Patent Publication Number: US-6338396-B1

Title: Active magnetic guide system for elevator cage

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims benefit of priority to Japanese Patent Application No. 11-192224 filed Jul. 6, 1999, the entire content of which is incorporated by reference herein. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to an active magnetic guide system guiding a movable unit such as an elevator cage. 
     2. Description of the Background 
     In general, an elevator cage is hung by wire cables and is driven by a hoisting machine along guide rails vertically fixed in a hoistway. The elevator cage may shake due to load imbalance or passenger motion, since the elevator cage is hung by wire cables. The shake is restrained by guiding the cage along guide rails. 
     Guide systems that include wheels rolling on guide rails and suspensions, are usually used for guiding the elevator cage along the guide rails. However, unwanted noise and vibration caused by irregularities in the rail such as warps and joints, are transferred to passengers in the cage via the wheels, spoiling the comfortable ride. 
     In order to resolve the above problem, various alternative approaches have been proposed, which are disclosed in Japanese patent publication (Kokai) No. 51-116548, Japanese patent publication (Kokai) No. 6-336383, and Japanese patent publication (Kokai) No. 7-187552. These references disclose an elevator cage provided with electromagnets operating attractive forces on guide rails made of iron, whereby the cage may be guided without contact with the guide rails. 
     Japanese patent publication (Kokai) No. 7-187552 discloses an electromagnet having a pair of coils wound on an E-shaped core, which guides an elevator cage by a magnetic force. According to this technology, the comfortable ride is provided, the number of components of an electromagnet unit is reduced, the structure is simplified, and the reliability is improved. 
     However, in the present guide systems for elevators as described above, there are some following problems. 
     If a guide system is designed so as to strictly trace the guide rails, the cage may shake in response to irregularities in the rail, as a result of which a comfortable ride may worsen. Accordingly, a guide system is designed to support the elevator cage with low rigidity. However, if the cage is supported by a guide system having low rigidity, the guide system requires a large stroke in order to permit a vibration of the cage, since an amplitude of a shake of the cage becomes larger in response to disturbance forces in the guiding direction. In order to control such large stroke by using magnetic force, a gap between an electromagnet and the guide rail should be large. However, if the gap is widened, the effective flux of the electromagnet reduces due to the increase of the magnetic resistance, as a result, a guiding force for the cage remarkably reduces in proportion to the squares of the flux. 
     According to a magnetic guide system composed of electromagnets, an attractive force operating on guide rails is inversely proportional to the about squares of the gap and is proportional to the about squares of an excitation current. In general, a linear control is widely employed with respect to an attractive force control for an electromagnet. In this case, even if the elevator-cage stops at an appropriate position, the electromagnet is excited in a predetermined excitation current for the following reasons. 
     Assume that an elevator cage stops at an appropriate position. Properly speaking, it may be thought that an excitation current is set to zero, because a guiding force is not needed. However, since an attractive force of an electromagnet is proportional to the squares of the excitation current, if the attractive force is made a linear approximation on the assumption that the excitation current is zero at a steady state, a coefficient term of an infinitesimal fluctuation of a gap, and a coefficient term of an infinitesimal fluctuation of an excitation current become zero. That is, where f is an attractive force of an electromagnet, x is a gap, i is an excitation current, partial differential terms of the attraction forces with regard to the gap x and the excitation current i, which are ∂f/∂x and ∂f/∂i, become zero. Consequently, it is difficult to design a linear control system. 
     Further, in order to obtain a satisfactory performance of the linear control system, the ∂f/∂x and the ∂f/∂i have a certain large value. The value is inversely proportional to the gap and is proportional to a magnetomotive force that at is the product of the excitation current and the number of turns of an electromagnet coil. Therefore, the ∂f/∂x and the ∂f/∂i are given appropriate values by increasing the excitation current or increasing the number of turns of the electromagnet coil. Accordingly, in case of a guide system composed of an electromagnet, in order to obtain a guide system having a satisfactory performance and a low rigidity, the electromagnet is excited with a large current in advance or an electromagnet coil having a large number of turns is used. 
     However, if the excitation current is made large, a cooling system is needed due to generation of heat. Further, if the number of turns of the electromagnet coil increases, the electromagnet become large in size and weight. According to a magnetic guide system composed of an electromagnet, as the magnetic guide system becomes larger, the weight gets heavier. This results in making an entire system of an elevator large, and increasing a cost. 
     As for a technology for restraining the generation of heat of the electromagnet coil, for example, as disclosed in Japanese patent publication (Kokai) No. 60-32581 and Japanese patent publication (Kokai) No. 61-102105, it is known that a magnetic guide system forms a common magnetic circuit made by an electromagnet and a permanent magnet at a gap between the magnetic guide system and a guide rail. The object of this technology is addressed to balance a gravitational force and an attractive force in the vertical direction of the magnetic guide system, operating on guide rail, since the technology is used for carrying articles with no contact with the guide rail. Finally, the magnetic guide system operates the attractive force on at least one guide rail in only one direction so as to support a weight of a supported material and to equalize a width of the magnetic guide system with the guide rail thereof. The supported material is guided along the guide rail by an allying force operating on the guide rail. 
     Generally speaking, since a weight of an elevator cage itself is supported by wire cables, it is not required that the guide rail be strong enough to receive more than a force for supporting a horizontal motion of the elevator cage. Therefore, the rigidity of the installation for the guide rails is not always high because of reducing an installation cost of the guide rails. According to an elevator having such feature, if a magnetic guide system operates an attractive force on guide rails in only one direction, the guide rails shift off the installed position. This gives rise to a difference in level at a joint of the guide rail and a deformation, thereby spoiling the comfortable ride. 
     Moreover, if a gap between the magnetic guide system and the guide rail is widened to reduce an attractive force operating on the guide rail, an allying force of an electromagnet reduces and the guidance by the allying force is hardly expected. In case the guidance by the allying force does not work well, an additional magnetic guide system is required. Consequently, the magnetic guide system becomes larger in size and weight, resulting in a large system for an elevator, and increasing its cost. 
     SUMMARY OF THE INVENTION 
     Accordingly, one object of this invention is to provide a magnetic guide system for an elevator, which improves a comfortable ride by restraining a shake of an elevator cage effectively. 
     Another object of the present invention is to provide a minimized and simplified magnetic guide system for an elevator. 
     Another object of the present invention is to provide a magnetic guide system for an elevator, which may not entail high cost. 
     The present invention provides a magnetic guide system for an elevator, including a movable unit configured to move along a guide rail, a magnet unit attached to the movable unit, having a plurality of electromagnets having magnetic poles facing the guide rail with a gap, at least two of the magnetic poles are disposed to operate attractive forces in opposite directions to each other on the guide rail, and a permanent magnet providing a magnetomotive force for guiding the movable unit, and forming a common magnetic circuit with one of the electromagnets at the gap, a sensor configured to detect a condition of the common magnetic circuit formed with the magnet unit and the guide rail, and a guide controller configured to control excitation currents to the electromagnets in response to an output of the sensor so as to stabilize the magnetic circuit. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
     FIG. 1 is a perspective view of a magnetic guide system for an elevator cage of a first embodiment of the present invention; 
     FIG. 2 is a perspective view showing a relationship between a movable unit and guide rails; 
     FIG. 3 is a perspective view showing a structure of a magnet unit of the magnetic guide system; 
     FIG. 4 is a plan view showing magnetic circuits of the magnet unit; 
     FIG. 5 shows motion characteristics of the magnetic circuits of the magnet unit; 
     FIG. 6 is a block diagram showing a circuit of a controller; 
     FIG. 7 is a block diagram showing a circuit of a controlling voltage calculator of the controller; 
     FIG. 8 is a block diagram showing a circuit of another controlling voltage calculator of the controller; 
     FIG. 9 is a perspective view showing a structure of a magnet unit of a magnetic guide system of a second embodiment; 
     FIG. 10 is a plan view showing the magnet unit of the second embodiment; and 
     FIG. 11 is plan view showing a structure of a magnet unit of a magnetic guide system of a third embodiment. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, the embodiments of the present invention are described below. 
     The present invention is hereinafter described in detail by way of an illustrative embodiment. 
     FIGS. 1 through 4 show a magnetic guide system for an elevator cage of a first embodiment of the present invention. As shown in FIG. 1, guide rails  2  and  2 ′ made of ferromagnetic substance are disposed on the inside of a hoistway  1  by a conventional installation method. A movable unit  4  ascends and descends along the guide rails  2  and  2 ′ by using a conventional hoisting method (not shown), for example, winding wire cables  3 . 
