Modern Control Engineering

Example Problems and Solutions 623

Thus,K= 40. Hence

Next, we plot a Bode diagram of

MATLAB Program 8–10 produces a Bode diagram of G(s)as shown in Figure 8–53.

G(s)=

40 (s+0.1)

s(s^2 + 1 )

Gc(s)=

40

s

Gˆc(s)

We need the phase margin of 50° and gain margin of 10 dB or more. Let us choose to be

Then Gc(s)will contribute up to 90° phase lead in the high-frequency region. By simple MATLAB

trials, we find that a= 0.1526 gives the phase margin of 50° and gain margin of +qdB.

Gˆc(s)=as+ 1 (a 70 )

Gˆc(s)

MATLAB Program 8–10

% Bode Diagram

num = [40 4];

den = [1 0.000000001 1 0];

bode(num,den)

title('Bode Diagram of G(s) = 40(s+0.1)/[s(s^2+1)]')

Figure 8–53
Bode diagram of
G(s)=
40 (s+0.1)/[s(s^2 +1)]. Frequency (rad/sec)

Bode Diagram of G(s) = 40(s + 0.1)/[s(s^2 + 1)]

−2 00

− 50

− 100

−1 50

0

− 100

Phase (deg); Magnitude (dB)

0

300

200

100

10 −^310 −^210 −^1100101