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

Direct Torque Control with Space Vector Modulation
The GΨ ( z)
is discrete transfer function for voltage-flux relationship with zero hold order
(ZOH) can be calculated as:
−1
GΨ
() s z−1 1
GΨ
( z) = (1 − z ) Z[ ] = Z[ ]
(5.15)
2
s z s
Using table of Z transformation [2]. Finally, it gives
G
Ψ
( z −1)
zTs
AΨ
d
2
z ( z −1) ( z−1)
( z)
= =
(5.16)
Where A = Ψ d
T and s
T
s
is sampling time of the discrete system.
Hence, the closed loop transfer function between Ψ
s
( z)
and Ψ ( z)
is obtained as:
_ ref
s
G
Ψ _ closed
K
pΨ
Ψ
s
( z) _ ref CΨ( z) GΨ( z) D( z)
( z)
= =
Ψ ( z) 1 + C ( z) G ( z) D( z)
A
Ψd
( −1)
z z
K A
= =
K A z z K A
1+
z z
pΨ
Ψd
2
pΨ Ψd − +
pΨ Ψd
( −1)
s
Ψ
Ψ
(5.16)
The flux step response depended on poles placement of closed flux control loop. The pole
placement can be selected by setting the
K
p Ψ
.
Assuming, that CΨd = KpΨAΨd
the GΨ _ closed
( z)
expressed by equations (5.16) will take the
following form:
G
CΨd
( z) =
z − z+
C
Ψ _ closed
2
Ψd
(5.17)
The nomogram of Fig. 5.9 shows the relationship between overshoot M
p[%]
, rise time t r
and
settling time t s
in respect to
C Ψ d
.
Please not that t r
is time calculate from 10% to 90% of output signals and t s
is the time it
takes the system transient to decay +-1%.
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