Modern Control Engineering

784 Chapter 10 / Control Systems Design in State Space

Next, we shall check the frequency-response characteristics. The Bode diagram of the

open-loop system just designed is shown in Figure 10–22. The phase margin is about 40°

and the gain margin is ±qdB. The Bode diagram of the closed-loop system is shown in

Figure 10–23. The bandwidth of the system is approximately 3.8 rad/sec.

x^1

02468

t (sec)

02468

t (sec)

02468

t (sec)

02468

t (sec)

02468

t (sec)

−0.5

0

0.5

1

e^2

− 3

− 2

− 1

0

x^2

−1.5

−0.5

− 1

0

0.5

x^3

− 5

5

0

10

15

e^1

0

1

0.5

1.5

Figure 10–21

Response to the

given initial

condition;x 1 (0)=1,

x 2 (0)=0, x 3 (0)=0,

e 1 (0)=1, e 2 (0)=0.

Frequency (rad/sec)

Bode Diagram of System 2 — Open Loop

− 200

− 150

− 100

− 50

− 100

Phase (deg); Magnitude (dB)

− 50

0

50

100

10 −^310 −^210 −^1100101102

Figure 10–22

Bode diagram for the

open-loop transfer

function of System 2.

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