     The movable unit  4  includes an elevator cage  10  for accommodating passengers and loads, and guide units  5   a ˜ 5   d . The guide units  5   a ˜ 5   d  include a frame  11  having a certain strength in order to maintain respective positions of the guide units  5   a ˜ 5   d.    
     The guide units  5   a ˜ 5   d  are respectively attached at the upper and lower corners of the frame  11  and face the guide rails  2  and  2 ′ respectively. As illustrated in detail in FIGS. 3 and 4, each of the guide units  5   a ˜ 5   d  includes a base  12  made of non-magnetic substance such as Aluminum, Stainless Steel or Plastic, an x-direction gap sensor  13 , a y-direction gap sensor  14  and a magnet unit  15   b . In FIGS. 3 and 4, only one guide unit  5   b  is illustrated, and other guide units  5   a ,  5   c  and  5   d  are the same structure as the guide unit  5   b . A suffix “b” represents components of the guide unit  5   b.    
     The magnet unit  15   b  includes a center core  16 , permanent magnets  17  and  17 ′, and electromagnets  18  and  18 ′. The same poles of the permanent magnets  17  and  17 ′ are facing each other putting the center core between the permanent magnets  17  and  17 ′, thereby forming an E-shape as a whole. The electromagnet  18  includes an L-shaped core  19 , a coil  20  wound on the core  19 , and a core plate  21  attached to the top of the core  19 . Likewise, the electromagnet  18 ′ includes an L-shaped core  19 ′, a coil  20 ′ wound on the core  19 ′, and a core plate  21 ′ attached to the top of the core  19 ′. As illustrated in detail in FIG. 3, solid lubricating materials  22  are disposed on the top portions of the center core  16  and the electromagnets  18  and  18 ′ so that the magnet unit  15   d  does not adsorb the guide rail  2 ′ due to an attractive force caused by the permanent magnets  17  and  17 ′, when the electromagnets  18  and  18 ′ are not excited. For example, a material containing Teflon, black lead or molybdenum disulfide may be used for the solid lubricating materials  22 . 
     In the following description, to simplify an explanation of the illustrated embodiment, suffixes “a”˜“d” are respectively added to figures indicating the main components of the respective guide units  5   a ˜ 5   d  in order to distinguish them. 
     The coils  20  and  20 ′ of the magnet unit  15   b  are individually excited. Attractive forces in both the y-direction and x-direction operating on the guide rail  2 ′ are individually controlled by the coils  20  and  20 ′. As shown in FIGS. 4 and 5, l m  is a length in the polarization direction of the permanent magnets  17  and  17 ′, H m  is a coersive force, R gb1  is a magnetic reluctance of a gap Gb between the electromagnet  18  and the guide rail  2 ′ in a magnetic circuit Mcb formed with the permanent magnet  17 , the electromagnet  18 , the guide rail  2 ′ and the center core  16 , R gb2  is a magnetic reluctance of a gap Gb′ between the electromagnet  18 ′ and the guide rail  2 ′ in a magnetic circuit Mcb′ formed with the permanent magnet, 17 ′, the electromagnet  18 ′, the guide rail  2 ′ and the center core  16 , R gb3  is a magnetic reluctance of a gap Gb″ between the center core  16  and the guide rail  2 ′, N is the number of turns of the coils  20  and  20 ′, R c1  is a magnetic reluctance in common of magnetic circuits Mlb and Mlb′ concerning a leakage flux caused by magnetomotive forces of the coils  20  and  20 ′, R p  is an internal magnetic reluctance in common of the permanent magnets  17  and  17 ′, R p1  is a magnetic reluctance in common of magnetic circuits Mpb and Mpb′ concerning a leakage flux caused by magnetomotive forces of the permanent magnets  17  and  17 ′, R ic  is an internal magnetic reluctance of a core which directs a common magnetic path of the magnetic circuits Mcb and Mcb′, R id  is an internal magnetic reluctance of a core which does not direct a common magnetic path of the magnetic circuits Mcb and Mcb′, i b1  and i b2  are excitation currents of the coils  20  and  20 ′, Φ b1  and Φ b2  are main fluxes of the magnetic circuits Mcb and Mcb′, Φ lb1  and Φ lb2  are main fluxes of the magnetic circuits Mlb and Mlb′, and Φ pb  and Φ pb2  are main fluxes of the magnetic circuits Mpb and Mpb′, a magnetic circuit formula with respect to the magnetic circuits Mcb, Mcb′, Mlb, Mlb′, Mpb, and Mpb′ is given by the following formula 1.        (     Formula                 1     )           {                 (       R   id     +     R   gb1       )          Φ   b1       +       (       R   ic     +     R   gb3       )          (       Φ   b1     +     Φ   b2       )       +       R   p          (       Φ   b1     +     Φ   pb1       )         =       Ni   b1     +       H   m          l   m                           (       R   id     +     R   gb2       )          Φ   b2       +       (       R   ic     +     R   gb3       )          (       Φ   b1     +     Φ   b2       )       +       R   p          (       Φ   b2     +     Φ   pb2       )         =       Ni   b2     +       H   m          l   m                         R   cl          Φ   lb1       =     Ni   b1                     R   cl          Φ   lb2       =     Ni   b2                       R   pl          Φ   pb1       +       R   p          (       Φ   b1     +     Φ   pb1       )         =       H   m          l   m                         R   pl          Φ   pb2       +       R   p          (       Φ   b2     +     Φ   pb2       )         =       H   m          l   m                               
     In the above formula 1, R gb1  and R gb2  vary, when the magnet unit  15   b  moves in the y-direction, and R gb3  varies, when the magnet unit  15   b  moves in the x-direction. In formulas 1, μ 0  is a permeability in a vacuum, S y  is an effective cross section of a magnetic path forming the magnetic reluctances R gb1  and R gb2 , S X  is an effective cross section of a magnetic path forming the magnetic reluctances R gb3 , S p  is an effective cross section of a magnetic path forming the magnetic reluctances R p , l r  is the sum of gap lengths concerning the magnetic reluctances R gb1  and R gb2 . The reluctances R gb1 , R gb2 , R gb3  and R p  are given by the following formula 2, assuming that a position of the magnet unit  15   b  where the lengths of the gaps Gb and Gb′ are the same each other is a home position of the y-direction.                  R   gb1     =           l   r     2     +     y   b           μ   0          S   y           ,       R   gb2     =           l   r     2     -     y   b           μ   0          S   y           ,       R   gb3     =       x   b         μ   0          S   x           ,       R   p     =       l   m         μ   0          S   p                   (     Formula                 2     )                         
     The term X b  is a length of the gap Gb″ of the magnet unit  15   b . The term Y b  is a change in they-direction from the home position. 
     To simplify calculations, assuming that the internal magnetic reluctances Rid and Ric, and leakage fluxes Φ lb1 , Φ lb2 , Φ pb1 , Φ pb2  are small enough to be disregarded, main fluxes Φ b1 , Φ b2 , Of the magnet circuits Mcb and Mcb′ are calculated as functions of X b , Y b , i b1 , i b2  as the following formula 3.                    Φ   b1          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       =         2                   μ   0          S   p          S   y                   l   r   2          S   p   2          S   x       +     4        l   r          S   p            S   y          (         l   m          S   x       +       S   p          x   b         )         +     4        l   m   2          S   x          S   y   2       +                 8        l   m          S   p          S   y   2          x   b       -     4                   S   p   2          S   x          y   b   2                 ×     (         H   m          l   m            S   x          (         l   r          S   p       +     2        l   m          S   y       -     2        S   p          y   b         )         +       Ni   b1          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     2        S   p          S   y          x   b       -     2        S   p          S   x          y   b         )       -     2        Ni   b2          S   p          S   y          x   b         )              
              Φ   b2          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       =         2                   μ   0          S   p          S   y                   l   r   2          S   p   2          S   x       +     4        l   r          S   p            S   y          (         l   m          S   x       +       S   p          x   b         )         +     4        l   m   2          S   x          S   y   2       +                 8        l   m          S   p          S   y   2          x   b       -     4                   S   p   2          S   x          y   b   2                 ×     (         H   m          l   m            S   x          (         l   r          S   p       +     2        l   m          S   y       +     2        S   p          y   b         )         -     2        Ni   b1          S   p          S   y          x   b       +       Ni   b2          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     2        S   p          S   y          x   b       +     2        S   p          S   x          y   b         )         )                 (     Formula                 3     )                         
     The following formula 4 shows respective attractive forces F b1 , F b2 , F b3  of the gaps Gb, Gb′, Gb′ of the magnet unit  15   b .                    F   b1          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       =       -     1     2        μ   0          S   y                    Φ   b1          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       2              
              F   b2          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       =       1     2        μ   0          S   y                  Φ   b2          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       2              
                    F   b3          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       =                  -     1     2        μ   0          S   y                (         Φ   b1          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       +                                        Φ   b2          (       x   b     ,     y   b     ,     i   b1     ,     i   b2       )       )       2                   (     Formula                 4     )                         
     Therefore, a force F xb  operating the magnet unit  15   b  in the x-direction and a force F yb  operating the magnet unit  15   b  in the y-direction are given by the following formula 5. 
     
