Higher harmonic airgap inductances are what you might expect:

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Higher harmonic air-gap inductances are what you
might expect
And there are equivalent leakage reactances for
the harmonic orders
2
And the equivalent resistances are
Note that these resistances are calculated at the
right harmonic frequencies
Involved slips are
And this turns into electromagnetic energy
conversion
3
Back to fundementals note that slot impedance is
most important here. If the slot is deep
Which evaluates to
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Which leads us to the arbitrary slot model (this
is current research)
What we do is to break the slot up into a
(sometimes large) number of slices vertically
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Current in one of those layers would be
Reactance of that layer is
And resistance
This leads to an equivalent circuit
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It is necessary, in most cases. To correct for
end ring resistance
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Speed Control Note that flux is the ratio of
voltage to current. We would expect constant flux
control might be a way of controlling an
induction motor. Start by ignoring stator
resistajce
This can be reduced to a simple equivalent
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Current and torque are found (quite simply) to be
Defining slip and voltage with respect to base
quantities
We find torque with respect to an absolute slip
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Above that base speed assume constant voltage
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With a more realistic motor model