Modern Control Engineering

658 Chapter 9 / Control Systems Analysis in State Space

For the case where the system has multiple inputs and multiple outputs, see

Example9–4.

EXAMPLE 9–3 Obtain the transfer function of the system defined by the following state-space equations:

MATLAB Program 9–2 will produce the transfer function for the given system. The transfer

function obtained is given by

Y(s)

U(s)

=

25.04s+5.008

s^3 +5.0325s^2 +25.1026s+5.008

y =[1 0 0]C

x 1

x 2

x 3

S

C

x

1

x# 2

x# 3

S = C

0

0

- 5.008

1

0

- 25.1026

0

1

- 5.03247

SC

x 1

x 2

x 3

S +C

0

25.04

- 121.005

Su

MATLAB Program 9–2

A = [0 1 0;0 0 1;-5.008 -25.1026 -5.03247];

B = [0;25.04; -121.005];

C = [1 0 0];

D = [0];

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

num =

0 -0.0000 25.0400 5.0080

den =

1.0000 5.0325 25.1026 5.0080

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

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

num =

0 -0.0000 25.0400 5.0080

den =

1.0000 5.0325 25.1026 5.0080

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