);
t = 0:0.1:200;
u = t;
[y,t,x] = lsim(sys_cl,u,t);
plot(t,y,'y',t,u,'m')
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).

## Parabolic Input

```num = 1;
den = conv([1 2],[1 3]);
sys = tf(num,den);
sys_cl = feedback(sys,1);
t = 0:0.1:200;
u = 0.5*t.*t;
[y,t,x] = lsim(sys_cl,u,t);
plot(t,y,'y',t,u,'m')
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).