Patent Publication Number: US-9890778-B2

Title: Method for operating a linear compressor

Description:
FIELD OF THE INVENTION 
     The present subject matter relates generally to linear compressors, such as linear compressors for refrigerator appliances. 
     BACKGROUND OF THE INVENTION 
     Certain refrigerator appliances include sealed systems for cooling chilled chambers of the refrigerator appliances. The sealed systems generally include a compressor that generates compressed refrigerant during operation of the sealed systems. The compressed refrigerant flows to an evaporator where heat exchange between the chilled chambers and the refrigerant cools the chilled chambers and food items located therein. 
     Recently, certain refrigerator appliances have included linear compressors for compressing refrigerant. Linear compressors generally include a piston and a driving coil. A current is induced in the driving coil that generates a force for sliding the piston forward and backward within a chamber. During motion of the piston within the chamber, the piston compresses refrigerant. Motion of the piston within the chamber is generally controlled such that the piston does not crash against another component of the linear compressor during motion of the piston within the chamber. Such head crashing can damage various components of the linear compressor, such as the piston or an associated cylinder. 
     While head crashing is preferably avoided, it can be difficult to determine a position of the piston within the chamber. For example, parameters of the linear compressor can vary due to material and/or production differences. In addition, utilizing a sensor to measure the position of the piston can require sensor wires to pierce a hermetically sealed shell of the linear compressor. Passing the sensor wires through the shell provides a path for contaminants to enter the shell. 
     Accordingly, a method for detecting head crashing within a linear compressor would be useful. In particular, a method for detecting head crashing within a linear compressor that does not require a sensor to determine a position of the piston would be useful. 
     BRIEF DESCRIPTION OF THE INVENTION 
     The present subject matter provides a method for operating a linear compressor. The method includes measuring a current induced in a motor of the linear compressor and calculating an observed current of the motor of the linear compressor using at least an electrical dynamic model for the linear compressor and a robust integral of the sign of the error feedback. The method also includes detecting a head crash within the linear compressor if an error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor is greater than a crash threshold. Additional aspects and advantages of the invention will be set forth in part in the following description, or may be apparent from the description, or may be learned through practice of the invention. 
     In a first exemplary embodiment, a method for operating a linear compressor is provided. The method includes supplying a motor of the linear compressor with a time varying voltage, measuring a current induced in the motor of the linear compressor during the step of supplying and calculating an observed current of the motor of the linear compressor using at least an electrical dynamic model for the linear compressor and a robust integral of the sign of the error feedback. The method also includes determining an error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor and detecting a head crash within the linear compressor if the error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor is greater than a crash threshold. 
     In a second exemplary embodiment, a method for operating a linear compressor is provided. The method includes supplying a motor of the linear compressor with a time varying voltage, measuring a current induced in the motor of the linear compressor during the step of supplying, filtering the measured current induced in the motor of the linear compressor and calculating an observed current of the motor of the linear compressor using at least an electrical dynamic model for the linear compressor and a robust integral of the sign of the error feedback. The method also includes determining an error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor, obtaining a moving average of the error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor and detecting a head crash within the linear compressor if the moving average of the error between the observed current of the motor of the linear compressor and the measured current induced in the motor of the linear compressor is greater than a crash threshold. 
     These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures. 
         FIG. 1  is a front elevation view of a refrigerator appliance according to an exemplary embodiment of the present subject matter. 
         FIG. 2  is schematic view of certain components of the exemplary refrigerator appliance of  FIG. 1 . 
         FIG. 3  provides a perspective view of a linear compressor according to an exemplary embodiment of the present subject matter. 
         FIG. 4  provides a side section view of the exemplary linear compressor of  FIG. 3 . 
         FIG. 5  provides an exploded view of the exemplary linear compressor of  FIG. 4 . 
         FIG. 6  illustrates a method for operating a linear compressor according to an exemplary embodiment of the present subject matter. 
         FIG. 7  illustrates a method for operating a linear compressor according to another exemplary embodiment of the present subject matter. 
         FIGS. 8, 9 and 10  illustrate exemplary plots of experimental electrical motor parameter estimates. 
         FIGS. 11, 12 and 13  illustrate exemplary plots of experimental head crash detection. 
     
    
    