       
         F xb (X b ,Y b ,i b1 ,i b2 )=F b3 (X b ,Y b ,i b1 ,i b2 ) 
       
     
     
       
         F yb (X b ,Y b ,i b1 ,i b2 )=F b1 (X b ,Y b ,i b1 ,i b2 )+F b2 (X b ,Y b ,i b1 ,i b2 )  (Formula 5) 
       
     
     Where the excitation currents i b1  and i b2  of the electromagnets  18  and  18 ′ are zero, the gap Gb″ is X o , and the magnet unit  15   b  is positioned at a home position(Y=0) of the y-axis, infinitesimal fluctuations dF xb  and dF yb  of attractive forces F xb  and F yb  concerning infinitesimal fluctuations d xb , d yb , di b1  and di b2  of x b , y b , i b1  and i b2  are given by transforming the formula 5 in accordance with the Euler&#39;s equations of motion, and then approximating in a linear equation.                     F   xb       =         (       ∂     F   xb         ∂     x   b         )               x   b         +       (       ∂     F   xb         ∂     y   b         )               y   b         +       (       ∂     F   xb         ∂     i   b1         )               i   b1         +       (       ∂     F   xb         ∂     i   b2         )               i   b2                   (     Formula                 6     )                         
     Where xb=x0, yb=0, ib 1 =0 and ib 2 =0, partial differential in parentheses is as follows.          (       ∂     F   xb         ∂     x   b         )     =       128                   H   m   2          l   m   2          μ   0   2          S   p   3          S   x   2          S   y   3           (         l   r          S   p          S   x       +     2        l   m          S   x          S   p       +     4        S   p          S   y          x   0         )     3                 (       ∂     F   xb         ∂     y   b         )     =   0             (       ∂     F   xb         ∂     i   b1         )     =         -   16                     H   m          l   m          μ   0   2          NS   p   2          S   x   2          S   y   2           (         l   r          S   p          S   x       +     2        l   m          S   x          S   p       +     4        S   p          S   y          x   0         )     2                 (       ∂     F   xb         ∂     i   b2         )     =         -   16                     H   m          l   m          μ   0   2          NS   p   2          S   x   2          S   y   2           (         l   r          S   p          S   x       +     2        l   m          S   x          S   p       +     4        S   p          S   y          x   0         )     2                                                  F   xb       =                    (       ∂     F   xb         ∂     x   b         )               x   b         +       (       ∂     F   xb         ∂     y   b         )               y   b         +                                  (       ∂     F   xb         ∂     i   b1         )               i   b1         +       (       ∂     F   xb         ∂     i   b2         )               i   b2                        
            (       ∂     F   yb         ∂     x   b         )     =   0          
            (       ∂     F   yb         ∂     y   b         )     =       32                   H   m   2          l   m   2          μ   0   2          S   p   3          S   x   2          S   y   2           (         l   r          S   p       +     2        l   m          S   y         )            (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )     2                
            (       ∂     F   yb         ∂     i   b1         )     =         -   8                     H   m          l   m          μ   0   2          NS   p   2          S   x          S   y   2           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                
            (       ∂     F   yb         ∂     i   b2         )     =       8                   H   m          l   m          μ   0   2          NS   p   2          S   x          S   y   2           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                   (     Formula                 7     )                         
     According to the above formulas, it is realized that the F xb  does not change, even if the magnet unit  15   b  shifts a little in the y-direction, and further the F yb  does not change, even if the magnet unit  15   b  shifts a little in the x-direction. Moreover, since the following formula 8 is set up, if F x  is (i b1 +i b2 ), and F y  is (i b1 −i b2 ), it is realized that the F x  and F y  may be controlled individually.                    ∂     F   xb         ∂     i   b1         =       ∂     F   xb         ∂     i   b2           ,         ∂     F   yb         ∂     i   b1         =     -       ∂     F   yb         ∂     i   b2                     (     Formula                 8     )                         
     All partial differential terms contain a coefficient of magnetomotive forces H m l m  of the permanent magnets  17  and  17 ′. Consequently, if the magnet unit  15   b  does not include a permanent magnet, and the magnetomotive force is zero, all partial differential terms become zero, and as a result, attractive forces of the magnet unit  15  may not be controlled. That is, if a magnet unit includes only electromagnets, the magnet unit may not control attractive force where excitation currents for the electromagnets are near zero. Values of all partial differential terms in the formula 6 and 7 are made large enough by selecting a permanent magnet having a large residual magnetic flux density and coersive force which contains Samarium-Cobalt or Neodymium-Iron-Boron(Nd—Fe—B) as the main ingredients, thereby facilitating an attractive force control by an excitation current to electromagnets. In the following descriptions, parentheses for partial differential are omitted for convenience at a steady state, that is, x=x 0 , y=0, i b1 =0, i b2 =0. 
     Likewise, where attractive forces in the x-direction of the magnet units  15   a ,  15   c  and  15   d  are put into F xa , F xc  and F xd  respectively, and attractive forces in the y-direction of the magnet units  15   a ,  15   c  and  15   d  are put into F ya , P yc  and F yd  respectively, the following formulas 9 and 10 are obtained.                      ∂     F   xa         ∂     x   a         =     -       ∂     F   xb         ∂     x   b             ,         ∂     F   xa         ∂     y   a         =   0     ,     
              ∂     F   xa         ∂     i   a1         =     -       ∂     F   xb         ∂     i   b1             ,         ∂     F   xa         ∂     i   a2         =     -       ∂     F   xb         ∂     i   b2                    
                ∂     F   xc         ∂     x   c         =       ∂     F   xb         ∂     x   b           ,         ∂     F   xc         ∂     y   c         =   0     ,     
              ∂     F   xc         ∂     i   c1         =       ∂     F   xb         ∂     i   b1           ,         ∂     F   xc         ∂     i   c2         =       ∂     F   xb         ∂     i   b2                  
                ∂     F   xd         ∂     x   d         =     -       ∂     F   xb         ∂     x   b             ,         ∂     F   xd         ∂     y   d         =   0     ,     
              ∂     F   xd         ∂     i   d1         =     -       ∂     F   xb         ∂     i   b1             ,         ∂     F   xd         ∂     i   d2         =     -       ∂     F   xb         ∂     i   b2                       (     Formula                 9     )                       ∂     F   ya         ∂     x   a         =   0     ,         ∂     F   ya         ∂     y   a         =       ∂     F   yb         ∂     y   b           ,     
              ∂     F   ya         ∂     i   a1         =       ∂     F   yb         ∂     i   b1           ,         ∂     F   ya         ∂     i   a2         =       ∂     F   yb         ∂     i   b2                  
                ∂     F   yc         ∂     x   c         =   0     ,         ∂     F   yc         ∂     y   c         =       ∂     F   yb         ∂     y   b           ,     
              ∂     F   yc         ∂     i   c1         =       ∂     F   yb         ∂     i   b1           ,         ∂     F   yc         ∂     i   c2         =       ∂     F   yb         ∂     i   b2                  
                ∂     F     y                 d           ∂     x   d         =   0     ,         ∂     F     y                 d           ∂     y   d         =       ∂     F   yb         ∂     y   b           ,     
              ∂     F     y                 d           ∂     i   d1         =       ∂     F   yb         ∂     i   b1           ,         ∂     F     y                 d           ∂     i   d2         =       ∂     F   yb         ∂     i   b2                     (     Formula                 10     )                         
     The above respective partial differentials of the magnet units  15   a ,  15   c  and  15   d  are in a condition of x a =x 0 , y a =0, i a1 =0, i a2 =0, x b1 =xc0, y b =0, i b1 =0, i b2 =0, x c =x 0 , y c =0, i c1 =0, i c2 =0, X d =x 0 , y d =0, i d1 =0 and i d2 =0. 
