Page 635 - The Mechatronics Handbook

0066_Frame_C20.fm Page 105 Wednesday, January 9, 2002 1:44 PM

Load
T
bs Magnetic Axis L
B m
as′ ω r T , e
Stator Quadrature Magnetic Axis
u cs + u bs + ω
r r cs Rotor bs
s s t
d
L ss L ss θ = ∫ ω (τ ) τ + θ 0
0 t
i i bs
cs
as Magnetic Axis
N s
L
ss
i bs′ cs′
as
r s
as
cs Magnetic Axis Direct Magnetic Axis
u as +
FIGURE 20.130 Three-phase synchronous reluctance micromotor.
Three-Phase Synchronous Reluctance Micromotors: Modeling and Analysis
Our goal is to address and solve a spectrum of problems in analysis, modeling, and control of synchronous
reluctance micromachines. The electromagnetic features must be thoroughly analyzed before attempt to
control micromotors. In fact, electromagnetic features significantly restrict the control algorithms to be
applied. Depending upon the conceptual methods employed to analyze synchronous reluctance micro-
machines, different control laws can be designed and implemented using ICs. Analysis and control of
synchronous reluctance micromotors can be performed using different modeling, analysis, and optimi-
zation concepts. Complete lumped-parameter mathematical models of synchronous reluctance micro-
motors in the machine (abc) and in the quadrature, direct, and zero (qd0) variables should be developed
in the form of nonlinear differential equations. In particular, the circuitry lumped-parameters mathe-
matical model is found using the Kirchhoff’s voltage law. We have, see Fig. 20.130,

u abcs = r s i abcs + dy abcs
--------------
dt

where u as , u bs , and u cs are the phase voltages; i as , i bs , and i cs are the phase currents; ψ as , ψ bs , and ψ cs are the
flux linkages,

r s 00
y abcs = L s i abcs , r s = 0 r s 0

00 r s



L ls + L m – L ∆m cos ( 2q r ) – 1 L ∆m cos 2 q r – 1  – 1 L ∆m cos 2 q r + 1 
--L m –
--p
--p
--L m –
2  3  2  3 


L s = – 1 L ∆m cos 2 q r – 1  L ls + L m – L ∆m cos 2 q r – 2  – 1 L ∆m cos 2 q r + p)
(
--L m –
--p
--p
--L m –
2  3   3  2
1  1  1  2 
(
– --L m – L ∆m cos 2 q r + --p – --L m – L ∆m cos 2 q r + p) L ls + L m – L ∆m cos 2 q r + --p


2 3  2 3 
-- L md –(
-- L mq +(
L m = 1 L md ) and L ∆m = 1 L mq )
3 3
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