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Chapter 6
Pole Place Synthesis
Integral Action Mode
Xmath Interactive Control Design Module
We can write this polynomial equation as follows:
b
0
0
b
b
1
0
b
b
2
1
b
b
n 1
n 2
–
–
b
b
n
n 1
–
0
b
n
0
0
0
0
These 2n linear equations are solved to find the 2n controller parameters
x
, ..., x
and y
, ..., y
1
n
1
n
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
determine the controller parameters given the closed-loop pole locations.
0
1
a
0
1
a
0
x
2
1
·
a
b
n 1
0
–
·
+
a
b
n
1
·
0
b
2
x
n
0
b
3
0
b
n
a
1
a
n
+
=
0
2n
0
.
Normal Mode
6-4
0
0
1
0
a
0
1
y
1
·
a
1
n 2
–
·
a
a
n 1
1
–
·
a
a
n
2
y
0
a
n
3
0
a
n
1
section are used to
+
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