ECE 595S

IFOC

Aaron CramerCarlos Rodríguez

Torque Command Performance

• Constant speed (1700 RPM)• Torque command stepped from 0.0 Nm to

3.0 Nm at 2.0 s• First with machine having “cold”

parameters• Then with machine having “warm”

parameters

“Cold” Performance

“Warm” Performance

Torque Command Performance

• When the machine has the “cold”parameters, IFOC effective

• When the machine has the “warm”parameters, steady-state torque error

• Also, steady-state error in the commanded flux linkages

Speed Control Performance

• Speed command stepped from 0.0 rad/s to 180.0 rad/s at 2.0 s

• Torque command limited to ±3.5 Nm• Simple PI loop around IFOC• First with “cold” parameters• Then with “warm” parameters

“Cold” Performance

“Warm” Performance

Speed Control Performance

• In both situations, the control is limited by the torque limit

• In both situations, the steady-state speed error is zero

• In both situations, the steady-state flux linkage error is zero

• In this situation the performance is acceptable• We will not consider the application of speed

control further in this discussion

IM model

• Consider the following representation of the IM in the stationary reference frame

( )

( )

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+−

+

+−

+

++−

++−

=

+==

+=

Mlrlsrr

ssr

Mlrlsrr

Mr

Mlrlsrr

ssr

Mlrlsrr

Mr

Mlslrss

Ms

Mlslrss

rrs

Mlslrss

Ms

Mlslrss

rrs

rr

r

LLLLLr

LLLLLr

LLLLLr

LLLLLr

LLLLLr

LLLLLr

LLLLLr

LLLLLr

''

'

''

'

''

'

''

'

''

'

''

'

00

00

00

00

I

III

A

AAACxy

BuxAx

ωω

ω

IM model

[ ][ ][ ]Ts

dssqs

Tsds

sqs

Tsdr

sqr

sds

sqs

Mlrlsrr

M

Mlslrss

rr

Mlrlsrr

M

Mlslrss

rr

ii

vv

LLLLL

LLLLL

LLLLL

LLLLL

=

=

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−

+

+−

+=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

=

y

u

x

C

B

AII

''

'''

'

'''

'

00

00

00001001

0100100000000000

λλλλ

TSK model

Stable if

( )

( )

min,max,

max,21

max,2

min,

1

1

1

1

rr

rr

r

r

K

kk

K

kk

ωωωω

αα

ωω

α

αα

α

−−

=−=

+=

+=

=

=

+=

∑

∑

=

=

III

III1

k

AAAAAA

AA

BuxAx

{ }0PAPA

0PP

kk <+

∈∀>=∃

T

T

Kk ,...,2,1

S.H. Żak, Systems and Control

G. Strang, Linear Algebra and its Applications

Observer design

Try placing poles very deep in the left half plane

{ }

( ) ( )xCyLBuxAx

ZPL

ZCZCPPAPA

Z0PP

kk

ˆˆˆ

2,...,2,1

1

−++=

=

+>++

∈∀∃

>=∃

−

α

α TTT

T

Kk

S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan,Linear Matrix Inequalities in System and Control Theory

M. Corless, AAE 666 Course Notes

[ ]( )2000Re −<λ

“Cold” Performance

“Cold” Performance

• Observer error is less than 5.0×10-5 Vs

• It takes longer to establish the flux

• No steady-state torque error

• Some steady-state flux linkage error

“Warm” Performance

“Warm” Performance

• Observer error is rather large (not decaying)

• There seems to be no convergence

• Torque actually becomes negative in response to a step command

What happened?

( )

( ) ( )

( ) ( )( ) ( ) ( )( )( ) ( )∫ −+=

−=

−=

−+−=

−=−++=

=+=

−−−−t

t

ttt detet0

0ˆˆˆ

0ˆˆˆ

ˆ

ˆ

ˆˆˆˆ

ˆˆˆˆˆ

τττ xL∆∆∆Aee

CC∆C

AA∆A

xL∆∆∆AeCLAe

xxexCyLBuxAx

CxyBuAxx

CLACLA

“Cold” Performance

“Cold” Performance

• Observer error is less than 5.0×10-5 Vs

• It takes longer to establish the flux

• No steady-state torque error

• Some steady-state flux linkage error

“Warm” Performance

“Warm” Performance

• Observer error is smaller than before

• No steady-state torque error

• Uses same input measurements as IFOC (± a voltage sensor or two)

Tr adaptation

( ) ( )

( .)

L L RMS RATED L L RMS EXPECTED

SYNC Rotor Mech slip

V Vω ω ω

− −=+

Tr offset adapted(wrm=1800 rpm)

Tr offset should be0.65 s

Warm performance(Tr)

At low speed(wrm=50 rpm)