reference will now be made in detail to the embodiments of the present invention , examples of which are illustrated in the accompanying drawings , wherein like reference numerals refer to like elements throughout . the embodiments are described below to explain the present invention by referring to the figures . as shown in fig6 , the linear compressor 710 according to the present invention includes a cylinder 712 , a piston 714 and a motor stator 718 . the piston 714 is directly connected to a motor mover 713 such that it can perform reciprocation in the cylinder 712 . when alternating current is applied to motor windings , based on operation of a permanent magnet 716 , the piston 714 reciprocates . the piston 714 performs a compression cycle and an absorption cycle alternatively . here , when the center point of the reciprocation of the piston 714 is concurrent with the center point of teeth 718 a of the stator 718 , it is located at a resonant point . when the piston 714 reciprocates at the resonant point , maximum efficiency is secured . therefore , the compressor 710 is assembled , such that the center point of the reciprocation of the piston 714 is concurrent with the teeth 718 a of the stator 718 . although the center point of piston reciprocation is coincident with the resonant point when the compressor 710 is assembled , when the linear compressor 710 mounted on a refrigerator or air conditioner , is substantially driven , piston pushing appears based on loads . as a result , the center point of reciprocation moves . as shown in fig7 , when operating under a normal load , the center point cc of piston reciprocation is located at the center of the teeth 718 a of the stator . when operating under overload , the center point cl of reciprocation is moved to an absorption cycle side of the center point cc of the reciprocation under normal load . when operating under a small load , the center point cr of reciprocation is moved to a compression cycle side . as such , in order to rule out the effects of piston pushing , resonant tracing is required such that the center point of reciprocation can reach the resonant point according to load change . namely , when operating under overload , the center point cc of reciprocation is moved to the compression cycle side , such that it can reach the resonant point . on the other hand , when operating under a small load , the center point cr of reciprocation is moved to the absorption cycle side , such that it can reach the resonant point . as shown in fig8 , a controller of the linear compressor according to the present invention includes an electric circuit to apply ac power 220v , 60 hz , to the linear compressor 710 through a triac tr 1 . a controlling unit 750 outputs a trigger signal to turn on the triac tr 1 . the triac tr 1 applies ac power of 60 hz to the motor of the linear compressor 710 according to the trigger signal , such that the motor can be driven . when driving the motor , a current zero - crossing detection unit 720 detects crossing of the current applied to the linear compressor 710 , and a position detection unit 730 detects displacement of the motor of the linear compressor 710 . here , the position detection unit 730 includes coils to detect displacement of the motor thereon , such that the displacement can be detected by using the change of magnetic fields which is induced to the coils based on the position of the piston . a resonant point determination unit 740 determines a resonant point based on a current crossing detected by the current zero - crossing detection unit 720 and the phase difference of motor displacement detected by the position detection unit 730 . after that , the resonant point determination unit 740 outputs information corresponding to phase difference to a controlling unit 750 and a load determination unit 760 . here , the phase difference information refers to a phase difference magnitude . a load determination unit 760 determines whether a load is a normal load , an overload , or a small load ( non - load ), based on the phase difference information , and then provides the determination result to the controlling unit 750 . when the displacement of the motor leads by more than a phase of current to which 90 ° is added , it determines that the load is normal . on the other hand , when the displacement of the motor leads by more than a phase of current to which a value greater than 90 ° is added , it determines that the load is a small load ( non - load ). also , when the displacement of the motor leads by more than a phase of current to which a value smaller than 90 ° is added , it determines that the load is an overload . the load determination unit provides load information to the controlling unit . the controlling unit 750 determines turn - on time of the triac , based on phase difference information from the resonant point determination unit and load information from the load determination unit , and then applies a trigger signal according to the determination result to the triac tr 1 . namely , when the controlling unit 750 determines that the load is an overload , it delays turn on time of the triac tr 1 at an absorption cycle such that the center point of reciprocation can reach the resonant point or moves up turn on time of the triac tr 1 at a compression cycle , such that the center point of reciprocation can reach the resonant point . when the controlling unit determines that the load is a small load , it moves up turn on time of the absorption cycle , such that the center point of reciprocation can reach the resonant point , or delays turn on time of the triac tr 1 at the compression cycle such that the center point of reciprocation can reach the resonant point . the controller of the linear compressor 710 , which is constructed as above , will be described in detail below . first of all , the relationship between the motor current and the phase for displacement thereof is described as follows . as show in fig9 , when a turn on period of a triac is 100 %, the motor current phase lm is periodically changed between positive and negative . when zero crossing of the motor current is detected , a current zero crossing signal lmz is obtained by the current zero crossing detection unit 720 . when the linear compressor 710 is operated under a normal load , motor displacement is obtained by the position detection unit 730 . namely , a first displacement lm + 90 °, which is lead by 90 ° with respect to the phase of the motor current lm , is detected . at this time , since the center point of piston reciprocation coincides with the teeth of the stator , it is located at the resonant point . when the linear compressor is operated at the overload , motor displacement is obtained by the position detection unit 730 . namely , a second displacement lm + 90 °+ p 1 , which is lead by 90 ° plus a phase p 1 with respect to the phase of the motor current lm , is detected . at this time , the center point of piston reciprocation is moved to the absorption cycle side from the resonant point . in this situation , in order to move the center point of reciprocation to the resonant point , the controller applies a trigger signal to reduce the length of the absorption cycle or increase the length of the compression cycle to the triac tr 1 . on the other hand , when the linear compressor 710 is operated at the small load , motor displacement is obtained by the position detection unit 730 . namely , a third displacement lm + 90 °− p 2 , which is lead by 90 ° minus a phase p 2 with respect to the phase of the motor current lm , is detected . at this time , the center point of piston reciprocation is moved to the compression cycle side from the resonant point . in this situation , in order to move the center point of reciprocation to the resonant point , the controller applies a trigger signal to reduce the length of the compression cycle or increase the length of the absorption cycle to the triac tr 1 . here , when the length of the absorption cycle is increased , as shown in fig1 , the trigger signal is applied to the triac tr 1 at time t 12 prior to time t 2 . then , as the turn on period of the trigger signal is increased , when motor current is increased , since the piston cycle length increases , the center point of reciprocation is moved to the center of the teeth of the stator , thereby reaching the resonant point . as such , when the length of the compression cycle is varied , as shown in fig1 , the trigger signal is move up in the + direction , such that the turn on period of the triac tr 1 is increased ( in the case of an overload ), or the trigger signal is delayed in the − direction such that the turn on period of the triac tr 1 is shortened ( in the case of a small load ). referring to fig1 , a method for controlling a linear compressor according to the present invention is described below . when the linear compressor 710 is driven at 801 , the resonant point determination unit 740 provides a current zero crossing signal , detected by the current zero crossing detection unit 720 , and information for the phase difference of motor displacement , detected by the position detection unit 730 , to the controller 750 and the load determination unit 760 at 803 . the load determination unit 760 determines whether the operation is an overload operation , a normal load operation or a small load operation , based the phase difference information , and then provides the load information to the controller 750 at 805 . the controller 750 determines whether the center point of piston reciprocation is the resonant point based on the phase difference information at 807 . if the center point is located at the resonant point , the compressor 710 keeps its drive . on the other hand , if the center point is not located at the resonant point , the controller determines whether it is operated under an overload based on the load information at 809 . when it is operated under the overload , in order to increase the length of the compression cycle , a trigger signal of the compression cycle is moved up to be applied to the triac tr 1 , or in order to reduce the length of the absorption cycle , the trigger signal of the absorption is delayed to be applied to the triac tr 1 at 811 . on the other hand , if the operation is not under the overload , the controller 750 determines whether it is operated at the small or low load based on the load information at 813 . when the operation is at the small operation , in order to reduce the compression cycle , the trigger signal of the compression cycle is delayed to be applied to the triac tr 1 , or in order to increase the length of the absorption cycle , the trigger signal of the absorption cycle is moved up to be applied to the triac at 815 . although the above - mentioned embodiment of the present invention is implemented such that the position detection unit 730 directly detects motor displacement , modification thereof is possible , as shown in fig1 . namely , as shown in fig1 , another embodiment of the present invention is configured such that it can input motor current applied to a motor and motor voltage applied to both ends of the compressor 710 , and includes a position calculation unit 780 which calculates motor displacement based on the motor current and motor voltage . the motor displacement calculated in the position calculation unit is provided to the resonant point determination unit 740 , such that the resonant point determination unit 740 can provide the motor current and information corresponding to phase difference of the motor displacement to the controlling unit 750 and the load determination unit 760 , respectively . although methods for obtaining the motor displacements are different between the embodiments of the present invention , since trigger signals to trace the resonant point are identically processed between the same embodiments , detailed description thereof will be omitted . as mentioned above , although load conditions are varied , since the center point of piston reciprocation is controlled to coincide with the center of the teeth of the stator , and then resonant trace to maintain the resonant point , is performed , the linear compressor according to the present invention can be operated at a relatively high compression ratio and with high efficiency . also , since the resonant point and load can be determined based on the motor current and phase difference of motor displacement , and then turn on time of the triac is controlled , it is easy to trace resonance . furthermore , since the present invention does not require a relatively expensive controller to control inverters , it is cost - effective . although a few embodiments of the present invention have been shown and described , it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention , the scope of which is defined in the claims and their equivalents .