velocity tracking of ac motor using smc
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Velocity Tracking of AC Motor Using SlidingMode Control and Kalman Filter for State
Auralius Manurung
RIS-Lab, GSNUDecember, 2009
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Model Identification
X-axis -> voltage sent to the inverter through the ADC of our controller.
Y-axis -> measured linear velocity of our AC motor.
Required voltage (V) to get certain desired velocity (v) can be stated as:
This model will be used as an estimated model for designing Sliding Mode Control.
2854.0
0595.0+=v
V
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Control Design Sliding surface is defined as:
where:
and
21xxs +=
vvx d =1 aadt
dxx d ==
12
,
; if
; if
Finally, control signal can be stated as:
is estimated control signal based on our previous estimated
model.
)sgn(sKusmc = >)(sabs
sKusmc =
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Control Design (contd)
Only position is available as feedback.
Deriving position respect to time to get
velocity and acceleration will generate huge
, . Kalman filter is used to estimate velocity and
acceleration based on kinematic model of
motion.
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Control Design (contd)
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Control Design (contd)Kalman filter:
Given a linear stochastic difference equation:
kkk
kkkk
vCxy
wBuAxx
+=
++= 111
QAAPP
BuxAxT
kk
kkk
+=
+=
1
11
=
+=
+=
kkk
kkkkk
T
k
T
kk
PCKP
yyKxx
RCCPCPK
)1(
)(
)( 1
w an v are process an measurement no se w tprobability of q and r respectively.
Predict
Correct
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Control Design (contd) Algorithm for 1-Dimensional Kalman filter:
Define value of q and r
Loop:
_ k _ k-1
pk= pk-1 + q
kalman_gain = pk/ (pk+ r)
est_valk= est_valk+ kalman_gain*(measured_valk- estimated_valk)
pk= pk* (1 kalman_gain)End loop
me p a e
(Predict)
MeasurementUpdate
(Correct)
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Experiment Results NI LabVIEW 8.5
NI CompactRIO-9004
AC induction motor (1.5 kw, 4 poles, 60Hz, 1680 rpm).
LS variable frequency drives (SV-iG5A)
NI cRio AC induction motor and inverter
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Experiment Results (contd) Kalman Filter will reject huge noises based on
predict-and-correct method very nicely.
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Experiment Results (contd)
Velocity and acceleration response to sinusoidal input at 0.1 Hz with amplitude of 1 m/s.
Desired acceleration is set as half of differentiation of desired velocity.
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Experiment Results (contd)
Velocity and acceleration response to sinusoidal input at 0.3 Hz and with amplitude of 0.5 m/s.
Desired acceleration is set as half of differentiation of desired velocity.
The performance is deteriorating, especially at deceleration due to high inertia.
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Experiment Results (contd) Disturbance Rejection
Sinusoidal input at 0.3 Hz and with amplitude of 0.5 m/s
Loaded with an object about 70 kg of mass.
Velocity Acceleration
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Experiment Results (contd) SMC parameters:
K = 2 Lambda = 10
Delta = 2
q = 0.001
r = 500
Kalman filter parameters for velocity : q = 0.01
r = 15
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Conclusions We have implemented Sliding Mode Controller in AC motor.
Sliding Mode controller is suitable for AC motor whererobustness is important in its application.
Kalman filter provides a reliable state estimation required by
.
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References Greg Welch and Gary Bishop, An Introduction to the Kalman Filter,
University of North Carolina, USA, 2006
Marcus, http://interactive-matter.org/2009/12/filtering-sensor-data-with-
a-kalman-filter/
Bondhan Novandy, http://bono02.files.wordpress.com/2008/07/pismc.pdf
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