Synchronous Motor Synchronous Motor Drive Control System Drive Control System

with Prescribed Closed-with Prescribed Closed-Loop Speed DynamicsLoop Speed Dynamics

Synchronous Motor Synchronous Motor Drive Control System Drive Control System

with Prescribed Closed-with Prescribed Closed-Loop Speed DynamicsLoop Speed Dynamics

Dodds, J., Stephen*, Vittek, Ján**Dodds, J., Stephen*, Vittek, Ján**

*University of East London, School of Computing & *University of East London, School of Computing & Technology, UKTechnology, UK

**University of Žilina, Faculty of Electrical Engineering,**University of Žilina, Faculty of Electrical Engineering,

Dept. of Power Electrical Systems, SKDept. of Power Electrical Systems, SK

Model of Permanent Model of Permanent Magnet Synchronous Magnet Synchronous MotorMotor

Model of Permanent Model of Permanent Magnet Synchronous Magnet Synchronous MotorMotor

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.

d

dt

idiq

RsLd

p r

LqLd

p rLdLq

RsLq

idiq

p rLq PM

Ld

Lq

uduq

0

10

01

d

dt Jc i L L i ir

PM q d q d q L

1

5

d

dtr

r

d

dt Jr

el L

1

outer loop sub-plant

inner loop sub-plant Master control

law

estimator and

observers

slavecontrol

law d

dt

idiq

RsLd

p r

Lq

Ld

p rLdLq

RsLq

idiq

p rLq PM

Ld

Lq

uduq

0

10

01

d

dt Jc i L L i i

Jr

PM q d q d q L el L

1 1

5

d

dtr

r

r

rL

I

U

inner loopouter loop

Idem

dem

Control System Structure Control System Structure For PM Synchronous MotorFor PM Synchronous Motor

SJDSJD

Complete control structure of electric drive Complete control structure of electric drive with synchronous motorwith synchronous motor

Transf.

dq /

and

a,b,c

Master

control law SMPM

Slave control

law

Transf.

abc /

and

d,q

Angular velocity

Extractor

Discrete

two phase

oscillator

Mg. flux

calculator

Sliding mode Observer

Filtering observer

iqidud uq

iq

id

ua,b,c

d

q

vd_ekv

vq_ekv

r

L

r

id

iq

ia ib

ua

ub

uc

ib_dem

ia_dem

ic_dem

id_dem

iq_dem

r d_

ibia ic

POWER

electronics

Discrete Time Two-Phase Discrete Time Two-Phase OscillatorOscillator

The discrete time two-phase oscillator produces the transformation matrix elements, needed for the transformation

blocks.

x x p h x

x x p h x

x x p h x

k k r k

k k r k

k k r k

1 1 1 2

2 1 2 1 1

3 1 1 112 2 1

where the new transformation matrix elements

are equal to and . sin r kt X 2 1 cos

r kt X 3 1

Master Control Law Master Control Law

demanded dynamic

d

d t Tr

d r

1

1

d

d t Jc i ir

d q q d L

15

d d q qi i a

a I cos( )

linearising function

1 15

1Jc i i

Td q q d L d r

vector control terms

90o

a 0

i

i

JT

c

d dem

q dem

L d r

d q

q

d

1

52 2

d d q qi i 0

demanded values of the current components

motor equation

Acceleration Demands for Three Acceleration Demands for Three Various DynamicsVarious 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 10

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

A High Gain Proportional Control Law with Voltage Saturation Limits was used for simulation

Bang-Bang Control Law Operating in the Sliding Mode (switching strategy for two-phase version is

satisfactory determined).

Slave Control LawSlave Control Law

U sgn I I Udmax

U sat I I U GI d

,max

Proportional High Gain Slave Control Law

Bang-Bang Slave Control Law

The Sliding Mode Observer and The Sliding Mode Observer and Angular Velocity ExtractorAngular 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 is

equivalent values

where is high a 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 ObserverThe Filtering Observer

where:

needs adjustment of the one parameter only.

1

s

d

1

s

K K

r

15~ ~ ~ ~ ~

Jc i L L i iPM q d q d q

k J T 2~k J T ~

2

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

e

Jc i L L i i k e

k e

r

r PM q d q d q L

L

~

15

rL

VJ

EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

Electric drive with synchronous motor consists of synchronous machine with nominal parameters:

,, ,, P = 4 , ,P Wn 750[ ] n rad s314 [ / ] Rs 2 2. [ ]

L mH L mHd q 6 06 5 73. [ ] , . [ ] PM Vs0119. [ ],, ,,

J kgm0 00035 2. [ ] ..