     Further, infinitesimal fluctuations of the main fluxes Φ b1  and Φ b2  in reference to x, y, i b1  and i b2  are given by the following formulas 11 and 12.                       Φ   b1       =         (       ∂     Φ   b1         ∂     x   b         )               x   b         +       (       ∂     Φ   b2         ∂     y   b         )               y   b         +       (       ∂     Φ   b2         ∂     i   b1         )               i   b1         +       (       ∂     Φ   b1         ∂     i   b2         )               i   b2                  
          {             (       ∂     Φ   b1         ∂     x   b         )     =         -   8          H   m          l   m          μ   0          S   p   2          S   x          S   y   2           (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )     2                     (       ∂     Φ   b1         ∂     y   b         )     =         -   4          H   m          l   m          μ   0          S   p   2          S   x          S   y           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                       (       ∂     Φ   b1         ∂     i   b1         )     =       2        μ   0          NS   p            S   y          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     2        S   p          S   y          x   0         )             (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                       (       ∂     Φ   b1         ∂     i   b2         )     =         -   4          μ   0          NS   p   2                     S   y   2          x   0           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                           (     Formula                 11     )                        Φ   b2       =         (       ∂     Φ   b2         ∂     x   b         )               x   b         +       (       ∂     Φ   b2         ∂     y   b         )               y   b         +       (       ∂     Φ   b2         ∂     i   b1         )               i   b1         +       (       ∂     Φ   b2         ∂     i   b2         )               i   b2                  
          {             (       ∂     Φ   b2         ∂     x   b         )     =         -   8          H   m          l   m          μ   0          S   p   2          S   x          S   y   2           (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )     2                     (       ∂     Φ   b2         ∂     y   b         )     =         -   4          H   m          l   m          μ   0          S   p   2          S   x          S   y           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                       (       ∂     Φ   b2         ∂     i   b1         )     =         -   4          μ   0          NS   p   2                     S   y   2          x   0           (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                       (       ∂     Φ   b2         ∂     i   b2         )     =       2        μ   0          NS   p                       S   y          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     2        S   p          S   y          x   0         )             (         l   r          S   p       +     2        l   m          S   y         )          (         l   r          S   p          S   x       +     2        l   m          S   x          S   y       +     4        S   p          S   y          x   0         )                           (     Formula                 12     )                         
     Where an amount of an infinitesimal fluctuation is represented by a mark Δ, currents ib 1  and ib 2  flowing in the coils  20  and  20 ′ are presented by the following voltage equations 13 and 14.                      L   x0        Δ                   i   b1   ′       +       M   x0        Δ                   i   b2   ′         =         -   N            ∂     Φ   b1         ∂   x          Δ                   x   b   ′       -     N          ∂     Φ   b1         ∂   y          Δ                   y   b   ′       -     R                 Δ                   i   b1       +     e   b1              
              L   x0     =       L   ∞     +     N          ∂     Φ   b1         ∂     i   b1               ,       M   x0     =     N          ∂     Φ   b1         ∂     i   b1                       (     Formula                 13     )                         
     Symbols “′” represent a first differentiation.                      L   x0        Δ                   i   b1   ′       +       M   x0        Δ                   i   b2   ′         =         -   N            ∂     Φ   b2         ∂   x          Δ                   x   b   ′       -     N          ∂     Φ   b2         ∂   y          Δ                   y   b   ′       -     R                 Δ                   i   b2       +     e   b2              
              L   x0     =       L   ∞     +     N          ∂     Φ   b2         ∂     i   b2               ,       M   x0     =     N          ∂     Φ   b2         ∂     i   b2                       (     Formula                 14     )                         
     In case of controlling attractive forces F x  and F y  individually, voltage equations for excitation current are as follows. 
     Where an excitation current condition is presented (i b1 +i b2 ),                    (       L   x0     +     M   x0       )        Δ                   i   xb   ′       =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   x   b   ′       -     R                 Δ                   i   xb       +     e   xb              
              i   xb     =       i   b1     +       i   b2     2         ,       e   xb     =         e   b1     +     e   b2       2                 (     Formula                 15     )                         
     Where an excitation current condition is presented (i b1 −i b2 ) ,            (       L   x0     -     M   x0       )        Δ                   i   yb   ′       =         -   N            ∂     Φ   b1         ∂     y   b            Δ                   y   b   ′       -     R                 Δ                   i   yb       +     e   yb                   i   yb     =         i   b1     -     i   b2       2       ,       e   yb     =         e   b1     -     e   b2       2                       
     Likewise, with respect to the magnet units  15   a ,  15   c  and  15   d , the respective voltage equations in conditions of (i a1 +i a2 ), (i c1 +i c2 ) and (i d1 +i d2 ) are as follows.                    (       L   x0     +     M   x0       )        Δ                   i   xa   ′       =         -   N            ∂     Φ   a1         ∂     x   a            Δ                   x   a   ′       -     R                 Δ                   i   xa       +     e   xa              
              i   xa     =       i   a1     +       i   a2     2         ,       e   xa     =         e   a1     +     e   a2       2                 (     Formula                 17     )                     (       L   x0     +     M   x0       )        Δ                   i   xc   ′       =         -   N            ∂     Φ   c1         ∂     x   c            Δ                   x   c   ′       -     R                 Δ                   i   xc       +     e   xc              
              i   xc     =       i   c1     +       i   c2     2         ,       e   xc     =         e   c1     +     e   c2       2                 (     Formula                 18     )                     (       L   x0     +     M   x0       )        Δ                   i   xd   ′       =         -   N            ∂     Φ   d1         ∂     x   d            Δ                   x   d   ′       -     R                 Δ                   i   xd       +     e   xd              
              i   xd     =         i   d1     +     i   d2       2       ,       e   xd     =         e   d1     +     e   d2       2                 (     Formula                 19     )                         
     Where excitation current conditions are respectively presented (i a1 −i a2 ), (i c1 −i c2) and (i   d1 −i d2 ) ,                    (       L   x0     -     M   x0       )        Δ                   i   ya   ′       =         -   N            ∂     Φ   a1         ∂     y   a            Δ                   y   a   ′       -     R                 Δ                   i   ya       +     e   ya              
              i   ya     =         i   a1     -     i   a2       2       ,       e   ya     =         e   a1     -     e   a2       2                 (     Formula                 20     )                     (       L   x0     -     M   x0       )        Δ                   i   yc   ′       =         -   N            ∂     Φ   c1         ∂     y   c            Δ                   y   c   ′       -     R                 Δ                   i   yc       +     e   yc              
