Modern Control Engineering

42 Chapter 2 / Mathematical Modeling of Control Systems

EXAMPLE 2–4 Obtain the transfer function of the system defined by the following state-space equations:

MATLAB Program 2-3 will produce the transfer function for the given system. The transfer func-

tion obtained is given by

Y(s)

U(s)

=

25 s+ 5

s^3 + 5 s^2 + 25 s+ 5

y =[1 0 0]C

x 1

x 2

x 3

S

C

x# 1

x

2

x# 3

S =C

0

0

- 5

1

0

- 25

0

1

- 5

SC

x 1

x 2

x 3

S + C

0

25

- 120

Su

MATLAB Program 2–3

A = [0 1 0; 0 0 1; -5 -25 -5];

B = [0; 25; -120];

C = [1 0 0];

D = [0];

[num,den] = ss2tf(A,B,C,D)

num =

0 0.0000 25.0000 5.0000

den

1.0000 5.0000 25.0000 5.0000

% The same result can be obtained by entering the following command:

[num,den] = ss2tf(A,B,C,D,1)

num =

0 0.0000 25.0000 5.0000

den =

1.0000 5.0000 25.0000 5.0000

or

[num,den] = ss2tf(A,B,C,D,1)

may be used. For the case where the system has multiple inputs and multiple outputs,

see Problem A–2–12.

Openmirrors.com