Modern Control Engineering

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Section 5–5 / Transient-Response Analysis with MATLAB 209

Response to Initial Condition

t Sec

0 0.5 1 1.5 2 2.5 3

State Variables

x^1

and

x^2

3

− 2

− 3

1

− 1

0

2

x 1

Figure 5–32 x^2
Response of system
in Example 5–9 to
initial condition.

For an illustrative example of how to use Equations (5–58) and (5–60) to find the re-

sponse to the initial condition, see Problem A–5–16.

Obtaining Response to Initial Condition by Use of Command Initial. If the

system is given in the state-space form, then the following command

initial(A,B,C,D,[initial condition],t)

will produce the response to the initial condition.

Suppose that we have the system defined by

where

x 0 = B

2

1

R

A= B

0

- 10

1

- 5

R, B= B

0

0

R, C=[0 0], D= 0

y=Cx+Du

x

=Ax+Bu, x(0)=x 0