Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Direct Torque Control with Space Vector Modulation
G
Ψ _ closed
Ψ
s
() s
_ ref CΨ() s GΨ()
s
() s = =
Ψ () s 1 + C () z G () s
s
Ψ
Ψ
(5.46)
Substituting transfer function for CΨ ( s)
and GΨ ( s)
one becomes
G
_ closed
() s
⎛ K ⎞
iΨ
KpΨ
s+
⎜ K ⎟
⎝ pΨ
⎠ ⎛ 1 ⎞
⎛ K ⎞
iΨ
⎜ ⎟ KpΨ
s+
s s A
⎜ K ⎟
⎝ + ⎠ pΨ
=
⎝ ⎠
⎛ K ⎞
s + ( A + Kp
) s+
K
iΨ
KpΨ
s+
⎜ K ⎟
pΨ
⎛ 1 ⎞
1+ ⎝ ⎠
⎜ ⎟
s ⎝s+
AΨ
⎠
Ψ
Ψ
=
2
Ψ Ψ iΨ
(5.47)
Discrete design
z −1
Using backward difference method for discretization process ( s = ) [2] the transfer
Tz
function of equation (5.45) for flux PI controller in discrete system is expressed as:
s
K
pΨ
( KpΨ
+ KiΨ)( z−
)
Tz
K
s
pΨ
+ KiΨ
CΨ( z) = KpΨ(1 + ) =
T ( z−1) ( z−1)
iΨ
(5.48)
Where:
K
s
K
pΨ
iΨ
= Ts; s
Ti
Ψ
Ψ
_
( z)
ref
T - sampling time.
C
Ψ
( z)
W( z)
U sx
Dz ( )
z −1
GΨ
( z)
}
ZOH
1
s+
A Ψ
Ψ
s
( z)
Figure 5.28. Block diagram of flux control loop in discrete domain.
Where: CΨ ( z)
discrete transfer function of PI controller, Dz ( )
1
z − - one sampling time delay
for voltage generation from PWM, and W( z)
- disturbance voltage due to cross coupling
between x-y axis (see Fig. 5.28).
The GΨ ( z)
is discrete transfer function of voltage-flux relationship with zero order hold
(ZOH) block can be calculated as:
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