Modern Control Engineering

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Section 5–5 / Transient-Response Analysis with MATLAB 211

MATLAB Program 5–17

t = 0:0.05:10;

A = [0 1 0;0 0 1;-10 -17 -8];

B = [0;0;0];

C = [1 0 0];

D = [0];

y = initial(A,B,C,D,[2;1;0.5],t);

plot(t,y)

grid

title('Response to Initial Condition')

xlabel('t (sec)')

ylabel('Output y')

Output

y

t (sec)

Response to Initial Condition

0.5

1

1.5

2

2.5

0

012345678910

Figure 5–34
Responsey(t)to
initial condition.

By defining the state variables as

we obtain the following state-space representation for the system:

A possible MATLAB program to obtain the response y(t)is given in MATLAB Program 5–17.

The resulting response curve is shown in Figure 5–34.

y=[ 1 0 0 ]C

x 1

x 2

x 3

S

C

x# 1

x# 2

x# 3

S = C

0

0

- 10

1

0

- 17

0

1

- 8

SC

x 1

x 2

x 3

S, C

x 1 ( 0 )

x 2 ( 0 )

x 3 ( 0 )

S =C

2

1

0.5

S

x 3 =y$

x 2 =y#

x 1 =y