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 Mode
The 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.
b000
b1b00
b2b10
……
bn1bn2b0
bnbn1b1
0bnb2
00 b3
……
00bn
x1
·
·
·
xn
100
a110
a2a10
……
an1an21
anan1a1
0ana2
00 a3
……
00an
+
y1
·
·
·
yn
+
a1
an
0
0
α1
α2n
=+