Parameters of IGBT FUJI 6MBI-060 are as follows:- nominal voltage: 600 [V] , nominal current: 6x10 [A].

Current sensors are as follows:- LEM LTA 50P/SPI.

Measured Results for Synchronous Motor with Constant Acceleration

T1 = 0.1 s , d = 60 rad/s

-0.2

-2

Complex Current Current v. t

Mg. Flux v. t

Rotor SpeedObserved Values-0.2

0.5 1 0 0.5 1

0

2

0

2

0 0.5-2

0

2

0

0.2

0

Complex Mg. Flux

0 0.5-0.2

0

0.2

0

50

-500

50

100100

-2

0.2

0 -0.5

Measured Results for Synchronous Measured Results for Synchronous Motor with Constant Acceleration - Motor with Constant Acceleration -

osciloscope screenosciloscope screen

1 - angular velocity, 2 - current in phase A1 - angular velocity, 2 - current in phase A

T1 = 0.1 s , d = 60 rad/s

Experimental results for idle running Experimental results for idle running synchronous motor and first order speed synchronous motor and first order speed

demanddemand .

-5 5-5

0

5Complex Current

0 0.4-5

0

5Current v. t

-0.2 0.2-0.2

0

0.2Complex Mg. Flux

0 0.4-0.2

0

0.2Mg. Flux v. t

0 0.5 1-50

0

50

100Observed Values

-0.5 0 0.5 1-50

0

50

100Rotor Speed

T1 = 0.05 s , d = 80 rad/s

Experimental results for idle running Experimental results for idle running synchronous motor and second order synchronous motor and second order speed demand -speed demand - osciloscope screenosciloscope screen

1 - angular velocity, 2 - current in phase A1 - angular velocity, 2 - current in phase A

Tset = 0.15 s , d = 80 rad/s

Experimental results for idle running Experimental results for idle running synchronous motor and second order synchronous motor and second order

speed demandspeed demand

-5 5-5

0

5Complex Current

0 0.4-5

0

5Current v. t

-0.2 0.2-0.2

0

0.2Complex Mg. Flux

0 0.4-0.2

0

0.2Mg. Flux v. t

0 0.5 1-50

0

50

100Observed Values

-0.5 0 0.5 1-50

0

50

100Rotor Speed

Tset = 0.15 s , d = 80 rad/s

Experimental results for idle running Experimental results for idle running synchronous motor and first order speed synchronous motor and first order speed

demand -demand - osciloscope screenosciloscope screen

1 - angular velocity, 2 - current in phase A1 - angular velocity, 2 - current in phase A

T1 = 0.05 s , d = 80 rad/s

-0.2 0 0.2 0.4 0.6 0.8

60

-10

0

10

20

30

40

50

Experiments with 2Experiments with 2ndnd Order Order Dynamic for Various DampingDynamic for Various Damping

Tsettl=0.3 s , d = 40 rad/s

Experimental ResultsExperimental Results for Synchronous Motor Drive for Synchronous Motor Drive Experimental ResultsExperimental Results for Synchronous Motor Drive for Synchronous Motor Drive

Constant Acceleration

First Order Dynamic

Second Order Dynamic

d=600 rpm,Tramp=0.05 s

d=800 rpm,Tsettl=0.3 s

d=600 rpm,Tsettl=0.3 s

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Vector Animation "Stator current & Rotor flux"

Real axis

Imaginary Axis

0.0145Time [s]

0.0086Flux Norm [Vs*Vs]

81.5866Angle [deg]

Zilina1998Control of theControl of theangle between angle between rotor flux and rotor flux and stator current stator current vectorsvectors

Conclusions and RecommendationsConclusions and Recommendations

A new approach to the control of electric drives with A new approach to the control of electric drives with permanent magnet synchronous motors, based on permanent magnet synchronous motors, based on feedback linearisation has been developed and feedback linearisation has been developed and experimentally proven.experimentally proven.

Three various prescribed dynamics to speed demands Three various prescribed dynamics to speed demands were achieved.were achieved.

Further research will focus on the application of the Further research will focus on the application of the new approach to enhancement of control system for new approach to enhancement of control system for outer loop based on MRAC or SMC to improve outer loop based on MRAC or SMC to improve precision of control.precision of control.