     DETAILED DESCRIPTION 
     Reference now will be made in detail to embodiments of the invention, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents. 
       FIG. 1  depicts a refrigerator appliance  10  that incorporates a sealed refrigeration system  60  ( FIG. 2 ). It should be appreciated that the term “refrigerator appliance” is used in a generic sense herein to encompass any manner of refrigeration appliance, such as a freezer, refrigerator/freezer combination, and any style or model of conventional refrigerator. In addition, it should be understood that the present subject matter is not limited to use in appliances. Thus, the present subject matter may be used for any other suitable purpose, such as vapor compression within air conditioning units or air compression within air compressors. 
     In the illustrated exemplary embodiment shown in  FIG. 1 , the refrigerator appliance  10  is depicted as an upright refrigerator having a cabinet or casing  12  that defines a number of internal chilled storage compartments. In particular, refrigerator appliance  10  includes upper fresh-food compartments  14  having doors  16  and lower freezer compartment  18  having upper drawer  20  and lower drawer  22 . The drawers  20  and  22  are “pull-out” drawers in that they can be manually moved into and out of the freezer compartment  18  on suitable slide mechanisms. 
       FIG. 2  is a schematic view of certain components of refrigerator appliance  10 , including a sealed refrigeration system  60  of refrigerator appliance  10 . A machinery compartment  62  contains components for executing a known vapor compression cycle for cooling air. The components include a compressor  64 , a condenser  66 , an expansion device  68 , and an evaporator  70  connected in series and charged with a refrigerant. As will be understood by those skilled in the art, refrigeration system  60  may include additional components, e.g., at least one additional evaporator, compressor, expansion device, and/or condenser. As an example, refrigeration system  60  may include two evaporators. 
     Within refrigeration system  60 , refrigerant flows into compressor  64 , which operates to increase the pressure of the refrigerant. This compression of the refrigerant raises its temperature, which is lowered by passing the refrigerant through condenser  66 . Within condenser  66 , heat exchange with ambient air takes place so as to cool the refrigerant. A fan  72  is used to pull air across condenser  66 , as illustrated by arrows A C , so as to provide forced convection for a more rapid and efficient heat exchange between the refrigerant within condenser  66  and the ambient air. Thus, as will be understood by those skilled in the art, increasing air flow across condenser  66  can, e.g., increase the efficiency of condenser  66  by improving cooling of the refrigerant contained therein. 
     An expansion device (e.g., a valve, capillary tube, or other restriction device)  68  receives refrigerant from condenser  66 . From expansion device  68 , the refrigerant enters evaporator  70 . Upon exiting expansion device  68  and entering evaporator  70 , the refrigerant drops in pressure. Due to the pressure drop and/or phase change of the refrigerant, evaporator  70  is cool relative to compartments  14  and  18  of refrigerator appliance  10 . As such, cooled air is produced and refrigerates compartments  14  and  18  of refrigerator appliance  10 . Thus, evaporator  70  is a type of heat exchanger which transfers heat from air passing over evaporator  70  to refrigerant flowing through evaporator  70 . 
     Collectively, the vapor compression cycle components in a refrigeration circuit, associated fans, and associated compartments are sometimes referred to as a sealed refrigeration system operable to force cold air through compartments  14 ,  18  ( FIG. 1 ). The refrigeration system  60  depicted in  FIG. 2  is provided by way of example only. Thus, it is within the scope of the present subject matter for other configurations of the refrigeration system to be used as well. 
       FIG. 3  provides a perspective view of a linear compressor  100  according to an exemplary embodiment of the present subject matter.  FIG. 4  provides a side section view of linear compressor  100 .  FIG. 5  provides an exploded side section view of linear compressor  100 . As discussed in greater detail below, linear compressor  100  is operable to increase a pressure of fluid within a chamber  112  of linear compressor  100 . Linear compressor  100  may be used to compress any suitable fluid, such as refrigerant or air. In particular, linear compressor  100  may be used in a refrigerator appliance, such as refrigerator appliance  10  ( FIG. 1 ) in which linear compressor  100  may be used as compressor  64  ( FIG. 2 ). As may be seen in  FIG. 3 , linear compressor  100  defines an axial direction A, a radial direction R and a circumferential direction C. Linear compressor  100  may be enclosed within a hermetic or air-tight shell (not shown). The hermetic shell can, e.g., hinder or prevent refrigerant from leaking or escaping from refrigeration system  60 . 
     Turning now to  FIG. 4 , linear compressor  100  includes a casing  110  that extends between a first end portion  102  and a second end portion  104 , e.g., along the axial direction A. Casing  110  includes various static or non-moving structural components of linear compressor  100 . In particular, casing  110  includes a cylinder assembly  111  that defines a chamber  112 . Cylinder assembly  111  is positioned at or adjacent second end portion  104  of casing  110 . Chamber  112  extends longitudinally along the axial direction A. Casing  110  also includes a motor mount mid-section  113  and an end cap  115  positioned opposite each other about a motor. A stator, e.g., including an outer back iron  150  and a driving coil  152 , of the motor is mounted or secured to casing  110 , e.g., such that the stator is sandwiched between motor mount mid-section  113  and end cap  115  of casing  110 . Linear compressor  100  also includes valves (such as a discharge valve assembly  117  at an end of chamber  112 ) that permit refrigerant to enter and exit chamber  112  during operation of linear compressor  100 . 
     A piston assembly  114  with a piston head  116  is slidably received within chamber  112  of cylinder assembly  111 . In particular, piston assembly  114  is slidable along a first axis A 1  within chamber  112 . The first axis A 1  may be substantially parallel to the axial direction A. During sliding of piston head  116  within chamber  112 , piston head  116  compresses refrigerant within chamber  112 . As an example, from a top dead center position, piston head  116  can slide within chamber  112  towards a bottom dead center position along the axial direction A, i.e., an expansion stroke of piston head  116 . When piston head  116  reaches the bottom dead center position, piston head  116  changes directions and slides in chamber  112  back towards the top dead center position, i.e., a compression stroke of piston head  116 . It should be understood that linear compressor  100  may include an additional piston head and/or additional chamber at an opposite end of linear compressor  100 . Thus, linear compressor  100  may have multiple piston heads in alternative exemplary embodiments. 
     Linear compressor  100  also includes an inner back iron assembly  130 . Inner back iron assembly  130  is positioned in the stator of the motor. In particular, outer back iron  150  and/or driving coil  152  may extend about inner back iron assembly  130 , e.g., along the circumferential direction C. Inner back iron assembly  130  extends between a first end portion  132  and a second end portion  134 , e.g., along the axial direction A. 