              i   yc     =         i   c1     -     i   c2       2       ,       e   yc     =         e   c1     -     e   c2       2                 (     Formula                 21     )                     (       L   x0     -     M   x0       )        Δ                   i     y                 d     ′       =         -   N            ∂     Φ   d1         ∂     y   d            Δ                   y   d   ′       -     R                 Δ                   i     y                 d         +     e     y                 d                
              i     y                 d       =         i   d1     -     i   d2       2       ,       e     y                 d       =         e   d1     -     e   d2       2                 (     Formula                 22     )                         
     A relationship of the respective main fluxes Φ a1 , Φ a2 , Φ b1 , Φ b2 , Φ c1 , Φ c2 , Φ d1 , Φ d2  of the magnet units  15   a ˜ 15   d  is presented by the following formulas 23 and 24.                      ∂     Φ   a1         ∂     x   a         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   a1         ∂     y   a         =       ∂     Φ   b1         ∂     y   b           ,     
              ∂     Φ   a1         ∂     i   a1         =       ∂     Φ   b1         ∂     i   b1           ,         ∂     Φ   a1         ∂     i   a2         =       ∂     Φ   b1         ∂     i   b2                  
                ∂     Φ   c1         ∂     x   c         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   c1         ∂     y   c         =       ∂     Φ   b1         ∂     y   b           ,     
              ∂     Φ   c1         ∂     i   c1         =       ∂     Φ   b1         ∂     i   b1           ,         ∂     Φ   c1         ∂     i   c2         =       ∂     Φ   b1         ∂     i   b2                  
                ∂     Φ   d1         ∂     x   d         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   d1         ∂     y   d         =       ∂     Φ   b1         ∂     y   b           ,     
              ∂     Φ   d1         ∂     i   d1         =       ∂     Φ   b1         ∂     i   b1           ,         ∂     Φ   d1         ∂     i   d2         =       ∂     Φ   b1         ∂     i   b2                     (     Formula                 23     )                       ∂     Φ   a2         ∂     x   a         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   a2         ∂     y   a         =     -       ∂     Φ   b1         ∂     y   b             ,     
              ∂     Φ   a2         ∂     i   a1         =       ∂     Φ   b1         ∂     i   b2           ,         ∂     Φ   a2         ∂     i   a2         =       ∂     Φ   b1         ∂     i   b1                  
                ∂     Φ   b2         ∂     x   b         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   b2         ∂     y   b         =     -       ∂     Φ   b1         ∂     y   b             ,     
              ∂     Φ   b2         ∂     i   b1         =       ∂     Φ   b1         ∂     i   b2           ,         ∂     Φ   b2         ∂     i   b2         =       ∂     Φ   b1         ∂     i   b1                  
                ∂     Φ   c2         ∂     x   c         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   c2         ∂     y   c         =     -       ∂     Φ   b1         ∂     y   b             ,     
              ∂     Φ   c2         ∂     i   c1         =       ∂     Φ   b1         ∂     i   b2           ,         ∂     Φ   c2         ∂     i   c2         =       ∂     Φ   b1         ∂     i   b2                  
                ∂     Φ   d2         ∂     x   d         =       ∂     Φ   b1         ∂     x   b           ,         ∂     Φ   d2         ∂     y   d         =       ∂     Φ   b1         ∂     y   b           ,     
              ∂     Φ   d2         ∂     i   d1         =       ∂     Φ   b1         ∂     i   b2           ,         ∂     Φ   d2         ∂     i   d2         =       ∂     Φ   b1         ∂     i   b2                     (     Formula                 24     )                         
     The attractive forces of the guide units  5   a ˜ 5   d  are controlled by a controller  30  in FIG. 6, whereby the movable unit  4  are guided along the guide rails  2  and  2 ′ with no contact. 
     The controller  30  is divided as shown in FIG. 1, but functionally combined as a whole as shown in FIG.  6 . The following is an explanation of the controller  30 . In FIG. 6, arrows represent signal paths, and solid lines represent electric power lines around coils  20   a ,  20 ′ a ˜ 20   d ,  20 ′ d . The controller  30 , which is attached on the elevator cage  4 , includes a sensor  31  detecting variations in magnetomotive forces or magnetic reluctances of magnetic circuits formed with the magnet units  15   a ˜ 15   d , or in a movement of the movable unit  4 , a calculator  32  calculating voltages operating on the coils  20   a ,  20 ′ a ˜ 20   d ,  20 ′ d  on the basis of signals from the sensor  31  in order for the movable unit  4  to be guided with no contact with the guide rails  2  and  2 ′, power amplifiers  33   a ,  33 ′ a  ˜ 33   d ,  33 ′ d  supplying an electric power to the coils  20   a ,  20 ′ a  ˜ 20   d ,  20 ′ d  on the basis of an output of the calculator  32 , whereby attractive forces in the x and y directions of the magnet units  15   a ˜ 15   d  are individually controlled. 
     A power line  34  supplies an electric power to the power amplifiers  33   a ,  33 ′ a ˜ 33   d ,  33 ′ d  and also supplies an electric power to a constant voltage generator  35  supplying an electric power having a constant voltage to the calculator  32 , the x-direction gap sensors  13   a ,  13 ′ a ˜ 13   d ,  13 ′ d  and the y-direction gap sensors  14   a ,  14 ′ a ˜ 14   d ,  14 ′ d . A power supply  34  functions to transform an alternating current power, which is supplied from the outside of the hoistway  1  with a power line (not shown), into an appropriate direct current power in order to supply the direct current power to the power amplifiers  33   a ,  33 ′ a  ˜ 33   d ,  33 ′ d  for lighting or opening and closing doors. 
     The constant voltage generator  35  supplies an electric power with a constant voltage to the calculator  32  and the gap sensors  13  and  14 , even if a voltage of the power supply  34  varies due to an excessive current supply, whereby the calculator  32  and the gap sensors  13  and  14  may normally operate. 
     The sensor  31  includes the x-direction gap sensors  13   a ,  13 ′ a ˜ 13   d ,  13 ′ d , the y-direction gap sensors  14   a ,  14 ′ a ˜ 14   d ,  14 ′ d  and current detectors  36   a ,  36 ′ a ˜ 36   d ,  36 ′ d  detecting current values of the coils  20   a ,  20 ′ a ˜ 20   d ,  20 ′ d.    
     The calculator  32  controls magnetic guide controls for the movable unit  4  in every motion coordinate system shown in FIG.  1 . The motion coordinate system is constituted of a y-mode (back and forth motion mode) representing a right and left motion along a y-coordinate on a center of the movable unit  4 , an x-mode(right and left motion mode) representing a right and left motion along a x-coordinate, a θ-mode(roll mode) representing a rolling around the center of the movable unit  4 , a ξ-mode (pitch mode) representing a pitching around the center of the movable unit  4 , a φ-mode(yaw-mode) representing a yawing around the center of the movable unit  4 . In addition to the above modes, the calculator  32  also controls every attractive force of the magnet units  15   a ˜ 15   d  operating on the guide rails, a torsion torque around the y-coordinate caused by the magnet units  15   a ˜ 15   d , operating on the frame  11 , and a torque straining the frame  11  symmetrically, caused by rolling torques that a pair of magnet units  15   a  and  15   d , and a pair of magnet units  15   b  and  15   c  operate on the frame  11 . In brief, the calculator  32  additionally controls a ζ-mode (attractive mode), a δ-mode (torsion mode) and a γ-mode (strain mode). Accordingly, the calculator  32  controls in a way that excitation currents of coils  20  converge to zero in the above described eight modes, which is so-called zero power control, in order to keep the movable unit  4  steady by only attractive forces of the permanent magnets  17  and  17 ′ irrespective of a weight of a load. 
     This control method is disclosed in detail in Japanese Patent Publication(Kokai) No. 6-178409. However, the theory such control is based on is explained, since the four magnet units  15   a ˜ 15   d  control to guide the movable unit  4  in this embodiment. 
