Modern Control Engineering

Since the static velocity error constant Kvis specified as 4 sec–1, we have

Thus

Next, we plot a Bode diagram of

MATLAB Program 8–2 produces a Bode diagram of G(s). The resulting Bode diagram

is shown in Figure 8–14.

G(s)=

4

sAs^2 + 1 B

Gc(s)=

4 (as+ 1 )(bs+ 1 )

s

=K= 4

Kv=lim

sS 0

sGc(s)

1

s^2 + 1

=lim

sS 0

s

K(as+ 1 )(bs+ 1 )

s

1

s^2 + 1

578 Chapter 8 / PID Controllers and Modified PID Controllers

Figure 8–13

Control system.

Gc(s)^1

s^2 + 1

+–

MATLAB Program 8–2

num = [4];

den = [1 0.00000000001 1 0];

w = logspace(-1,1,200);

bode(num,den,w)

title('Bode Diagram of 4/[s(s^2+1)]')

Frequency (rad/sec)

Bode Diagram of 4/[s(s^2 + 1)]

− 300

− 100

− 50

− 150

− 200

− 250

0

− 50

0

Phase (deg); Magnitude (dB)

50

10 −^1100101

Figure 8–14

Bode diagram of

4/CsAs^2 +1BD.

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