National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 18)

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