     Inner back iron assembly  130  also has an outer surface  137 . At least one driving magnet  140  is mounted to inner back iron assembly  130 , e.g., at outer surface  137  of inner back iron assembly  130 . Driving magnet  140  may face and/or be exposed to driving coil  152 . In particular, driving magnet  140  may be spaced apart from driving coil  152 , e.g., along the radial direction R by an air gap AG. Thus, the air gap AG may be defined between opposing surfaces of driving magnet  140  and driving coil  152 . Driving magnet  140  may also be mounted or fixed to inner back iron assembly  130  such that an outer surface  142  of driving magnet  140  is substantially flush with outer surface  137  of inner back iron assembly  130 . Thus, driving magnet  140  may be inset within inner back iron assembly  130 . In such a manner, the magnetic field from driving coil  152  may have to pass through only a single air gap (e.g., air gap AG) between outer back iron  150  and inner back iron assembly  130  during operation of linear compressor  100 , and linear compressor  100  may be more efficient than linear compressors with air gaps on both sides of a driving magnet. 
     As may be seen in  FIG. 4 , driving coil  152  extends about inner back iron assembly  130 , e.g., along the circumferential direction C. Driving coil  152  is operable to move the inner back iron assembly  130  along a second axis A 2  during operation of driving coil  152 . The second axis may be substantially parallel to the axial direction A and/or the first axis A 1 . As an example, driving coil  152  may receive a current from a current source (not shown) in order to generate a magnetic field that engages driving magnet  140  and urges piston assembly  114  to move along the axial direction A in order to compress refrigerant within chamber  112  as described above and will be understood by those skilled in the art. In particular, the magnetic field of driving coil  152  may engage driving magnet  140  in order to move inner back iron assembly  130  along the second axis A 2  and piston head  116  along the first axis A 1  during operation of driving coil  152 . Thus, driving coil  152  may slide piston assembly  114  between the top dead center position and the bottom dead center position, e.g., by moving inner back iron assembly  130  along the second axis A 2 , during operation of driving coil  152 . 
     A piston flex mount  160  is mounted to and extends through inner back iron assembly  130 . A coupling  170  extends between piston flex mount  160  and piston assembly  114 , e.g., along the axial direction A. Thus, coupling  170  connects inner back iron assembly  130  and piston assembly  114  such that motion of inner back iron assembly  130 , e.g., along the axial direction A or the second axis A 2 , is transferred to piston assembly  114 . Piston flex mount  160  defines an input passage  162  that permits refrigerant to flow therethrough. 
     Linear compressor  100  may include various components for permitting and/or regulating operation of linear compressor  100 . In particular, linear compressor  100  includes a controller (not shown) that is configured for regulating operation of linear compressor  100 . The controller is in, e.g., operative, communication with the motor, e.g., driving coil  152  of the motor. Thus, the controller may selectively activate driving coil  152 , e.g., by supplying voltage to driving coil  152 , in order to compress refrigerant with piston assembly  114  as described above. 
     The controller includes memory and one or more processing devices such as microprocessors, CPUs or the like, such as general or special purpose microprocessors operable to execute programming instructions or micro-control code associated with operation of linear compressor  100 . The memory can represent random access memory such as DRAM, or read only memory such as ROM or FLASH. The processor executes programming instructions stored in the memory. The memory can be a separate component from the processor or can be included onboard within the processor. Alternatively, the controller may be constructed without using a microprocessor, e.g., using a combination of discrete analog and/or digital logic circuitry (such as switches, amplifiers, integrators, comparators, flip-flops, AND gates, field programmable gate arrays (FPGA), and the like) to perform control functionality instead of relying upon software. 
     Linear compressor  100  also includes a spring assembly  120 . Spring assembly  120  is positioned in inner back iron assembly  130 . In particular, inner back iron assembly  130  may extend about spring assembly  120 , e.g., along the circumferential direction C. Spring assembly  120  also extends between first and second end portions  102  and  104  of casing  110 , e.g., along the axial direction A. Spring assembly  120  assists with coupling inner back iron assembly  130  to casing  110 , e.g., cylinder assembly  111  of casing  110 . In particular, inner back iron assembly  130  is fixed to spring assembly  120  at a middle portion  119  of spring assembly  120 . 
     During operation of driving coil  152 , spring assembly  120  supports inner back iron assembly  130 . In particular, inner back iron assembly  130  is suspended by spring assembly  120  within the stator or the motor of linear compressor  100  such that motion of inner back iron assembly  130  along the radial direction R is hindered or limited while motion along the second axis A 2  is relatively unimpeded. Thus, spring assembly  120  may be substantially stiffer along the radial direction R than along the axial direction A. In such a manner, spring assembly  120  can assist with maintaining a uniformity of the air gap AG between driving magnet  140  and driving coil  152 , e.g., along the radial direction R, during operation of the motor and movement of inner back iron assembly  130  on the second axis A 2 . Spring assembly  120  can also assist with hindering side pull forces of the motor from transmitting to piston assembly  114  and being reacted in cylinder assembly  111  as a friction loss. 
       FIG. 6  illustrates a method  600  for operating a linear compressor according to an exemplary embodiment of the present subject matter. Method  600  may be used to operate any suitable linear compressor. For example, method  600  may be used to operate linear compressor  100  ( FIG. 3 ). Thus, method  600  is discussed in greater detail below with reference to linear compressor  100 . Utilizing method  600  various mechanical and electrical parameters or constants of linear compressor  100  may be established or determined. For example, method  600  may assist with determining or establishing a spring constant of spring assembly  120 , a motor force constant of the motor of linear compressor  100 , a damping coefficient of linear compressor  100 , a resistance of the motor of linear compressor  100 , an inductance of the motor of linear compressor  100 , a moving mass (such as mass of piston assembly  114  and inner back iron assembly  130 ) of linear compressor  100 , etc. Knowledge of such mechanical and electrical parameters or constants of linear compressor  100  may improve performance or operation of linear compressor  100 , as will be understood by those skilled in the art. 
     At step  610 , an electrical dynamic model for the motor of linear compressor  100  is provided. Any suitable electrical dynamic model for the motor of linear compressor  100  may be provided at step  610 . For example, the electrical dynamic model for the motor of linear compressor  100  may be 
     
