Section 2–6 / Transformation of Mathematical Models with MATLAB 39or
(2–37)
(2–38)
where
In this state-space representation, matrices AandCare exactly the same as those for
the system of Equation (2–30). The derivatives on the right-hand side of Equation (2–33)
affect only the elements of the Bmatrix.
Note that the state-space representation for the transfer function
is given also by Equations (2–37) and (2–38).
There are many ways to obtain state-space representations of systems. Methods for
obtaining canonical representations of systems in state space (such as controllable canon-
ical form, observable canonical form, diagonal canonical form, and Jordan canonical
form) are presented in Chapter 9.
MATLAB can also be used to obtain state-space representations of systems from
transfer-function representations, and vice versa. This subject is presented in Section 2–6.
2–6 TRANSFORMATION OF MATHEMATICAL MODELS WITH MATLAB
MATLAB is quite useful to transform the system model from transfer function to state
space, and vice versa. We shall begin our discussion with transformation from transfer
function to state space.
Y(s)
U(s)
=
b 0 sn+b 1 sn-^1 +p+bn- 1 s+bn
sn+a 1 sn-^1 +p+an- 1 s+an
B= G
b 1
b 2
bn- 1
bn
W, C=[1 0 p 0], D=b 0 =b 0
x= G
x 1
x 2
xn- 1
xn
W, A=G
0 0 0
- an
1 0 0
- an- 1
0 1 0
- an- 2
p
p
p
p
0 0 1
- a 1
W