magnetical axis of phase a in the stator
aphase a in a threephase system
arotational unit vector of 120°
rotational unit vector of 240°
[A]phase transformation matrix
bphase b in a threephase system
cphase c n a threephase system
Ccondenser capacity
Dfixed of statororiented direct axis
Ddiode
[D]rotational matrix operator of a twophase axis system
arbitrarily rotating of fieldoriented direct axis
airgap fieldoriented direct axis
resultant rotor fieldoriented direct axis
resultant stator fieldoriented direct axis
rotororiented direct axis
space phasor of the electromotive force
stator voltage and stator current frequency
stator current oriented direct axis
space vector or space phasor of a current
armature current in a DC machine
active component of the current space phasor
DC link current
magnetizing current
rotorflux based magnetizing current
statorflux based magnetizing current
Rereal axis of the complex plane and real part of the complex expression
Imimaginary axis of the complex plane and imaginary part of the complex expression
rotor current
reactive component of the current space phasor
stator current
jrotational unit vector of 90°
[j]rotational matrix operator of 90° for a twophase system of magnitudes without zerosequence component
Jtotal equivalent moment of inertia
proportional coefficient between the magnitude of the stator current space phasor and the d.c. link current
Ktorque constant of a DC machine
[K]rotational matrix operator of 90° for a threephase system of magnitudes
space phasor definition (constant) coefficient
referring constant of the currents and magneto motoric force
torque constant of an AC machine
torque constant of the induction machine containing the rotor leakage coefficient
torque constant of the induction machine containing the stator leakage coefficient
power coefficient matrix
referring constant of the resistances and inductances
scale coefficient of the space phasor
reffering constant of the voltages and electro motoric force
inductance of the main magnetic circuit
useful inductance of the rotorphase winding
total perphase inductance of the rotor
useful inductance of the statorphase winding
total perphase inductance of the stator
rotor’s own perphase leakage inductance
stator’s own perphase leakage inductance
inductance of the thyristor commutation coil
DC link current filtering inductance
threephase resultant mutual (useful) inductance
threephase resultant (total) rotor inductance
zerosequence inductance of the rotor
threephase resultant (total) stator inductance
zerosequence inductance of the stator
resultant leakage inductance of the rotor
resultant leakage inductance of the stator
mmutual inductance between a stator and a rotor phase
electromagnetic torque
dynamic torque
resistent load torque
mutual leakage inductance between two rotor phases
mutual leakage inductance between two stator phases
number of rotor phases
number of stator phases
[q]matrix of the oscillator output quantities
pinstantaneous power or power losses
instantaneous mechanical power
projection of a space vector or space phasor
qfixed or statororiented quadrature axis
[Q]rotational matrix of 90° for a twophase system of magnitudes including the zerosequence component
statorcurrent oriented quadrature axis
arbitrarily rotating or fieldoriented quadrature axis
airgap fieldoriented quadrature axis
resultant rotor fieldoriented quadrature axis
resultant stator fieldoriented quadrature axis
rotororiented quadrature axis
Rereal axis of the complex plane
Rereal part of a complex expression
resistance of diode
rotor perphase resistance
stator perphase resistance
resistance of thyristor or transistor
ttime
[t]threephase projection matrix
[T]rotational matrix operator of threephase axis system
space phasor of voltage
voltage drop
DC link output/inverter input voltage
rotor voltage
rectifier output/DC link input voltage
stator voltage
Nturn number of winding
number of the polipairs
angular position of the magnetizingcurrent space phasor
angular position of the rotorcurrent space phasor
angular position of the statorcurrent space phasor
angular position of an arbitrarily rotating direct axis or of a fieldoriented axis
angular position of the airgap resultant flux space phasor
angular position of the rotor resultant flux space phasor
angular position of the stator resultant flux space phasor
electrical angular position of the rotor axis
mechanical angular position of the rotor axis
resultant (total) leakage coefficient
rotor leakage coefficient
stator leakage coefficient
space vector or space phasor of flux linkage
space vector of armature reaction flux in DC machine
space vector of compensating flux in DC machine
space vector of exciting flux
airgap flux
resultant rotor flux
resultant stator flux
rotor leakage flux
rotational matrix of threephase axis system, when the zerosequence component is missing
time constant of the rotor
time constant of the stator
electrical angular speed of the rotor
synchronous electrical angular speed
mechanical angular speed of the rotor
rotational speed of the magnetizingcurrent space phasor
rotational speed of the rotorcurrent space phasor
rotational speed of the statorcurrent space phasor
angular speed of an arbitrarity rotating axis system or of a fieldoriented axis
rotational speed of the airgap flux space phasor
rotational speed of the resultant rotor flux space phasor
rotational speed of the resultant stator flux space phasor
NAME 
Symbols within the text 
Symbols within the formulae describing implementations and simulations 
Stator and rotor currents 

iS, iR 
Stator current threephase coordinates 

iS_a, iS_b, iS_c 
twophase coordinates 

iS_alpha, iS_beta 
field coordinates 

iS_d, iS_q 
Magnetising current 

ImR 
Stator voltage 

US 
Rotor flux 

Psi_R 
Rotor, rotor flux and slip angular velocity 
, 
omega_Rotor, omega_Flux, omega_Slip 
Reference speed 

Omega_ref 
Rotor, rotor flux and slip angle 
, , 
eps_Rotor,eps _Flux eps_Slip 
Load torque 

torque_L 
Stator and rotor resistance and Time constants 
, , 
Rs, Rr, Ts, Tr, 
Stator, rotor and main inductance 
, , 
Ls, Lr, Lm 
Leakage factor 

Sigma 
Number of poles 

P 
Moment of inertia 

J 
System noise variance 

 
Output/Measurement noise variance 

 
Kalman gain 
K 
K 
Estimated motor state variable 

i_alpha_est; i_beta_est Psi_R_alpha_est; Psi_R_beta_est i_d_est; i_q_est  
cross vectorial product
complex conjugate
element of (contained in)
not element of (not contained in )
null set
implication
biimplication
negation (complement)
identity
equivalence
union (disjunction)
OR
intersection (conjunction)
AND
ordered pair
Cartesian product
fuzzy intersection operator (fuzzy AND), Tnorm
fuzzy union operator (fuzzy OR), Snorm, Tconorm
subset of (A’ÍB’ means that A’ is subset of B’)
proper subset of (A’ÌB’ means that A’ is proper subset of B’)
not proper subset of
Ttranspose
Xuniverse of discourse (sample space)
ççx  yúú Euclidean distance between vectors x and y
mmembership function, MF (degree of belongingness)
x1, x2, …symbol 125 \f "Symbol" \s 10crisp set of numbers
AI artificial intelligence
AIB artificialintelligencebased
ANN artificial neural network
ASM asynchronous motor
CSI current source inverter
DSP digital signal processor
DTC direct torque control
EKF extended Kalman Filter
ELO extended Luenberger Observer
FLC fuzzy logic controller
FLEOC fuzzy logic efficiency optimizer controller
FLSfuzzy logic system
GA genetic algorithm
IM induction machine
KFKalman Filter
LO Luenberger Observer
MRAC model reference adaptive control
NRAS model reference adaptive system
NARMAX nonlinear auto regressive moving average model
p.m. permanent magnet
PWM pulsewidth modulator/modulation
SRM switched reluctance machine
SYRM synchronous reluctance machine
TDL tapped delay line
VSI voltage source inverter
NL negative large
NM negative medium
NS negative small
ZE zero
PS positive small
PM positive medium
PL positive large