an investigation of dual stator winding induction machines

The above algorithm requires that the output function h(
x)
295
y = has a relative degree
of r = n . If r < n , then the procedure can only proceed up to r steps. Under this
condition, part of the system dynamics described by the state components is
“unobservable” in the input-output linearization. This part of the dynamics is called the
internal dynamics and the issue of internal stability becomes important when a relative
degree is less than the number of state variables.
The internal dynamics are simply determined by the locations of the zeros in the
linear system, in which the internal dynamics are stable if all zeros are in the left-half
plane. The system with negative real parts for all the zeros is also called "minimum-phase
system". However, this cannot be directly used for the nonlinear system. In that case, the
zero-dynamic is defined in the nonlinear system to determine the stability of the internal
dynamics. When the system output is kept at zero by the input, it is internal dynamics of
the nonlinear system. Hence the study of the internal dynamics stability can be simplified
by studying that of the zero dynamics instead. A different control strategy has to be
applied if the zero dynamics are unstable.
8.5 Control Scheme
Since the system equations of the dual stator winding induction machine given in
(8.1-8.9) are nonlinear and coupled, the input-output linearization method with
decoupling is used to remove the non-linearity and coupled terms permitting the classic
linear system control methodology to be used to determine the parameters of the
controllers. This method is possible since the input-output linearization and decoupling
strategy ensure the linear relationship between the input control variables and the output