Chapter 11
Introduction to MIMO Design
Xmath Interactive Control Design Module
11-2
ni.com
u
denotes the plant input or actuator signal, which is a vector of size
n
u
r
denotes the reference or command input signal, which is a vector of
size
n
y
e
denotes the error signal, which is a vector of size
n
y
d
act
denotes the actuator disturbance signal, which is a vector of size
n
u
P
denotes the plant transfer function, which is a matrix of size
n
y
×
n
u
C
denotes the controller transfer function, which is a matrix of size
n
y
×
n
u
Figure 11-1 shows standard feedback connections and signals used in
ICDM for MIMO design. All of the signals are vectors.
Figure 11-1.
Standard Feedback Connections and Signals for MIMO Design
Transfer Functions
In ICDM, the plant and controller transfer function are required to be
strictly proper, that is,
where
A
,
B
, and
C
are matrices stored in the system object corresponding
to the plant, and similarly for the controller. The plant order or plant
(McMillan) degree is the size of
A
; that is, the number of plant states.
Similarly, the size of
A
contr
is the controller order or controller degree.
In ICDM, the multivariable transfer function is required to be strictly
proper; that is, have zero feedthrough term
D
= 0. The controller is required
to be proper.
P
r
–
y
C
d
act
–
–
e
–
–
–
u
n
u
n
y
P s
( )
C sI A
–
(
)
1
–
B
=
C s
( )
C
contr
sI A
contr
–
(
)
1
–
B
contr
=
