
Chapter 6 Pole Place Synthesis
Xmath Interactive Control Design Module 6-4 ni.com
We can write this polynomial equation as follows:
These 2n linear equations are solved to find the 2n controller parameters
x1, ...,xn and y1,...,y
n.
Integral Action ModeThe degree (number of poles) of the controller is fixed and equal to n+1,
so there are a total of 2n+1 closed-loop poles. In this case, the 2n+1
degrees of freedom in the closed-loop poles, along with the constraint that
the controller must have at least one pole at s=0, exactly determine the
controller transfer function. In fact, the closed-loop poles give a complete
parameterization of all controllers with at least one pole at s=0, and n or
fewer other poles.
Equations similar to those shown in the Normal Mode section are used to
determine the controller parameters given the closed-loop pole locations.
b00…0
b1b0…0
b2b1…0
……
bn1–bn2–b0
bnbn1–b1
0bnb2
00 b3
……
00…bn
x1
·
·
·
xn
10…0
a11…0
a2a1…0
……
an1–an2–1
anan1–a1
0ana2
00 a3
……
00…an
+
y1
·
·
·
yn
+
a1
…
an
0
…
0
α1
…
α2n
=+