an investigation of dual stator winding induction machines

The third type of error function was proposed in [10.24]. The cross product of the
back-EMF from the reference model and the adaptive model is used to calculate the
estimation speed as expressed in the following equation.
⎛ K i ⎞
ˆω r = ⎜ K p + ⎟ ⋅ ( eˆ
m ⊗ em
)
(1.12)
⎝ S ⎠
In the forth type of error function, the cross product of the back-EMF and the stator
current vector was used [10.24]. This type of error function is not well known and the
expression of speed adaptive scheme is:
⎛ K i ⎞
ωˆ r = ⎜ K p + ⎟ ⋅ ( is
⊗ em
)
(1.13)
⎝ S ⎠
The fifth type of error function can be found in [10.36], where the error function is
composed of two components. The first component is the cross product of the estimated
rotor flux vector and the error in the estimated back-EMF, while second component is the
dot product of those two quantities. A variable coefficient k has been inserted into the
error function as a partition factor between these two components. Better speed
estimation result has been claimed in [10.36]. The speed adaptive scheme for this error
function is given as:
⎛ K i ⎞
ˆ ωr = ⎜ K p + ⎟ ⋅ ( ψˆ
r ⊗ ∆em
+ k ⋅ψˆ
r ⋅ ∆em
)
(1.14)
⎝ S ⎠
Similar to the fifth error function, another error function has been proposed in
[10.39]. The real and imaginary part of the product of estimated rotor flux vector and
error in the stator current are used to formulate the speed adaptive scheme. A partition
factor k is also adopted to change the effect of each component to the output of error
function. The expression of speed estimation is:
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