Transfer Functions - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Chapter 11 Introduction to MIMO Design
–
r
–

Transfer Functions

Xmath Interactive Control Design Module
u denotes the plant input or actuator signal, which is a vector of size n
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
d denotes the actuator disturbance signal, which is a vector of size n
act
P denotes the plant transfer function, which is a matrix of size n
C denotes the controller transfer function, which is a matrix of size n
Figure 11-1 shows standard feedback connections and signals used in
ICDM for MIMO design. All of the signals are vectors.
e u
C
–
Figure 11-1. Standard Feedback Connections and Signals for MIMO Design
In ICDM, the plant and controller transfer function are required to be
strictly proper, that is,
P s C sI A
=
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
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.
d
act
–
P
n
u
1 –
B C s
–
is the controller order or controller degree.
contr
11-2
y
y
n
y
1 –
C sI A
= –
contr contr
u
u
n
y u
n
y u
B
contr
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