     To simplify the explanation, it is assumed that a center of the movable unit  4  exists on a vertical line crossing a diagonal intersection point of the center points of the magnet units  15   a ˜ 15   d  disposed on four corners of the movable unit  4 . The center is regarded as the origin of respective x, y and z coordinate axes. If a motion equation in every mode of magnetic levitation control system with respect to a motion of the movable unit  4 , and voltage equations of exciting voltages applying to the electromagnets  18  and  18 ′ of the magnet units  15   a ˜ 15   d  are linearized around a steady point, the following formulas 25 through 29 are obtained.              {                 M                 Δ                   y   ″       =       4          ∂     F   ya         ∂     y   a            Δ                 y     +     4          ∂     F   ya         ∂     i   a1            Δ                   i   y       +     U   y                       (       L   x0     -     M   x0       )        Δ                   i   y   ′       =         -   N            ∂     Φ   b1         ∂     y   a            Δ                   y   ′       -     R                 Δ                   i   y       +     e   y                    
        Δ                 y     =           Δ                   y   a       +     Δ                   y   b       +     Δ                   y   c       +     Δ                   y   d         4          
            Δ                   i   y       =           Δ                   i   ya       +     Δ                   i   yb       +     Δ                   i   yc       +     Δ                   i     y                 d           4          
            e   y     =         Δ                   e   ya       +     Δ                   e   yb       +     Δ                   e   yc       +     Δ                   e     y                 d           4                       (     Formula                 25     )               {                 M                 Δ                   x   ″       =       4          ∂     F   xb         ∂     x   b            Δ                 x     +     4          ∂     F   xb         ∂     i   b1            Δ                   i   x       +     U   x                       (       L   x0     +     M   x0       )        Δ                   i   x   ′       =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   x   ′       -     R                 Δ                   i   x       +     e   x                    
        Δ                 x     =             -   Δ                     x   a       +     Δ                   x   b       +     Δ                   x   c       -     Δ                   x   d         4          
            Δ                   i   x       =             -   Δ                     i   xa       +     Δ                   i   xb       +     Δ                   i   xc       -     Δ                   i     x                 d           4          
            e   x     =           -   Δ                     e   xa       +     Δ                   e   xb       +     Δ                   e   xc       -     Δ                   e     x                 d           4                       (     Formula                 26     )               {                   I   θ                   Δ                   θ   ″       =         l   θ   2            ∂     F   xb         ∂     x   b            Δ                 θ     +       l   θ   2            ∂     F   xb         ∂     i   b1            Δ                   i   θ       +     T   θ                       (       L   x0     +     M   x0       )        Δ                   i   θ   ′       =         -   N            ∂     Φ   b1         ∂     x   b              Δθ   ′       -     R                 Δ                   i   θ       +     e   θ                    
        Δ                 θ     =             -   Δ                     x   a       +     Δ                   x   b       -     Δ                   x   c       +     Δ                   x   d           2        l   θ              
            Δ                   i   θ       =             -   Δ                     i   xa       +     Δ                   i   xb       -     Δ                   i   xc       +     Δ                   i     x                 d             2        l   θ              
            e   θ     =           -   Δ                     e   xa       +     Δ                   e   xb       -     Δ                   e   xc       +     Δ                   e     x                 d             2        l   θ                           (     Formula                 27     )               {                   I   ξ                   Δ                   ξ   ″       =         l   θ   2            ∂     F   yb         ∂     y   b            Δ                 ξ     +       l   θ   2            ∂     F   yb         ∂     i   b1            Δ                   i   ξ       +     T   ξ                       (       L   x0     +     M   x0       )        Δ                   i   ξ   ′       =         -   N            ∂     Φ   b1         ∂     y   b              Δξ   ′       -     R                 Δ                   i   ξ       +     e   ξ                    
        Δ                 ξ     =             -   Δ                     y   a       -     Δ                   y   b       +     Δ                   y   c       +     Δ                   y   d           2        l   θ              
            Δ                   i   ξ       =             -   Δ                     i   ya       -     Δ                   i   yb       +     Δ                   i   yc       +     Δ                   i     y                 d             2        l   θ              
            e   ξ     =           -   Δ                     e   ya       -     Δ                   e   yb       +     Δ                   e   yc       +     Δ                   e     y                 d             2        l   θ                           (     Formula                 28     )               {                   I   θ                   Δ                   ψ   ″       =         l   ψ   2            ∂     F   yb         ∂     y   b            Δ                 ψ     +       l   ψ   2            ∂     F   yb         ∂     i   b1            Δ                   i   ψ       +     T   ψ                       (       L   x0     +     M   x0       )        Δ                   i   ψ   ′       =         -   N            ∂     Φ   b1         ∂     y   b              Δψ   ′       -     R                 Δ                   i   ψ       +     e   ψ                    
        Δ                 ψ     =           Δ                   y   a       -     Δ                   y   b       -     Δ                   y   c       +     Δ                   y   d           2        l   ψ              
            Δ                   i   ψ       =           Δ                   i   ya       -     Δ                   i   yb       -     Δ                   i   yc       +     Δ                   i     y                 d             2        l   ψ              
            e   ψ     =         Δ                   e   ya       -     Δ                   e   yb       -     Δ                   e   yc       +     Δ                   e     y                 d             2        l   ψ                           (     Formula                 29     )                         
     With respect to the above formulas, M is a weight of the movable unit  4 , I θ , I ξ  and I φ  are moments of inertia around w A respective y, x and z coordinates, U y  and U x  are the sum of external forces in the respective y-mode and x-mode, T θ , T ξ  and T φ  are the sum of disturbance torques in the respective θ-mode, ξ-mode and φ-mode, a symbol “′” represents a first time differentiation d/dt, a symbol “″” represents a second time differentiation d 2 /dt 2 , Δ is a infinitesimal fluctuation around a steady levitated state, L xo  is a self-inductance of each coils  20  and  20 ′ at a steady levitated state, M x0  is a mutual inductance of coils  20  and  20 ′, at a steady levitated state, R is a reluctance of each coils  20  and  20 ′, N is the number of turns of each coils  20  and  20 ′, i y , i x , i θ , i ξ  and i φ  are excitation currents of the respective y, x, θ, ξ and φ modes, e y , e x , e θ , e ξ  and e φ  are exciting voltages of the respective y, x, θ, ξ and φ modes,  1   θ  is each of the spans of the magnet units  15   a  and  15   d , and of the magnet units  15   b  and  15   c , and  1   φ  represents each of the spans of the magnet units  15   a  and  15   b , and of the magnet units  15   c  and  15   d.    
     Moreover, voltage equations of the remaining ζ, δ and γ modes are given as follows.                    (       L   x0     +     M   x0       )        Δ                   i   ζ   ′       =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   ζ   ′       -     R                 Δ                   i   ζ       +     e   ζ              
            Δ                 ζ     =         Δ                   x   a       +     Δ                   x   b       +     Δ                   x   c       +     Δ                   x   d         4            
            Δ                   i   ζ       =         Δ                   i   xa       +     Δ                   i   xb       +     Δ                   i   xc       +     Δ                   i     x                 d           4            
