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

Direct Torque Control with Space Vector Modulation
C
M
⎛ K ⎞
iM
KpM
s+
⎜
K ⎟
pM
() s =
⎝ ⎠
(5.28)
s
where
K
iM
=
K
T
pM
iM
M e _ ref
() ∆δ U = sβ Us
CM s Ψ
G ()
GM
() s
Mδ
s
M e
Figure 5.16. Block diagram of torque control loop represented in s-domain.
Hence, the transfer function between M
_
() s and M ( s ) is obtained as:
e
ref
e
G
M _ closed
() s
M () s C () s G () s G () s
e_
ref M M Mδ
= = (5.29)
M
e() s 1 + CM() z GM() s GMδ
() s
Substituting transfer function for CM
( s)
and GM
( s ) equation (5.29) becomes:
KiM
K Ψ p PMAMKpM( s +
Ψ
)
K
pM
GM
_ closed()
s = =
2
s + ( B + K A ) s+ C + K A
M pM M M iM M
(5.30)
Discrete design
The transfer function (equations 5.28) for PI controller in discrete system using
z −1
backward difference method for discretization process ( s = ) [2] is expressed as:
Tz
s
K
pM
( z − )
KpM
+ KiM
CM( z) = ( KpM + KiM)
( z −1)
(5.31)
where:
K
iM
K
pM
= Ts
,
s
TiM
T - sampling time, C ( z ) is the discrete transfer function of
M
torque PI controller, Dz ( )
1
z −
is one sampling time delay for voltage generation from
PWM, and
81