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

Direct Torque Control with Space Vector Modulation
−1 GΨ() s z −1
AΨ
GΨ
( z) = (1 − z ) Z[ ] = Z[ ] =
s z A s( s+
A )
( z − )
1 1 AΨ
Z[ ]
z A s( s+
A )
Ψ
Ψ
Ψ
Ψ
(5.49)
Using table of Z transformation [2] one can calculate:
G
Ψ
( z − )
− AΨTs
1 1 z(1 − e ) AΨ
d
( z)
=
− A T
z A
Ψ s
=
z 1( z−e
) z − B
Ψ
( − )
Ψd
(5.50)
Where:
A
Ψd
− AΨT (1 − e s
)
− A Ts
= , BΨ d
e Ψ
A
= and T
s
is sampling time.
Ψ
Hence, the transfer function of closed stator flux control loop can be expressed in the
following form:
G
Ψ _ closed
Ψ
s
( z) _ ref CΨ( z) GΨ( z) D( z)
( z)
= =
Ψ ( z) 1 + C ( z) G ( z) D( z)
s
K
pΨ
( KpΨ + KiΨ) AΨd( z−
)
KpΨ
+ KiΨ
=
K
pΨ
zz ( −1)( z− BΨd) + ( KpΨ + KiΨ) AΨd( z−
)
K + K
Ψ
Ψ
pΨ
iΨ
(5.51)
Now selecting
K Ψ
, K Ψ
is possible to obtain poles placement, which define the dynamic of
p
i
closed torque control loop.
Assuming, that
B
Ψd
=
K
K
pΨ
pΨ
+ K
iΨ
KpΨ − BΨdKpΨ KpΨ
⇒ KiΨ
= = (1 − BΨd)
B B
Ψd
Ψd
and the transfer function of closed stator flux control loop will take the following form:
G
( KpΨ + KiΨ)
AΨd
( z)
=
z − z+ ( K + K ) A
Ψ _ closed
2
pΨ iΨ Ψd
(5.52)
Putting into above equation
K
K
pΨ
pΨ
+ KiΨ
= one obtains:
BΨd
G
K
A
CΨd
K z − z+
C
pΨ
Ψd
BΨd
Ψ _ closed
( z)
= =
2
2
pΨ
z − z+
AΨ
d
BΨd
Ψd
(5.53)
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