an investigation of dual stator winding induction machines

determined by calculating the determinant of the Jacobian matrix. In the case of the two
parameters (α and β ) problem, the Jacobian matrix is defined as
∂R
∂R
∂α
J =
∂I
∂β
∂I
(10.115)
∂α
∂β
where R and I are the real and imaginary parts of the characteristic equation when
s = jω
is substituted into ( s)
F . If determinant of J ( det ( ) > 0
390
J ) is greater than 0, the
stable area in the parameter plane will be on the left hand side of the D-decomposition
curve when ω is increasing; if det ( J ) < 0 , then the stable area in the parameter plane
will be on the right hand side of the D-decomposition curve when ω is increasing. When
the D-decomposition curve is complicated, it is better to double check the stable and
unstable regions by calculating the real parts of the roots of the characteristic equations in
each individual region.
10.9 Speed Estimator Design
The full-order observer system based on Model Reference Adaptive Scheme (MRAS)
is used to estimate the flux linkages, the stator currents and rotor speed using the
measured stator voltage and stator current signals of the motor. The error between the
actual stator currents and the estimated stator currents is used in a specialized error
function to calculate an estimation error between the observer and the actual physical
system. Then the output of the error function is fed to the speed estimator to estimate the
rotor speed. The adaptive mechanism is established when the rotor speed estimated from