            e   ζ     =         Δ                   e   xa       +     Δ                   e   xb       +     Δ                   e   xc       +     Δ                   e     x                 d           4               (     Formula                 30     )                     (       L   x0     -     M   x0       )        Δ                   i   δ   ′       =         -   N            ∂     Φ   b1         ∂     y   b            Δ                   δ   ″       -     R                 Δ                   i   δ       +     e   δ              
            Δ                 δ     =         Δ                   y   a       -     Δ                   y   b       +     Δ                   y   c       -     Δ                   y   d           2        l   ψ                
            Δ                   i   δ       =             Δ                   i   ya       -     Δ                   i   yb       +     Δ                   i   yc       -     Δ                   i     y                 d             2        l   ψ              
          e   δ       =         Δ                   e   ya       -     Δ                   e   yb       +     Δ                   e   yc       -     Δ                   e     y                 d             2        l   ψ                     (     Formula                 31     )                     (       L   x0     +     M   x0       )        Δ                   i   γ   ′       =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   γ   ′       -     R                 Δ                   i   γ       +     e   γ              
            Δ                 γ     =         Δ                   x   a       +     Δ                   x   b       -     Δ                   x   c       -     Δ                   x   d           2        l   θ                
            Δ                   i   γ       =             Δ                   i   xa       +     Δ                   i   xb       -     Δ                   i   xc       -     Δ                   i     x                 d             2        l   θ              
          e   γ       =         Δ                   e   xa       +     Δ                   e   xb       -     Δ                   e   xc       -     Δ                   e     x                 d             2        l   θ                     (     Formula                 32     )                         
     With respect to the above formulas, y is a variation of the center of the movable unit  4  in the y-axis direction, x is a variation of the center of the movable unit  4  in the x-axis direction, θ is a rolling angle around y-axis, ξ is a pitching angle around x-axis, φ is a yawing angle around z-axis, and symbols y, x, θ, ξ and φ of the respective modes are affixed to excitation currents i and exciting voltages e respectively. Further, symbols a˜d representing which of the magnet units  15   a ˜ 15   d  are respectively affixed to excitation currents i and exciting voltages e of the magnet units  15   a ˜ 15   d . Levitation gaps x a ˜x d  and y a ˜y d  to the magnet units  15   a ˜ 15   d  are made by a coordinate transformation into y, x, θ, ξ and φ coordinates by the following formula 33.                y   =       1   4          (       y   a     +     y   b     +     y   c     +     y   d       )              
          x   =       1   4          (       -     x   a       +     x   b     +     x   c     -     x   d       )              
          θ   =       1     2        l   θ              (       -     x   a       +     x   b     -     x   c     +     x   d       )              
          ξ   =       1     2        l   θ              (       -     y   a       -     y   b     +     y   c     +     y   d       )              
          Ψ   =       1     2        l   ψ              (       y   a     -     y   b     -     y   c     +     y   d       )                 (     Formula                 33     )                         
     Excitation currents i a1 , i a2 ˜i d1 , i d2  to the magnet units  15   a ˜ 15   d  are made by a coordinate transformation into excitation currents i y , i x , i θ , i ξ , i φ , iζ, iδ and iγ of the respective modes by the following formula 34.                  i   y     =       1   8          (       i   a1     -     i   a2     +     i   b1     -     i   b2     +     i   c1     -     i   c2     +     i   d1     -     i   d2       )              
            i   x     =       1   8          (       -     i   a1       -     i   a2     +     i   b1     +     i   b2     +     i   c1     +     i   c2     -     i   d1     -     i   d2       )              
            i   θ     =       1     4        l   θ              (       -     i   a1       -     i   a2     +     i   b1     +     i   b2     -     i   c1     -     i   c2     +     i   d1     +     i   d2       )              
            i   ξ     =       1     4        l   θ              (       -     i   a1       +     i   a2     -     i   b1     +     i   b2     +     i   c1     -     i   c2     +     i   d1     -     i   d2       )              
            i   ψ     =       1     4        l   ψ              (       i   a1     -     i   a2     -     i   b1     +     i   b2     -     i   c1     +     i   c2     +     i   d1     -     i   d2       )              
            i   ζ     =       1   8          (       i   a1     +     i   a2     +     i   b1     +     i   b2     +     i   c1     +     i   c2     +     i   d1     +     i   d2       )              
            i   δ     =       1     4                   l   ψ              (       i   a1     -     i   a2     -     i   b1     +     i   b2     +     i   c1     -     i   c2     -     i   d1     +     i   d2       )              
            i   γ     =       1     4        l   θ              (       i   a1     +     i   a2     +     i   b1     +     i   b2     -     i   c1     -     i   c2     -     i   d1     -     i   d2       )                 (     Formula                 34     )                         
     Controlled input signals to levitation systems of the respective modes, that is, exciting voltages e y , e x , e θ , e ξ , e φ , e ζ , e δ  and e γ  which are the outputs of the calculator  32  are made by an inverse transformation to exciting voltages of the coils  20  and  20 ′ of the magnet units  15   a ˜ 15   d  by the following formula 35.                  e   a1     =       e   y     -     e   x     -         l   θ     2          e   θ       -         l   θ     2          e   ξ       +         l   ψ     2          e   ψ       +     e   ζ     +         l   ψ     2          e   δ       +         l   θ     2          e   γ                
            e   a2     =       -     e   y       -     e   x     -         l   θ     2          e   θ       -         l   θ     2          e   ξ       -         l   ψ     2          e   ψ       +     e   ζ     -         l   ψ     2          e   δ       +         l   θ     2          e   γ                             e   b1     =       e   y     +     e   x     +         l   θ     2          e   θ       -         l   θ     2          e   ξ       -         l   ψ     2          e   ψ       +     e   ζ     -         l   ψ     2          e   δ       +         l   θ     2          e   γ                
            e   b2     =       -     e   y       +     e   x     +         l   θ     2          e   θ       +         l   θ     2          e   ξ       +         l   ψ     2          e   ψ       +     e   ζ     +         l   ψ     2          e   δ       +         l   θ     2          e   γ                
            e   c1     =       e   y     +     e   x     -         l   θ     2          e   θ       +         l   θ     2          e   ξ       -         l   ψ     2          e   ψ       +     e   ζ     +         l   ψ     2          e   δ       -         l   θ     2          e   γ                
            e   c2     =       -     e   y       +     e   x     -         l   θ     2          e   θ       -         l   θ     2          e   ξ       +         l   ψ     2          e   ψ       +     e   ζ     -         l   ψ     2          e   δ       -         l   θ     2          e   γ                
            e   d1     =       e   y     -     e   x     +         l   θ     2          e   θ       +         l   θ     2          e   ξ       +         l   ψ     2          e   ψ       +     e   ζ     -         l   ψ     2          e   δ       -         l   θ     2          e   γ                
            e   d2     =       -     e   y       -     e   x     +         l   θ     2          e   θ       -         l   θ     2          e   ξ       -         l   ψ     2          e   ψ       +     e   ζ     +         l   ψ     2          e   δ       -         l   θ     2          e   γ                   (     Formula                 35     )                         
     With respect to the y, x, θ, ξ and φ modes, since motion equations of the movable unit  4  pairs with voltage equations thereof, the formulas 25˜29 are arranged to an equation of state shown in the following formula 36. 
     
