Implementation of a Sensorless Synchronous Motor Drive
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Transcript Implementation of a Sensorless Synchronous Motor Drive
MODEL REFERENCE
ADAPTIVE CONTROL OF
PERMANENT MAGNET
SYNCHRONOUS MOTOR
Model of Permanent Magnet
Synchronous Motor
Non-linear differential equations formulated in the
magnetic field-fixed d,q co-ordinate system describe
the permanent magnet synchronous motor and form
the basis of the control system development.
Control System Structure for PM
Synchronous Motor
Master & Slave Control Laws
Motor equation for id=0
d r 1
c5 PM i q L
dt
J
1. Vector control
condition
id 0
Demanded dynamic
d r 1
d r
dt
T1
MCL produces demanded values
of the current components
2. Linearising function
1
1
d r c5 PMiq L
T1
J
B. Slave control law
i d _ dem 0
1
i
q _ dem
c5 PM
u j U s sign i j dem i j ,
j 1, 2, 3
~
J
d
r
L
T
1
SET OF OBSERVERS
FOR STATE ESTIMATION
AND FILTERING
FOR SMPM
The pseudo-sliding
mode observer
These terms are treated
together as a disturbance
T
vector
v eq d
v eq q
Lq
Rs
1
0
pr
u
Ld id pr 0 Ld
d id Ld
d
i
1 uq
Ld Rs iq L pm
dt q
q
0
pr
L
Lq
Lq
q
The remainder of the motor equation forms the basis
of the real time model of the observer.
K sm
id
1
i s
1
Ld
i
d 1
1
Lq
q
iq
s
K sm
ud
uq
lim
~
~
Lq
Ksm Rs
~
p
~ i
0
rL
veqd L
p
d
r
d
d
~
v
~
~ i ~
L
R
Lq pm
q
eqq
d
s
pr ~
~
Lq
Lq
The Sliding Mode Observer and Angular Velocity
Extractor
The basic stator current vector pseudo
sliding-mode observer is given by:
1
L
d i*d
* d
dt i q
p
0
v
ud
eq
d
1 uq v
eq q
Lq
For the purpose of producing a useful
formula for v
perfect
constant parameter
eq
estimates may be assumed:
Rs
veq d Ld
v
L
eq q p*r d
Lq
Lq
p r i
p*r 0
Ld d
R s iq Lq PM
Lq
*
The required
estimates are
equivalent values
id i*d
veq d
v Ksm
*
iq iq
eq q
where K sm is a high
gain
unfiltered angular
velocity estimate
can be extracted:
*r
Lq veq q R s i q
p Ld i d PM
The Filtering Observer
r and L are produced by the
Filtered values of
observer based on Kalman filter
e r
1 c i
~ 5
r
PM q
J
L k e
Ld Lq id iq L ke
Load torque is modelled as a state variable
r
where design of:
~
k 81J 4Ts20
~
k 9 J Ts0
needs adjustment of the
one parameter only or as
two different poles:
~
~
k J 1 2 k J 1 2
1 ~ ~
~ c5 PM i q
J
L~
~
L
d
q
K
K
i
d
i q
1
s
Electrical torque of SM is treated as an external input to the model
1
s
r
L
Original control structure of speed
controlled synchronous motor
r _d
Master id_dem
Transf.
ia_dem
control
iq_dem
law
dq /α,β
ib_dem
and
ic_dem
ua
Slave
control
law
POWER
electronics
r
~
PM
r
ia ib ic
Discrete
two phase
oscillator
ua,b,c
cosq
sinq
id
iq
~
PM
id
ia ib
Transf.
abc / a,b
and
a,b / d,q
ud uq id
iq
Filtering observer
*r
SMPM
uc
α,β/a,b,c
L
ub
Angular
velocity
Extractor
vd_ekv
vq_ekv
Sliding mode
Observer
iq
~
PM
d
d
correction
loop
Inner & Middle Loop
(real system)
MRAC
outer loop
ˆ r
Kd
1 sT
Model TF
K mr
Reference model
(of closed-loop system)
1
1 K mr
1 sT
ˆ r s
d s
Kd
1 K mr
1 sT
Mason’s rule
d s
1
1 sT
Parameter mismatch
increases a correction
1
1 sT
Kd
1 sT
id
r s
r id
Kmr
K mr
r s
1
d s
1 sT
Experimental Verification
Parameters of the PMSM:
Pn=475 W; n=157 rad/s; Tn=0,47 Nm
Equivalent Circuit Parameters:
Rs=1,26 W; Ld=9,34 mH; Lq=9,2 mH;
p=2; J=0,0005 kg.m2; YPM=0,112 Vs
Parameters of IGBT Semikron 6MBI-060 are as follows:
nominal voltage: 1000 [V] , nominal current: 6x10 [A].
