Normal Mode - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Normal Mode

© National Instruments Corporation
where
d
p
Notice that the order of the plant is n, and allow the possibility that the plant
transfer function is not strictly proper; that is, the plant can have as many
zeros as poles.
In normal mode, the order (number of poles) of the controller is fixed and
equal to n (the order of the plant), so there are a total of 2n closed-loop
poles. In this case, the 2n degrees of freedom in the closed-loop poles
exactly determine the controller transfer function, which also has 2n
degrees of freedom.
In normal mode, the controller transfer function has order n and is strictly
proper:
where
d
c
n
Therefore, the closed-loop characteristic polynomial has degree 2n:
where , ..., are the closed-loop poles chosen by the user.
1 2n
n n–1 n–2
(s) = s + a s + a s
1 2
n n–1
n (s) = b s + b s + ... + ab
p 0 1
C(s) = n (s)/d
c c
n n–1 n–2
(s) = s + x s + x s
1 2
n–1 n–2
(s) = y s + y s
c 1 2
s n s n s d
= +
c p c
s s
= – –
1 2
2n 2n 1
–
s s
= + +
1
6-3 Xmath Interactive Control Design Module
Chapter 6 Pole Place Synthesis
+ ... + a
n
n
(s)
+ ... + x
n
+ ... + 2y
n
s d s
p
s
–
2n
n
+
2