Torque ripple reduction in switched reluctance motor drives
A method for controlling a switched reluctance motor, the method comprising: receiving a reference torque T e ref ; receiving an indication of a present rotor position θ for the switched reluctance motor; determining at least one of: a reference current i e _ ref(k−1) for a (k−1) th phase, a reference current i e _ ref(k) for a (k) th phase, and a reference current i e _ ref(k+1) for a (k+1) th phase; and outputting the determined at least one reference current to a current controller operatively coupled to the switched reluctance motor, wherein the determined at least one reference current is based on an objective function comprising the squares of phase current and derivatives of current reference.
1. A method for controlling a switched reluctance motor, the method comprising:
receiving a reference torque T e _ ref ;
receiving an indication of a present rotor position θ for the switched reluctance motor;
determining at least one of:
a reference current i e _ ref(k−1) for a (k−1) th phase,
a reference current i e _ ref(k) for a (k) th phase, and
a reference current i e _ ref(k+1) for a (k+1) th phase; and
outputting the determined at least one reference current to a current controller operatively coupled to the switched reluctance motor for controlling the switched reluctance motor,
wherein the determined at least one reference current is based on an objective function comprising:
min
J
=
mRi
k
-
1
2
(
θ
)
+
nRi
k
2
(
θ
)
+
s
[
i
k
-
1
(
θ
)
-
i
k
-
1
(
θ
0
)
Δθ
]
2
+
t
[
i
k
(
θ
)
-
i
k
(
θ
0
)
Δθ
]
2
subject to:
1
2
∂
L
(
θ
,
i
k
-
1
)
∂
θ
i
k
-
1
2
(
θ
)
+
1
2
∂
L
(
θ
,
i
k
)
∂
θ
i
k
2
(
θ
)
=
T
e
-
ref
,
i
k
-
1
≤
l
max
,
and
i
k
≤
l
max
;
wherein:
θ 0 is an indication of a previous rotor position for the switched reluctance motor,
i k−1 (θ 0 ) is a reference current for an outgoing phase at the previous rotor position θ 0 ,
i k−1 (θ) is a reference current for the outgoing phase at the present rotor position θ,
i k (θ 0 ) is a reference current for an incoming phase at the previous rotor position θ 0 ,
i k (θ) is a reference current for the incoming phase at the present rotor position θ,
Δθ=θ−θ 0 ,
R represents the resistance of the switched reluctance motor,
L(θ, i k ) is an incremental inductance for the switched reluctance motor for the incoming phase at the present rotor position θ,
L(θ, i k−1 ) is an incremental inductance for the switched reluctance motor for the outgoing phase at the present rotor position θ,
I max is an allowable peak current for the switched reluctance motor, and
m, n, s, and t are Tikhonov factors.
2. The method of claim 1 , wherein determining the at least one reference current comprises:
determining at least one of:
a reference torque T e _ ref(n−1) for a (k−1) th phase,
a reference torque T e _ ref(n) for a (k) th phase, and
a reference torque T e _ ref(n+1) for a (k+1) th phase; and
using the determined at least one reference torque, the present rotor position θ for the switched reluctance motor, and a set of torque-current-rotor position characteristics to determine the at least one reference current.
3. A switched reluctance motor system comprising:
a switched reluctance motor; and
a control system operatively coupled to a current controller for the switched reluctance motor, the control system configured to:
receive a reference torque T e _ ref ;
receive an indication of a present rotor position θ for the switched reluctance motor;
determine at least one of:
a reference current i e _ ref(k−1) for a (k−1) th phase,
a reference current i e _ ref(k) for a (k) th phase, and
a reference current i e _ ref(k+1) for a (k +1) th phase; and
output the determined at least one reference current to the current controller for controlling the switched reluctance motor,
wherein the determined at least one reference current is based on an objective function comprising:
min
J
=
mRi
k
-
1
2
(
θ
)
+
nRi
k
2
(
θ
)
+
s
[
i
k
-
1
(
θ
)
-
i
k
-
1
(
θ
0
)
Δθ
]
2
+
t
[
i
k
(
θ
)
-
i
k
(
θ
0
)
Δθ
]
2
subject to:
1
2
∂
L
(
θ
,
i
k
-
1
)
∂
θ
i
k
-
1
2
(
θ
)
+
1
2
∂
L
(
θ
,
i
k
)
∂
θ
i
k
2
(
θ
)
=
T
e
-
ref
,
i
k
-
1
≤
l
max
,
and
i
k
≤
l
max
;
wherein:
θ 0 is an indication of a previous rotor position for the switched reluctance motor,
i k−1 (θ 0 ) is a reference current for an outgoing phase at the previous rotor position θ 0 ,
i k−1 (θ) is a reference current for the outgoing phase at the present rotor position θ,
i k (θ 0 ) is a reference current for an incoming phase at the previous rotor position θ 0 ,
i k (θ) is a reference current for the incoming phase at the present rotor position θ,
Δθ=θ−θ 0 ,
R represents the resistance of the switched reluctance motor,
L(θ,i k ) is an incremental inductance for the switched reluctance motor for the incoming phase at the present rotor position θ,
L(θ, i k−1 ) is an incremental inductance for the switched reluctance motor for the outgoing phase at the present rotor position θ,
I max is an allowable peak current for the switched reluctance motor, and
m, n, s, and t are Tikhonov factors.
4. The switched reluctance motor system of claim 3 , wherein the control system is configured to determine the at least one reference current by:
determining at least one of:
a reference torque T e _ ref(n−1 ) for a (k−1) th phase,
a reference torque T e _ ref(n) for a (k) th phase, and
a reference torque T e _ ref(n+1) for a (k+1) th phase; and
using the determined at least one reference torque, the present rotor position θ for the switched reluctance motor, and a set of torque-current-rotor position characteristics to determine the at least one reference current.