Chapter 2
Introduction to SISO Design
©
National Instruments Corporation
2-3
Xmath Interactive Control Design Module
•
The closed-loop transfer function
T
is given by
T
=
PC
/(1 +
PC
).
T
is
the transfer function from
r
to
y
.
•
The characteristic polynomial of the system is defined as
X
=
n
c
n
p
+
d
c
d
p
. Its degree is equal to the order of the plant
plus the order of the controller.
•
The closed-loop poles are the zeros of the characteristic polynomial.
This definition avoids any problem with unstable pole-zero
cancellations between the plant and controller. The closed-loop zeros
are the zeros of
n
c
n
p
.
•
The output response to a unit step input (or just, the step response),
is the step response of the transfer function
T
; that is, the response of
y
when the command input
r
is a unit step.
•
The actuator step response is the step response of the transfer function
C
/(1 +
PC
), which is the transfer function from
r
to
u
.
•
Integral action means that the controller
C
has a pole at
s
= 0. Roughly
speaking, this means that the loop gain is very large at low frequencies.
Integral action implies that
S
(0) = 0, so if
r
is constant, the error
e
converges to zero, that is, the output
y
(
t
) approaches
r
as
t
→ ∞
.
Overview of ICDM
This section provides a broad overview of the architecture, concepts, and
major functions of ICDM, restricting our discussion to the case of SISO
plants and controllers. This section also provides a summary of how ICDM
works and what it does.
ICDM Windows
ICDM supports many windows that serve a variety of functions. The most
important windows are:
•
ICDM Main window
•
PID Synthesis window
•
Root Locus Synthesis window
•
Pole Place Synthesis window
•
LQG Synthesis
window
•
H
∞
Synthesis
window
•
History window
•
Alternate Plant window