       
         
           
             
               
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     where
         v a  is a voltage across the motor of linear compressor  100 ;   r i  is a resistance of the motor of linear compressor  100 ;   i is a current induced in the motor of linear compressor  100 ;   α is a motor force constant;   {dot over (x)} is a velocity of the motor of linear compressor  100 ; and   L i  is an inductance of the motor of linear compressor  100 .       

     The electrical dynamic model for the motor of linear compressor  100  includes a plurality of unknown constants. In the example provided above, the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  includes the resistance of the motor of linear compressor  100  (e.g., the resistance of driving coil  152 ), the inductance of the motor of linear compressor  100  (e.g., the inductance of driving coil  152 ), and the motor force constant. Knowledge or accurate estimates of such unknown constants can improve operation of linear compressor  100 , e.g., by permitting operation of linear compressor  100  at a resonant frequency without head crashing. 
     At step  610 , the electrical dynamic model for the motor of linear compressor  100  may also be solved for a particular variable, such as di/dt in the example provided above. Thus, as an example, the electrical dynamic model for the motor of linear compressor  100  may be provided in parametric form as 
     
       
         
           
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     However, di/dt is difficult to accurately measure or determine. Thus, a filtering technique may be used to account for this signal and provide a useable or implementable signal. In particular, the electrical dynamic model for the motor of linear compressor  100  may be filtered, e.g., with a low-pass filter, to account for this signal. Thus, a filtered electrical dynamic model for the motor of linear compressor  100  may be provided as
 
Φ f   W f θ e .
 
     In alternative exemplary embodiments, the electrical dynamic model for the motor of linear compressor  100  may be solved for {dot over (x)} at step  610 . Thus, the electrical dynamic model for the motor of linear compressor  100  may be provided in parametric form as 
             Φ   ⁢     =   Δ     ⁢     W   ⁢           ⁢     θ   e                 where               Φ   ⁢     =   Δ     ⁢     [       d   ⁢           ⁢   i       d   ⁢           ⁢   t       ]       ;                 W   ⁢     =   Δ     ⁢     [           v   a           -   i           -       d   ⁢           ⁢   i       d   ⁢           ⁢   t               ]       ;   and                 θ   e     ⁢     =   Δ     ⁢       [           1   ∝             r   i     ∝             L   i     ∝           ]     .           
Again, the electrical dynamic model for the motor of linear compressor  100  may be filtered, e.g., to account for di/dt.
 
     At step  620 , each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  is estimated. For example, a manufacturer of linear compressor  100  may have a rough estimate or approximation for the value of each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100 . Thus, such values of the each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  may be provided at step  620  to estimate each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100 . 
     At step  630 , the motor (e.g., driving coil  152 ) of linear compressor  100  is supplied with a time varying voltage, e.g., by the controller of linear compressor  100 . Any suitable time varying voltage may be supplied to the motor of linear compressor  100  at step  630 . For example, the time varying voltage may have at least two frequencies components at step  630  when the electrical dynamic model for the motor of linear compressor  100  is solved for di/dt. Thus, the time varying voltage may be
 
 v    a ( t )= v   0 [sin(2π f   1   t )+sin(2π f   2   t )]
 
     where
         v a  is a voltage across the motor of linear compressor  100 ;   f 1  is a first frequency; and   f 2  is a second frequency.
 
The first and second frequencies f 1 , f 2  may be about the resonant frequency of linear compressor  100 . In particular, the first and second frequencies f 1 , f 2  may be just greater than and just less than the resonant frequency of linear compressor  100 , respectively. For example, the first frequency f 1  may be within five percent greater than the resonant frequency of linear compressor  100 , and the second frequency f 2  may be within five percent less than the resonant frequency of linear compressor  100 . In alternative exemplary embodiments, the time varying voltage may have a single frequency at step  630 , e.g., when the electrical dynamic model for the motor of linear compressor  100  is solved for {dot over (x)}. When the time varying voltage has a single frequency at step  630 , the gas force of fluid within linear compressor  100  may be incorporated within the model for the motor of linear compressor  100 .
       

     A time varying current through the motor of linear compressor  100  may also be determined, e.g., during step  630 . An ammeter or any other suitable method or mechanism may be used to determine the time varying current through the motor of linear compressor  100 . A velocity of the motor of linear compressor  100  may also be measured, e.g., during step  630 . As an example, an optical sensor, a Hall effect sensor or any other suitable sensor may be positioned adjacent piston assembly  114  and/or inner back iron assembly  130  in order to permit such sensor to measure the velocity of the motor of linear compressor  100  at step  630 . Thus, piston assembly  114  and/or inner back iron assembly  130  may be directly observed in order to measure the velocity of the motor of linear compressor  100  at step  630 . In addition, a filtered first derivative of the current through the motor of linear compressor  100  with respect to time may also be measured or determined, e.g., during step  630 . Accordingly, the values or filtered values of W may be measured during step  630 . To permit such measuring, step  630  and the measurements described above may be conducted prior to sealing the motor of linear compressor  100  within a hermetic shell. 
     At step  640 , an error between a measured variable (e.g., di/dt or {dot over (x)}) of the electrical dynamic model at a first time and an estimated variable of the electrical dynamic model at the first time is calculated. For example, an estimate of θ e , {circumflex over (θ)} e , is available, e.g., from step  620 . An error between θ e  and {circumflex over (θ)} e  may be given as
 
{tilde over (θ)} e   θ e −{circumflex over (θ)} e .
 
However, θ e  may be unknown while Φ f  is known or measured. Thus, a related error signal may be used at step  640 . The related error signal may be given as
 
{tilde over (Φ)} f   Φ f −{circumflex over (Φ)} f .
 
The related error signal along with W f  may be used to update {circumflex over (θ)} e , as described in greater detail below.
 
