an investigation of dual stator winding induction machines

Pole 1
Pole 2
Figure 10.3 Diagram of pole placement using Butterworth method
ω0
The zeros of transfer function can also greatly influence the system performance. It is
well known that when any zero of a transfer function of a system has a positive real part
(the system is non-minimum phase), the closed-loop performance is compromised as the
right half-plane zero induces an additional phase shift of -180. The determination of
controller parameters should ensure the minimum phase system requirement.
The design methodology of the Butterworth method requires that none of the terms in
the denominator is missing. This becomes the limitation for the controller determination.
The reason for this limitation is simple. For example, the second order Butterworth
polynomial is given as:
2
2
S + 2ω
S + ω = 0
(10.45)
0
0
The absence of any term in (10.45) leads to the conclusion that ω 0 has to be zero,
which yields unreasonable controller parameters. On the other hand, zero value for ω 0
means that the poles of the controllers overlap the original point, which makes the system
unstable for practical purposes.
356
o
45