METHOD FOR OPERATING A LINEAR COMPRESSOR

1 . A method for operating a linear compressor, comprising:

providing an electrical dynamic model for a motor of the linear compressor;

supplying the motor of the linear compressor with a time varying voltage;

estimating a back-EMF of the motor of the linear compressor during said step of supplying using at least the electrical dynamic model for the motor of the linear compressor and a robust integral of the sign of the error feedback;

determining a velocity of the motor of the linear compressor based at least in part on the back-EMF of the motor from said step of estimating; and

calculating a stroke length of the motor of the linear compressor based at least in part on the velocity of the motor from said step of determining.

2 . The method of claim 1 , wherein the electrical dynamic model for the motor comprises



i



t

=

v

a

L

i

-

r

i



i

L

i

-

α





x

.

L

i

where

v a is a voltage across the motor of the linear compressor;

r i is a resistance of the motor of the linear compressor;

i is a current through the motor of the linear compressor;

α is a motor force constant;

{dot over (x)} is a velocity of the motor of the linear compressor; and

L i is an inductance of the motor of the linear compressor.

3 . The method of claim 2 , further establishing a time varying current through the motor of the linear compressor during said step of supplying.

4 . The method of claim 1 , wherein the linear compressor is positioned within a refrigerator appliance.

5 . The method of claim 1 , wherein estimating the back-EMF of the motor of the linear compressor during said step of supplying using the robust integral of the sign of the error feedback comprises solving

{circumflex over ( f )}=( K 1 +1) e ( t )+∫ t 0 t [( K 1 +1) e (σ)+ K 2 sgn( e (σ))] d σ−( K 1 +1) e ( t 0 )

where

{circumflex over (f)} is an estimated back-EMF of the motor of the linear compressor;

K 1 and K 2 are real, positive gains; and

e=î−i and ė=f−{circumflex over (f)}.

6 . The method of claim 5 , said step of determining the velocity of the motor of the linear compressor comprises solving

x

.

^

=

L

i

α



f

^

where

{dot over ({circumflex over (x)})} is an estimated velocity of the motor of the linear compressor;

α is a motor force constant; and

L i is an inductance of the motor of the linear compressor.

7 . The method of claim 6 , wherein said step of calculating the stroke length of the motor of the linear compressor comprises solving

X

=

L

i

α



∫

f

^





t

=

x

^

initial

+

x

^



(

t

)

where {circumflex over (x)} is an estimated position of the motor of the linear compressor.

8 . The method of claim 1 , further comprising adjusting the time varying voltage supplied to the motor of the linear compressor in order to operate the motor of the linear compressor at a resonant frequency of the motor of the linear compressor.

9 . The method of claim 1 , wherein said steps of estimating, determining and calculating are conducted with the motor of the linear compressor sealed within a hermitic shell of the linear compressor.

10 . A method for operating a linear compressor, comprising:

supplying the motor of the linear compressor with a time varying voltage, the motor of the linear compressor disposed within a hermetic shell of the linear compressor during said step of supplying;

estimating a back-EMF of the motor of the linear compressor during said step of supplying using a robust integral of the sign of the error feedback;

determining a velocity of the motor of the linear compressor based at least in part on the back-EMF of the motor from said step of estimating; and

calculating a stroke length of the motor of the linear compressor based at least in part on the velocity of the motor from said step of determining.

11 . The method of claim 10 , further comprising providing an electrical dynamic model for the motor of the linear compressor, the electrical dynamic model for the motor comprising



i



t

=

v

a

L

i

-

r

i



i

L

i

-

α





x

.

L

i

where

v a is a voltage across the motor of the linear compressor;

r i is a resistance of the motor of the linear compressor;

i is a current through the motor of the linear compressor;

α is a motor force constant;

{dot over (x)} is a velocity of the motor of the linear compressor; and

L i is an inductance of the motor of the linear compressor.

12 . The method of claim 11 , further establishing a time varying current through the motor of the linear compressor during said step of supplying.

13 . The method of claim 11 , the linear compressor is positioned within a refrigerator appliance.

14 . The method of claim 10 , wherein estimating the back-EMF of the motor of the linear compressor during said step of supplying using the robust integral of the sign of the error feedback comprises solving

{circumflex over ( f )}=( K 1 +1) e ( t )+∫ t 0 t [( K 1 +1) e (σ)+ K 2 sgn( e (σ))] d σ−( K 1 +1) e ( t 0 )

where

{circumflex over (f)} is an estimated back-EMF of the motor of the linear compressor;

K 1 and K 2 are real, positive gains; and

e=î−i and e=f−{circumflex over (f)}.

15 . The method of claim 14 , said step of determining the velocity of the motor of the linear compressor comprises solving

x

.

^

=

L

i

α



f

^

where

{dot over ({circumflex over (x)})} is an estimated velocity of the motor of the linear compressor;

α is a motor force constant; and

L i is an inductance of the motor of the linear compressor.

16 . The method of claim 15 , wherein said step of calculating the stroke length of the motor of the linear compressor comprises solving

X

=

L

i

α



∫

f

^





t

=

x

^

initial

+

x

^



(

t

)

where {circumflex over (x)} is an estimated position of the motor of the linear compressor.

17 . The method of claim 10 , further comprising adjusting the time varying voltage supplied to the motor of the linear compressor in order to operate the motor of the linear compressor at a resonant frequency of the motor of the linear compressor.