     At step  650 , the estimate for each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  are repeatedly updated at each time after the first time in order to reduce the error between a measured variable of the electrical dynamic model at each time after the first time and an estimated variable of the electrical dynamic model at each time after the first time. In particular, an adaptive least-squares algorithm may be utilized in order to drive the error between the measured value for the electrical dynamic model at each time after the first time and the estimated variable of the electrical dynamic model at each time after the first time towards zero. In particular, the Adaptive Least-Squares Update Law ensures that
 
{tilde over (θ)} e ( t )→0 as  t →∞:
 
                     θ   ^     .     e     ⁢     =   Δ     ⁢       -     k   e       ⁢         P   e     ⁢     W   f   T     ⁢       Φ   ~     f         1   +       γ   e     ⁢     W   f     ⁢     P   e     ⁢     W   f   T               ,         
{circumflex over (θ)} e (t 0 ) is estimated, e.g., at step  620 .
 
     where P e (t)ε   3×3  is the covariance matrix 
     
       
         
           
             
               
                 
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     where k e , γ e , ρ e , ε   +  are constant gains. 
     From {circumflex over (θ)} e , estimates of each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  may be given as 
                 α   ^     =         θ   ^       e   3           θ   ^       e   1           ,       R   ^     =         θ   ^       e   2           θ   ^       e   1           ,       L   ^     =     1       θ   ^       e   1                 
when the electrical dynamic model for the motor of linear compressor  100  is solved for di/dt at step  610  or
 
                 α   ^     =     1       θ   ^       e   1           ,       R   ^     =         θ   ^       e   2           θ   ^       e   1           ,       L   ^     =         θ   ^       e   3           θ   ^       e   1                 
when the electrical dynamic model for the motor of linear compressor  100  is solved for {dot over (x)} at step  610 .
 
       FIGS. 8, 9 and 10  illustrate exemplary plots of experimental electrical motor parameter estimates, e.g., taken during steps  640  and  650 . As may be seen in  FIGS. 8, 9 and 10 , the initial estimate provided for the electrical motor parameters of linear compressor  100  may be off an actual or previously determined value. However, the experimental electrical motor parameter estimates converge to the previously determined values over time. 
     With the unknown constants of the electrical dynamic model for the motor of linear compressor  100  suitably estimated, a final estimate for each unknown constant of the plurality of unknown constants of the electrical dynamic model for the motor of linear compressor  100  may be saved within the controller of linear compressor  100 . The saved constant values may be used to facilitate efficient and/or proper operation of linear compressor  100 . In particular, knowledge of the constants of the electrical dynamic model for the motor of linear compressor  100  may assist with operating linear compressor  100  at a resonant frequency while avoiding head crashing. 
     As discussed above, method  600  may also provide estimates of the mechanical parameters or constants of linear compressor  100 . Thus, method  600  may also include providing a mechanical dynamic model for linear compressor  100 . Any suitable mechanical dynamic model for linear compressor  100  may be provided. For example, the mechanical dynamic model for linear compressor  100  may be 
     
       
         
           
             
               F 
               m 
             
             = 
             
               
                 i 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     M 
                     α 
                   
                   ⁢ 
                   
                     x 
                     ¨ 
                   
                 
                 + 
                 
                   
                     C 
                     α 
                   
                   ⁢ 
                   
                     x 
                     . 
                   
                 
                 + 
                 
                   
                     K 
                     α 
                   
                   ⁢ 
                   x 
                 
               
             
           
         
       
     
     where
         M is a moving mass of linear compressor  100 ;   α is a motor force constant;   {umlaut over (x)} is an acceleration of the motor of linear compressor  100 ;   C is a damping coefficient of linear compressor  100 ;   {dot over (x)} is a velocity of the motor of linear compressor  100 ;   K is a spring stiffness of linear compressor  100 ; and   x is a position of the moving mass of linear compressor  100 .       

     The mechanical dynamic model for linear compressor  100  includes a plurality of unknown constants. In the example provided above, the plurality of unknown constants of the mechanical dynamic model of linear compressor  100  includes a moving mass of linear compressor  100  (e.g., a mass of piston assembly  114  and inner back iron assembly  130 ), a damping coefficient of linear compressor  100 , and a spring stiffness of linear compressor  100  (e.g., a stiffness of spring assembly  120 ). Knowledge or accurate estimates of such unknown constants can improve operation of linear compressor  100 , e.g., by permitting operation of linear compressor  100  at a resonant frequency without head crashing. 
     The mechanical dynamic model for linear compressor  100  may also be solved for a particular variable, such as i(t) in the example provided above. Thus, as an example, the electrical dynamic model for the motor of linear compressor  100  may be provided in parametric form as 
     
       
         
           
             Ψ 
             ⁢ 
             
               = 
               Δ 
             
             ⁢ 
             
               Y 
               ⁢ 
               
                   
               
               ⁢ 
               
                 θ 
                 m 
               
             
           
         
       
       
         
           
             w 
             ⁢ 
             here 
           
         
       
       
         
           
             
               Ψ 
               ⁢ 
               
                 = 
                 Δ 
               
               ⁢ 
               
                 [ 
                 i 
                 ] 
               
             
             ; 
           
         
       
       
         
           
             
               Y 
               ⁢ 
               
                 = 
                 Δ 
               
               ⁢ 
               
                 [ 
                 
                   
                     
                       
                         x 
                         ¨ 
                       
                     
                     
                       
                         x 
                         . 
                       
                     
                     
                       x 
                     
                   
                 
                 ] 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               θ 
               m 
             
             ⁢ 
             
               = 
               Δ 
             
             ⁢ 
             
               
                 
                   [ 
                   
                     
                       
                         
                           M 
                           ∝ 
                         
                       
                       
                         
                           C 
                           ∝ 
                         
                       
                       
                         
                           K 
                           ∝ 
                         
                       
                     
                   
                   ] 
                 
                 T 
               
               . 
             
           
         
       
     
     However, {umlaut over (x)} is difficult to accurately measure or determine. Thus, a filtering technique may be used to account for this signal and provide a measurable variable. In particular, the mechanical dynamic model for linear compressor  100  may be filtered, e.g., with a low-pass filter, to account for this signal. Thus, a filtered electrical dynamic model for the motor of linear compressor  100  may be provided as
 
Ψ f   Y f θ m .
 
Each unknown constant of the plurality of unknown constants of the mechanical dynamic model for linear compressor  100  may also be estimated, and the motor (e.g., driving coil  152 ) of linear compressor  100  may be supplied with a time varying voltage, e.g., in the manner described above for steps  620  and  630 .
 
