MODEL REFERENCE ADAPTIVE CONTROL OF PERMANENT

MAGNET SYNCHRONOUS MOTOR DRIVE WITH FORCED DYNAMICS

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 Control System Structure for PM Synchronous MotorSynchronous Motor

Master & Slave Control Laws Master & Slave Control Laws

1. Vector control condition

id 0Demanded dynamic

d

d t Tr

d r

1

1

d

d t Jc ir

PM q L

15

Motor equation for id=0

2. Linearising function

1 1

15T J

c id r PM q L

MCL produces demanded values of

the current components

i

ic

J

T

d dem

q demPM

L d r

_

_

~

0

1

5 1

B. Slave control law

u U sign i i jj s j dem j , , ,1 2 3

SET OF OBSERVERS FOR STATE ESTIMATION

AND FILTERINGFOR SMPM

These terms are treatedtogether as a disturbancevector

d

d t

i

i

R

Lp

L

L

pL

L

R

L

i

ip

L

L

L

u

ud

q

s

dr

q

d

rd

q

s

q

d

q

r

q pm

d

q

d

q

01

0

01

v veq d eq q

T

The remainder of the motor equation forms the basis

of the real time model of the observer.

id

iq

1

s

1

s

Ksm

Ksm

iq

id

ud

uq

1

Ld

1

Lq

v

v

K R

Lp

L

L

pL

L

R

L

i

ip

Leq d

eq q

sm s

dr

q

d

rd

q

s

q

d

q

r

q pm

lim ~

~

~

~

~

~

~

~

~ ~

0

The pseudo-slidingThe pseudo-slidingmode observermode observer

The Sliding Mode Observer and Angular Velocity Extractor

The basic stator current vector pseudo sliding-mode observer is given by:

d

dt

i

i

L

pL

u

uv

vd

q

d

q

d

q

eq d

eq q

*

*

10

1

The required estimates are

equivalent values

where is a high gain

v

v Ki i

i i

eq d

eq qsm

d d

q q

*

*

K sm

veq

unfiltered angular velocity estimate

can be extracted:

rq eq q s q

d d PM

L v R i

p L i*

For the purpose of producing a useful formula for perfect constant parameter estimates may be assumed:

v

v

R

Lp

L

L

pL

L

R

L

i

ip

Leq d

eq q

s

dr

q

d

rd

q

s

q

d

q

r

q PM

*

*

* 0

The Filtering Observer

r

L

1

s

1

s

K K

r

15~ ~ ~ ~ ~

Jc i L L i iPM q d q d q

Filtered values of and are produced by the observer based on Kalman filter

r

e

Jc i L L i i k e

k e

r

r PM q d q d q L

L

~

15

L

where design of:

needs adjustment of the one parameter only or as two different poles:

k J Ts 9 0

~k J Ts 81 4 0

2~

k J ~ 1 2 k J ~1 2

Electrical torque of SM is treated as an external input to the model

Load torque is modelled as a state variable

Original control structure of speed controlled synchronous motor

Master

control law SMPM

Slave control

law

Angular velocity

Extractor

Discrete

two phase

oscillator

Sliding mode Observer

Filtering observer

iqidud uq

iq

id

ua,b,c

~PM

vd_ekv

vq_ekv

r

L

r

r*

idiq

ia ib

ua

ub

uc

ib_dem

ia_dem

ic_dem

id_dem

iq_dem

r d_

ibia ic

POWER

electronics

cossin

~PM

~PM

Transf.

dq /α,β

and

α,β/a,b,c

Transf.

abc /

and

/ d,q

Reference model (of closed-loop system)

Inner & Middle Loop(real system)

correction loop

mrK

Ts

Kd1

Ts1

1

dr̂d

id

Parameter mismatch increases a correction

Kmr r id

Ts

KK

sTK

Ts

K

s

s

dmr

mrd

d

r

11

11

11ˆ

Mason’s rule

Kmr

r

d

s

s sT

1

1

MRAC outer loop

Model TF

r

d

s

s sT

1

1

Experimental Verification

Parameters of the PMSM:

Pn=475 W; n=157 rad/s; Tn=0,47 Nm

Equivalent Circuit Parameters:Rs=1,26 ; Ld=9,34 mH; Lq=9,2 mH;p=2; J=0,0005 kg.m2; PM=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 1EXPERIMENTAL RESULTS 1

0 0.5 1 1.5 20

100

200

300

400

500

600

700

800

0 0.5 1 1.5 2-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.5 0 0.5 1 1.5 2-100

0

100

200

300

400

500

600

700

800Rotor Speed without MRACRotor Speed without MRAC

without without MRACMRAC

EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS 22

0 0.5 1 1.5 20

100

200

300

400

500

600

700

800

0 0.5 1 1.5 2-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-0.5 0 0.5 1 1.5 2-100

0

100

200

300

400

500

600

700

800

Rotor Speed Rotor Speed including MRACincluding MRAC

Simulation resultswithout outer loop and with outer loop

0 0.05 0.1 0.15 0.2-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.05 0.1 0.15 0.2-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-10

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

10

20

30

40

50

60

70

a) b)

c)

0 0.05 0.1 0.15 0.2-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.05 0.1 0.15 0.2-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-10

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

10

20

30

40

50

60

70

a) b)

c) d)d)

a) stator currents, b) rotor mg. fluxes, c) applied torque and estimatedtorque and rotor speed from filtering observer d) rotor speed and idealspeed from transfer function

Experimental Resultswithout outer loop and with outer loop

0 0.5 1 1.5 2-100

-50

0

50

100

150

200

0 0.5 1 1.5 2-150

-100

-50

0

50

100

150

200

250

0 0.5 1 1.5 2-50

0

50

100

150

200

0 0.5 1 1.5 2-50

0

50

100

150

200

250

a) a)

b)b)

a) ideal speed and estimated speed from filtering observer andb) ideal speed with real rotor speed from speed sensor.

Acceleration Demands for Three Various Dynamics

First Order DynamicFirst Order Dynamic

rd1

d T

1a dyn d r

J

T

1*

0 0.2 0.4 0.6 0.8 1 0

10

20

30

40

50

60

70

80

90

100

=f(t)

Second Order DynamicSecond Order Dynamic dyn dJ a *

d

dtf t

0 0.5 1 1.5-20

0

20

40

60

80

100

120

=1 =1.5 =0.5

=f(t)

Constant AccelerationConstant Acceleration

1

dd T

a

dyn d d rJ a sign * *

0 0.5 1 1.5 2 -100

-80

-60

-40

-20

0

20

40

60

80

100

d=f(t) id=f(t)

ndd

dnrd2ndnd

aa

ha2aa

_

_ *ˆ

Experimental ResultsExperimental Results for Synchronous Motor Drive for Synchronous Motor Drive

Constant Acceleration

d=600 rpm,Tramp=0.05 s

First Order Dynamic

d=800 rpm,Tsettl=0.3 s

Second Order Dynamic

d=600 rpm,Tsettl=0.3 s

-0.2 0 0.2 0.4 0.6 0.8

60

-10

0

10

20

30

40

50

Second Order Dynamics for Various Damping Factor

Tsettl=0.15 s , d = 40 rad/s

Conclusions: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.