Modern Control Engineering

426 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

Obtaining Bode Diagrams of Systems Defined in State Space. Consider the

system defined by

where state vector (n-vector)

output vector (m-vector)

control vector (r-vector)

state matrix (n*nmatrix)

control matrix (n*rmatrix)

output matrix (m*nmatrix)

direct transmission matrix (m*rmatrix)

A Bode diagram for this system may be obtained by entering the command

bode(A,B,C,D)

or others listed earlier in this section.

The command bode(A,B,C,D)produces a series of Bode plots, one for each input of

the system, with the frequency range automatically determined. (More points are used

when the response is changing rapidly.)

The command bode(A,B,C,D,iu), where iuis the ith input of the system, produces

the Bode diagrams from the input iu to all the outputs Ay 1 ,y 2 ,p,ymBof the system,

with a frequency range automatically determined. (The scalar iuis an index into the in-

puts of the system and specifies which input is to be used for plotting Bode diagrams).

If the control vector uhas three inputs such that

theniumust be set to either 1, 2, or 3.

If the system has only one input u, then either of the following commands may be

used:

bode(A,B,C,D)

or

bode(A,B,C,D,1)

EXAMPLE 7–7 Consider the following system:

This system has one input uand one output y. By using the command

bode(A,B,C,D)

y =[1 0]B

x 1

x 2

R

B

x

1

x# 2

R= B

0

- 25

1

- 4

RB

x 1

x 2

R+ B

0

25

R u

u= C

u 1

u 2

u 3

S

D=

C=

B=

A=

u=

y=

x=

y=Cx+Du

x

=Ax+Bu

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