Fuzzy Adaptive Controller for a DFI-Motor - Complex System Modelling and Control Through Intelligent Soft Computations - page 90

2 The DFI-Motor Model

The Concordia and Park transformation s application to the traditional abc DFI-

Motor model allows to write a dynamic model in a d-q synchronous reference frame
as follows

'

d u sd

R s R s M

dt ¼ L s r u sd þ L s L r r u rd þ x s u sq þ

u sd

d u sq
dt ¼

R s R s M

L s r u sq þ L s L r r u rq x s u sd þ

u sq

ð 1 Þ

d u rd R r R r M

dt ¼ L r r u rd þ L s L r r u sd þ x r u rq þ

u rd

d u rq
dt ¼

R r R r M

L r r u rq þ L s L r r u sq x r u rd þ

u rq

Stator and rotor fl flux equations are

u sd ¼ L s i sd þ Mi rd

u sq ¼ L s i sq þ Mi rq

ð 2 Þ

u rd ¼

L r i rd þ Mi sd

u rq ¼

L r i rq þ

Mi sq

The mechanical equation is given by

J d

dt ¼ C e C l

k f X ð 3 Þ

The electromagnetic torque is given by

pM
L s L r r

C e ¼ u sq u rd u sd u rq ð 4 Þ

where
s, r Rotor and stator indices

d, q Synchronous reference frame

α , ʲ Stationary reference frame

R, L, M Resistance, inductance and mutual in ductance

u, i, ˆ Voltage, current and fl ux

h s ; h r Stator and rotor electrical angles

h; X Rotor mechanical position and speed

d h s

dt

d h r

dt

Electrical frequencies of stator, rotor and shaft

d dt

x s ¼ ; x r ¼ ; x ¼

C l ; C e Load and electromagnetic torque

J, p Inertia, number of pole pairs

(M 2 /L s L r ) σ =1 − Leakage coef cient

In a DFI-Motor, the combined effect of the stator and rotor currents produces a
fundamental flux that is sinusoidally distributed around the air gap and that rotates