National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 88)

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
=