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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