     An error between a measured variable of the mechanical dynamic model at the first time and an estimated variable of the mechanical dynamic model at the first time may also be calculated. For example, an estimate of θ m , {circumflex over (θ)} m , is available as discussed above. An error between θ m  and {circumflex over (θ)} m  may be given as
 
{tilde over (θ)} m   θ m −{circumflex over (θ)} m .
 
However, θ m  may be unknown while Ψ f  is known or measured. Thus, a related error signal may be used. The related error signal may be given as
 
{tilde over (Ψ)} f   Ψ f −{circumflex over (Ψ)} f .
 
The related error signal along with Y f  may be used to update {circumflex over (θ)} m , as described in greater detail below.
 
     The estimate for each unknown constant of the plurality of unknown constants of the mechanical dynamic model for linear compressor  100  are repeatedly updated at each time after the first time in order to reduce the error between a measured variable of the mechanical dynamic model at each time after the first time and an estimated variable of the mechanical dynamic model at each time after the first time. In particular, an adaptive least-squares algorithm may be utilized in order to drive the error between the measured value for the mechanical dynamic model at each time after the first time and the estimated variable of the mechanical dynamic model at each time after the first time towards zero. In particular, the Adaptive Least-Squares Update Law ensures that 
     
       
         
           
             
               
                 
                   θ 
                   ~ 
                 
                 m 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             → 
             
               
                 0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 as 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 t 
               
               → 
               
                 ∞ 
                 ⁢ 
                 
                   : 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     θ 
                     ^ 
                   
                   . 
                 
                 m 
               
               ⁢ 
               
                 = 
                 Δ 
               
               ⁢ 
               
                 
                   - 
                   
                     k 
                     m 
                   
                 
                 ⁢ 
                 
                   
                     
                       P 
                       m 
                     
                     ⁢ 
                     
                       Y 
                       f 
                       T 
                     
                     ⁢ 
                     
                       
                         Ψ 
                         ~ 
                       
                       f 
                     
                   
                   
                     1 
                     + 
                     
                       
                         γ 
                         m 
                       
                       ⁢ 
                       
                         Y 
                         f 
                       
                       ⁢ 
                       
                         P 
                         m 
                       
                       ⁢ 
                       
                         Y 
                         f 
                         T 
                       
                     
                   
                 
               
             
             , 
             
               
                 
                   
                     θ 
                     ^ 
                   
                   m 
                 
                 ⁡ 
                 
                   ( 
                   
                     t 
                     0 
                   
                   ) 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               is 
               ⁢ 
               
                   
               
               ⁢ 
               
                 estimated 
                 . 
               
             
           
         
       
     
     where P m (t)ε   3×3  is the covariance matrix 
     
       
         
           
             
               
                 
                   P 
                   . 
                 
                 m 
               
               ⁢ 
               
                 = 
                 Δ 
               
               ⁢ 
               
                 
                   - 
                   
                     k 
                     m 
                   
                 
                 ⁢ 
                 
                   
                     
                       P 
                       m 
                     
                     ⁢ 
                     
                       Y 
                       f 
                       T 
                     
                     ⁢ 
                     
                       Y 
                       f 
                     
                     ⁢ 
                     
                       P 
                       m 
                     
                   
                   
                     1 
                     + 
                     
                       
                         γ 
                         m 
                       
                       ⁢ 
                       
                         Y 
                         f 
                       
                       ⁢ 
                       
                         Y 
                         f 
                         T 
                       
                     
                   
                 
               
             
             , 
             
               
                 
                   P 
                   m 
                 
                 ⁡ 
                 
                   ( 
                   
                     t 
                     0 
                   
                   ) 
                 
               
               = 
               
                 
                   ρ 
                   m 
                 
                 ⁢ 
                 
                   I 
                   3 
                 
               
             
           
         
       
     
     where k m , γ m , ρ m ε   +  are constant gains. 
     From {circumflex over (θ)} m  and the estimate of the motor force constant from step  650 , estimates of each unknown constant of the plurality of unknown constants of the mechanical dynamic model for linear compressor  100  may be given as
 
{circumflex over (M)}={circumflex over (α)}{circumflex over (θ)} m     1   ,Ĉ={circumflex over (α)}{circumflex over (θ)} m     2   ,{circumflex over (K)}={circumflex over (α)}{circumflex over (θ)} m     3   .
 
     With the unknown constants of the mechanical dynamic model for linear compressor  100  suitably estimated, a final estimate for each unknown constant of the plurality of unknown constants of the mechanical dynamic model for linear compressor  100  may be saved within the controller of linear compressor  100 . The saved constant values may be used to facilitate efficient and/or proper operation of linear compressor  100 . In particular, knowledge of the constants of the mechanical dynamic model for linear compressor  100  may assist with operating linear compressor  100  at a resonant frequency while avoiding head crashing. 
       FIG. 7  illustrates a method  700  for operating a linear compressor according to another exemplary embodiment of the present subject matter. Method  700  may be used to operate any suitable linear compressor. For example, method  700  may be used to operate linear compressor  100  ( FIG. 3 ). Thus, method  700  is discussed in greater detail below with reference to linear compressor  100 . Utilizing method  700 , a head crash (e.g., contact or impact between piston head  116  and discharge valve assembly  117 ) within linear compressor  100  may be detected. Detecting head crashes within linear compressor  100  may improve performance or operation of linear compressor  100 , as will be understood by those skilled in the art. 
     As may be seen in  FIG. 7 , the motor (e.g., driving coil  152 ) of linear compressor  100  is supplied with a time varying voltage, v a , e.g., by the controller of linear compressor  100 . Any suitable time varying voltage v a  may be supplied to the motor of linear compressor  100 . As an example, the motor (e.g., driving coil  152 ) of linear compressor  100  may be supplied with a time varying voltage v a  in the manner described above for step  630  of method  600 . Method  700  also includes measuring or determining a time varying current i a  induced in the motor of linear compressor  100 , e.g., while the time varying voltage v a  is supplied to the motor of linear compressor  100 . An ammeter or any other suitable method or mechanism may be used to determine the time varying current i a  induced in the motor of linear compressor  100 . As shown in  FIG. 7 , the measured current i a  induced in the motor of linear compressor  100  may be filtered, e.g., with a low pass or Butterworth filter. 
     Method  700  includes utilizing a robust integral of the sign of the error feedback (RISE) observer, e.g., within the memory of the controller of linear compressor  100 . The RISE observer utilizes at least an electrical dynamic model for the motor of linear compressor  100  and a mechanical dynamic model for the motor of linear compressor  100  to observe or estimate a current î through the motor of linear compressor  100 . An error between the measured current i a  induced in the motor of linear compressor  100  and the observed current î may be utilized to detect head crashing within linear compressor  100 . 
     Thus, method  700  includes providing an electrical dynamic model for the motor of linear compressor  100 . Any suitable electrical dynamic model for the motor of linear compressor  100  may be provided. For example, the electrical dynamic model for the motor of linear compressor  100  described above for method  600  may be used. A mechanical dynamic model for linear compressor  100  may also be provided. Any suitable mechanical dynamic model for linear compressor  100  may be provided. For example, the mechanical dynamic model for linear compressor  100  described above for method  600  may be used. As another example, the mechanical dynamic model for linear compressor  100  may be
 
