Question 2.9.2: Impulse Response of Second-Order Models In Example 2.6.4 we ...
Impulse Response of Second-Order Models
In Example 2.6.4 we obtained the response of the following model to a unit impulse:
\frac{X(s)}{F(s)}=\frac{1}{2s^2+14s+20}
Our analysis showed that if x(0−) = ẋ(0−) = 0, then x(0+) = 0 and ẋ(0+) = 1/2. Use the impulse function to verify these results.
The session is shown here.
≫sys1 = tf(1,[2,14,20]);
≫impulse(sys1)
The plot is shown in Figure 2.9.5. From it we see that x(0+) = 0 and that ẋ(0+) is positive as predicted. We are unable to determine the exact value of ẋ(0+) from this plot, so we multiply the transfer function by s to obtain the transfer function for v = ẋ.
\frac{X(s)}{F(s)}=\frac{1}{2s^2+14s+20}
We now use the impulse function on this transfer function.
≫sys2 = tf([1, 0],[2, 14, 20]);
≫impulse(sys2)
The plot is shown in Figure 2.9.6. From it we see that ẋ(0+) = 0.5 as predicted.
