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

Direct Torque Control with Space Vector Modulation
After differentiating of the above equation one obtains:
2
sy sy Ls
sy
= Rs + Ψ
s
+ pb
Ψ
PM
dU dI d I dΩm
( )
dt dt dt dt
Take into account that from equation (5.61) the y-axis current is equal
I
sy
(5.69)
2M
e
=
3p
Ψ ,
b
s
dΩ m 1 = ( M
e − M
l ) and under assumption that the motor is no loaded equation (5.69) takes
dt J
form:
dU dM L d M p
( )
dt p dt p dt J
2
sy 2 e s 2
e b
= Rs + Ψ
s
+ M
e
3
b
Ψs ΨPM 3
b
Ψs
(5.70)
Using Laplace transformation and after some arrangements the equation (5.70) can be written:
2Ls
2 2R
Ψs
p
s
b
sU
sy
= M
e
( s + s + )
3p Ψ 3p Ψ J
b PM b s
(5.71)
Hence, the transfer function between electromagnetic torque
be obtained as:
G
M
e
M
2
sy()
M M
M
e
and y-axis voltage
U
sy
can
M () s A s
() s = =
U s s + B s+ C
(5.72)
Where:
A
M
2
3pbΨ
PM
RsΨ
3 Ψ
PM
s
ΨPM pb
= and BM
= CM
=
2L
Ψ L
2JL
s
s
s
s
Using the motor parameters (see Appendices) we may calculates:
A = 198 , B = 115.3 and C = 9065
M
M
M
Continuous s-domain
The torque control loop of the block scheme DTC-SVM from Fig. 5.25 is shown in Fig. 5.35,
where CM
( s ) is a transfer function of the PI controller given by equation 5.28:
100