Current sensors are as follows: LEM LTA 50P/SPI.
EXPERIMENTAL RESULTS 1
800
800
Rotor Speed without MRAC
700
700
600
500
600
400
300
500
200
without
MRAC
100
0
0
400
0.5
1
1.5
2
0.4
300
0.3
200
0.2
0.1
100
0
-0.1
0
-0.2
-0.3
-0.4
0
0.5
1
1.5
2
-100
-0.5
0
0.5
1
1.5
2
EXPERIMENTAL RESULTS 2
800
800
700
700
600
500
600
400
300
500
200
100
0
0
400
0.5
1
1.5
Rotor Speed
including MRAC
2
300
0.15
0.1
200
0.05
0
100
-0.05
-0.1
0
-0.15
-0.2
-0.25
0
0.5
1
1.5
2
-100
-0.5
0
0.5
1
1.5
2
Simulation results
without outer loop and with outer loop
2
0.15
2
0.15
1.5
0.1
1.5
0.1
0.05
1
1
0.5
0.05
0.5
0
0
0
0
-0.05
-0.05
-0.5
a)
-1
-1.5
0
0.05
0.1
0.15
b)
-0.1
0.2
-0.15
0
70
70
60
60
-0.5
0.05
0.1
0.15
a)
-1
0.2
-1.5
0
0.05
0.1
0.15
0.2
-0.15
0
80
70
70
60
60
50
b)
-0.1
0.05
0.1
0.15
0.2
50
50
50
40
40
40
30
30
30
20
c)
0
-10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
d)
10
0.8
0
0
30
20
20
10
40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
20
c)
10
0
0.8
-10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
d)
10
0.8
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
a) stator currents, b) rotor mg. fluxes, c) applied torque and estimated
torque and rotor speed from filtering observer d) rotor speed and ideal
speed from transfer function
Experimental Results
without outer loop and with outer loop
200
250
200
150
150
100
100
50
50
0
0
-100
-50
a)
-50
0
0.5
1
1.5
a)
-100
2
-150
200
250
150
200
0
0.5
1
1.5
2
150
100
100
50
50
0
-50
0
b)
0.5
1
1.5
b)
0
2
-50
0
0.5
1
1.5
2
a) ideal speed and estimated speed from filtering observer and
b) ideal speed with real rotor speed from speed sensor.
Acceleration Demands for Three Various
Dynamics
100
80
Constant Acceleration
60
40
id=f(t)
d=f(t)
20
0
-20
-40
-60
-80
-100
0
0.5
1
1.5
2
90
=f(t)
70
J
1
r
a d d r dyn * d
T1
T1
60
50
40
30
20
10
0
0
0.2
0.4
0.6
0.8
80
Second Order Dynamic
=1
=0.5
=1.5
=f(t)
60
40
d
f t
dt
20
0
-20
0
0.5
1
1
120
100
r
dyn J * a d * sign d
First Order Dynamic
100
80
d
ad
T1
1.5
dyn J * a d
ˆ r 2n a d * h
a d _ n a d 2n d
ad ad _ n
Experimental Results
for Synchronous Motor Drive
First Order Dynamic
Constant Acceleration
d=
d=
600 rpm,
800 rpm,
Tramp=
Tsettl=
0.3 s
0.05 s
Second Order Dynamic
d=
600 rpm,
Tsettl=
0.3 s
Second Order Dynamics for Various
Damping Factor
60
z0.5
50
40
z2
30
20
z1
10
0
-10
-0.2
0
0.2
0.4
0.6
Tsettl=0.15 s , d = 40 rad/s
0.8
Conclusions:
A new approach to the control of electric drives with
permanent magnet synchronous motors, when
original forced dynamics control system was
completed with outer control loop based on MRAC,
has been developed and experimentally proven.
Three various prescribed dynamics to speed
demands were achieved and beneficial influence of
added control loops was observed.
Application to the vector controlled drive with
PMSM is possible. Further improvement of this
control technique can continue via application of
more sophisticated PWM strategy.