 F   m   =αi+F   gas   +F   HC   =M{umlaut over (x)}+C{dot over (x)}+K ( x−x   0 )
 
     where
         M is a moving mass of linear compressor  100 ;   α is a motor force constant;   {umlaut over (x)} is an acceleration of the motor of linear compressor  100 ;   C is a damping coefficient of linear compressor  100 ;   {dot over (x)} is a velocity of the motor of linear compressor  100 ;   K is a spring stiffness of linear compressor  100 ;   x is a position of the moving mass of linear compressor  100 ;   F gas  is a gas force; and   F HC  is a head crash force.
 
Solving for velocity, the mechanical dynamic model for linear compressor  100  shown above may be given as
       

               x   .     =         -     M   C       ⁢     x   ¨       -       K   C     ⁢     (     x   -     x   0       )       +       α   C     ⁢   i     +       1   C     ⁢     F   gas       +       1   C     ⁢       F   HC     .               
During head crashes, a sudden change or discontinuity in system states for linear compressor  100  occurs. The discontinuities in the piston velocity can be shown with Dirac delta functions in acceleration {umlaut over (x)} and the head crash force F HC . Thus, the head crash force F HC  may be modeled with the following
 
 F   HC =Σ n   f   n δ( t−t   n ), n= 1,2, . . .
 
     where
         t n  is a time of the n th  crash; and   f n  is a force of the n th  crash.       

     For the RISE observer, the electrical dynamic model for linear compressor  100  and the mechanical dynamic model for linear compressor  100  may be combined. For example, the exemplary electrical and mechanical dynamic models for linear compressor  100  provided above may be combined to yield 
               v   a     =         L   i     ⁢       d   ⁢           ⁢   i       d   ⁢           ⁢   t         +       r   i     ⁢   i     +         α   2     C     ⁢   i     +       α   C     ⁢     F   gas       +       α   C     ⁢     F   HC       -         α   ⁢           ⁢   M     C     ⁢     x   ¨       -         α   ⁢           ⁢   K     C     ⁢       (     x   -     x   0       )     .               
L, r i , α, M, C and K may be known or estimated, e.g., utilizing method  600 , and v a  may be measured or otherwise known during operation of linear compressor  100  (e.g., the time varying voltage v a ). The above combination of the exemplary electrical and mechanical dynamic models may be rewritten as
 
                 d   ⁢           ⁢   i       d   ⁢           ⁢   t       =         v   a       L   i       -         r   i     ⁢   i       L   i       -   w               where             w   =       1     L   i       ⁢       (           α   2     C     ⁢   i     +       α   C     ⁢     F   gas       +       α   C     ⁢     F   HC       -         α   ⁢           ⁢   M     C     ⁢     x   ¨       -         α   ⁢           ⁢   K     C     ⁢     (     x   -     x   0       )         )     .             
As will be understood by those skilled in the art, |w(t)|, |w′(t)| and |w″(t)| are bounded, except at head crash events, t=t n . With an accurate estimate of α and C, the above combination of the exemplary electrical and mechanical dynamic models may be rewritten as
 
     
       
         
           
             
               
                 d 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 i 
               
               
                 d 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 t 
               
             
             = 
             
               
                 
                   v 
                   a 
                 
                 
                   L 
                   i 
                 
               
               - 
               
                 
                   
                     r 
                     i 
                   
                   ⁢ 
                   i 
                 
                 
                   L 
                   i 
                 
               
               - 
               
                 
                   
                     α 
                     2 
                   
                   
                     CL 
                     i 
                   
                 
                 ⁢ 
                 i 
               
               - 
               
                 w 
                 1 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               w 
               1 
             
             = 
             
               
                 1 
                 
                   L 
                   i 
                 
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       
                         α 
                         C 
                       
                       ⁢ 
                       
                         F 
                         gas 
                       
                     
                     + 
                     
                       
                         α 
                         C 
                       
                       ⁢ 
                       
                         F 
                         HC 
                       
                     
                     - 
                     
                       
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           M 
                         
                         C 
                       
                       ⁢ 
                       
                         x 
                         ¨ 
                       
                     
                     - 
                     
                       
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           K 
                         
                         C 
                       
                       ⁢ 
                       
                         ( 
                         
                           x 
                           - 
                           
                             x 
                             0 
                           
                         
                         ) 
                       
                     
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     Utilizing the above, i′ is estimated or observed, î′, such that ŵ(t)→w(t) as t→∞. An expression relating î′ to ŵ may be written as, 
                 i   ^     ′     =         v   a       L   i       -         r   i     ⁢   i       L   i       -       w   ^     .             
Error signals of the above expression may be given as
 
e î−i;
 
and
 
 e′=î′−i′=w−ŵ     {tilde over (w)} ,
 
     where
         {tilde over (w)} is an estimation error.
 
