Section 8–3 / Design of PID Controllers with Frequency-Response Approach 579
MATLAB Program 8–3
num = [20 4];
den = [1 0.00000000001 1 0];
w = logspace(-2,1,101);
bode(num,den,w)
title('Bode Diagram of G(s) = 4(5s+1)/[s(s^2+1)]')
Frequency (rad/sec)
Bode Diagram of G(s) = 4(5s + 1)/[s(s^2 + 1)]
− 200
− 50
− 100
− 150
0
− 20
0
Phase (deg); Magnitude (dB)
60
20
40
10 −^210 −^1100101
Figure 8–15
Bode diagram of
G(s)=4(5s+1)/
CsAs^2 +1BD.
We need the phase margin of at least 50° and gain margin of 10 dB or more.
From the Bode diagram of Figure 8–14, we notice that the gain crossover frequency
is approximately v=1.8radsec. Let us assume the gain crossover frequency
of the compensated system to be somewhere between v=1andv=10radsec.
Noting that
we choose a=5.Then,(as+1)will contribute up to 90° phase lead in the high-
frequency region. MATLAB Program 8–3 produces the Bode diagram of
The resulting Bode diagram is shown in Figure 8–15.
4 ( 5 s+ 1 )
sAs^2 + 1 B
Gc(s)=
4 (as+ 1 )(bs+ 1 )
s