If e′(t)→0 as t→∞ then ŵ(t) converges to w(t). Thus, spikes in e(t) may be indicative of head crashes. From the above, a filtered or virtual error may be given as
 
s e′+e.
 
In addition, a time derivative of the filtered error may be given as
 
 s′=e″+e′=w′−ŵ′+e ′.
       

     For a stability analysis, a Lyapunov function may be defined as,
 
 V= ½ e   2 +½ s   2  
 
with a derivative of
 
 V′=ee′+ss′=−e   2   +s   2   +s ( w′−ŵ ′).
 
In turn, ŵ′(t) may be given as
 
{circumflex over ( w )}′=( K   1 +1) s+K   2  sgn( e )
 
     where
         K 1  and K 2  are real, positive gains; and   sgn is the signum or sign function.
 
With the above, V(t) and the error signals, e (t) and s(t), approach zero asymptotically, and e′ (t) also approaches zero asymptotically when |w(t)|, |w′(t)| and |w″(t)| are bounded. Thus, e (t) may be monitored using at least the electrical dynamic model for the motor of linear compressor  100  and a robust integral of the sign of the error feedback (i.e., with the RISE observer of the controller of linear compressor  100 ). Large spikes or changes in e (t) may correspond violations of the assumption that |w(t)|, |w′(t)| and |w″(t)| are bounded, which occurs at or due to head crashes.
       

     Thus, the RISE observer provides the observed current î through the motor of linear compressor  100 . As an example, the observed current î through the motor of linear compressor  100  may be calculated with the RISE observer by solving 
               i   ^     =         v   a       L   i       -         r   i     ⁢   i       L   i       -       (       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     )       .               
As shown in  FIG. 7 , the RISE observer also determines or calculates the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100 . As an example, the error may correspond to a difference between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100 .
 
     Method  700  also includes obtaining a moving average of the error between the observed current î of the motor of linear compressor  100  and the measured current i a  to the motor of linear compressor  100 . For example, the moving average may be taken over a period or window of about one millisecond. As used herein, the term “about” means within ten percent of the stated time when used in the context of times. Thus, it should be understood that the moving average of the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100  may also be used within the subsequent steps method  700  described below rather than the actual values of the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100 . However, it should be understood that the moving average need not be performed in various exemplary embodiments. 
     As discussed above, large spikes or changes in the error may correspond to head crashes. Thus, a head crash is detected within linear compressor  100  if the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100  is greater than a crash threshold. 
     The crash threshold may be any suitable value. For example, the crash threshold may be predetermined and stored within a memory of the controller of linear compressor  100 . As another example and as shown in  FIG. 4 , method  700  may include calculating a soft crash threshold T SC  and a hard crash threshold T HC . The soft and hard crash thresholds T SC , T HC  may be functions of a peak voltage of the time varying voltage v a  supplied to the motor of linear compressor  100 . In particular, the soft crash threshold T SC  may be calculated with the following 
     
       
         
           
             
               T 
               SC 
             
             = 
             
               
                 ( 
                 
                   min 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             
                               V 
                               peak 
                             
                             - 
                             194 
                           
                           40 
                         
                         + 
                         
                           5 
                           * 
                           
                             10 
                             
                               - 
                               4 
                             
                           
                         
                       
                       , 
                       
                         10 
                         
                           - 
                           3 
                         
                       
                     
                     } 
                   
                 
                 ) 
               
               * 
               2 
               * 
               
                 10 
                 
                   - 
                   4 
                 
               
             
           
         
       
     
     where
         V peak  is the peak voltage of the time varying voltage v a  supplied to the motor of linear compressor  100 .
 
Similarly, the hard crash threshold T HC  may be calculated with the following
       

               T   HC     =       (     min   ⁢     {             V   peak     -   194     40     +     5   *     10     -   4           ,     10     -   3         }       )     *   7   *       10     -   4       .             
Again, it should be understood that the above formula for calculating the soft crash threshold T SC  and the hard crash threshold T HC  are provided by way of example only. In alternative exemplary embodiments, the soft crash threshold T SC  and/or the hard crash threshold T HC  may be constants, functions of voltage, functions of current, functions of current and voltage, etc.
 
     Detecting the head crash may include detecting a soft head crash if the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100  is greater than the soft crash threshold T SC . For example, as shown in  FIG. 11 , mean(e) is less than the soft crash threshold T SC , thus method  700  does not detect head crashing in  FIG. 10 . Conversely, as shown in  FIG. 12 , mean(e) is greater than the soft crash threshold T SC . Thus method  700  detects soft head crashing in  FIG. 11 . In addition, detecting the head crash may include detecting a hard head crash if the error between the observed current î of the motor of linear compressor  100  and the measured current i a  induced in the motor of linear compressor  100  is greater than the hard crash threshold T HC . Thus, as shown in  FIG. 13 , mean(e) is greater than the hard crash threshold T HC . Thus, method  700  detects hard head crashing in  FIG. 13 . 
     It should be understood that method  700  may be performed with the motor of linear compressor  100  sealed within a hermitic shell of linear compressor  100 . Thus, method  700  may be performed at any suitable time during operation of linear compressor  100  in order to detect head crashing of linear compressor  100 , e.g., because moving components of linear compressor  100  need not be directly measured with a sensor. Knowledge of the head crashing within linear compressor  100  may assist with operating linear compressor  100  efficiently and/or properly. For example, such knowledge may assist with adjusting the time varying voltage supplied to the motor of the linear compressor  100  in order to operate the motor of linear compressor  100  at a resonant frequency of the motor of linear compressor  100  without or limited head crashing, e.g., as will be understood by those skilled in the art. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they include structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.