       
         X 3 ′=A 3 x 3 +b 3 e 3 +d 3 u 3   (Formula 36) 
       
     
     In the formula 36, vectors x 3 , A 3 , b 3  and d 3 , and u 3  are defined as follows.                    x   3     =     [                 Δ                 y               Δ                   y   ′                       Δ                   i   y             ]       ,     [                 Δ                 x               Δ                   x   ′                       Δ                   i   x             ]     ,     [                 Δ                 θ               Δ                   θ   ′                       Δ                   i   θ             ]     ,       [                 Δ                 ξ               Δ                   ξ   ′                       Δ                   i   ξ             ]                     or              [                 Δ                 ψ               Δ                   ψ   ′                       Δ                   i   ψ             ]              
            A   3     =     [         0       1       0             a   21         0         a   23             0         a   32           a   33           ]            
              b   3     =     [               0           0                   b   31           ]       ,       d   3     =     [               0             d   21                   0         ]              
              u   3     =     U   y       ,     U   x     ,     T   θ     ,     T   ξ     ,     or                   T   ψ                 (     Formula                 37     )                         
     Further, e 3  is a controlling voltage for stabilizing the respective modes. 
     
       
         e 3 =e y , e x , e θ , e ξ ore w   (Formula 38) 
       
     
     The formulas 30˜32 are arranged into an equation of state shown in the following formula 40, by defining a state variable as the following formula 39. 
     
       
         x 1 =Δi ζ , Δi δ , Δi γ   (Formula 39) 
       
     
     
       
         x l ′=A l x l +b l e l +d l u l   (Formula 40) 
       
     
     If offset voltages of the controller  32  in the respective modes are marked with V ζ , V δ  and V γ , the variables A 1 , b 1 , d 1 , and u 1  in each mode are presented as follows.                (ζ-mode)          
              A   l     =     -     R       L   x0     +     M   x0             ,       b   l     =     1       L   x0     +     M   x0           ,       d   l     =     1       L   x0     +     M   x0                  
            u   l     =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   ζ   ′       +     v   ζ              
          (δ-mode)          
              A   l     =     -     R       L   x0     -     M   x0             ,       b   l     =     1       L   x0     -     M   x0           ,       d   l     =     1       L   x0     -     M   x0                  
            u   l     =         -   N            ∂     Φ   b1         ∂     y   b            Δ                   δ   ′       +     v   δ              
          (γ-mode)          
              A   l     =     -     R       L   x0     +     M   x0             ,       b   l     =     1       L   x0     +     M   x0           ,       d   l     =     1       L   x0     +     M   x0                  
            u   l     =         -   N            ∂     Φ   b1         ∂     x   b            Δ                   γ   ′       +     v   γ                 (     Formula                 41     )                         
     The term e 1  is a controlling voltage of each mode. 
     
       
         e l =e ζ , e δ , ore γ   (Formula 42) 
       
     
     The formula 36 may achieve a zero power control by feedback of the following formula 43. 
     
       
         e 3 =F 3 x 3 +∫K 3 x 3 dt  (Formula 43) 
       
     
     In case of letting F a , F b , F c  be proportional gains, and K c  be integral gain, the following formula 44 is given. 
     
       
         F 3 =[F a F b F c ]  (Formula 44) 
       
     
     
       
         K 3 =[0 0 K c ] 
       
     
     Likewise, the formula 40 may achieve a zero power control by feedback of the following formula 45. 
      e l =F l x l +∫K l x l dt  (Formula 45) 
     F 1  is a proportional gain. K 1  is an integral gain. 
     As shown in FIG. 6, the calculator  32 , which achieves the above zero power control, includes subtractors  41   a ˜ 41   h ,  42   a  ˜ 42   h  and  43   a ˜ 43   h , average calculators  44   x  and  44   y , a gap deviation coordinate transformation circuit  45 , a current deviation coordinate transformation circuit  46 , a controlling voltage calculator  47 , and a controlling voltage coordinate inverse transformation circuit  48 . For the following explanation, the gap deviation coordinate transformation circuit  45 , the current deviation coordinate transformation circuit  46 , the controlling voltage calculator  47 , and the controlling voltage coordinate inverse transformation circuit  48  are treated as a guide controller  50 . 
     The subtractors  41   a ˜ 41   h  calculate x-direction gap deviation signals Δ gxa1 , Δ gxa2 ,˜Δ gxd1 , Δ gxd2  by subtracting the respective reference values X a01 , X a02 ,X d01 , X d02  from gap signals g xa1 , g xa2 ,g xd1 , g xd2  from the x-direction gap sensors  13   a ,  13 ′ a ˜ 13   d ,  13 ′ d . The subtractors  42   a ˜ 42   h  calculate y-direction gap deviation signals Δg ya1 , Δg ya2 , Δg yd1 , Δg yd2  by subtracting the respective reference values Y a01 , Y a02 ,˜Y d01 , Y d 02   from gap signals g ya1 , g ya2 , ˜g yd1 , g yd2  from the y-direction gap sensors  14   a ,  14 ′ a ˜ 14   d ,  14 ′ d . The subtractors  43   a ˜ 43   h  calculate current deviation signals Δi a1 , Δi a2 , Δi d1 , Δi d2  by subtracting the respective reference values i a01 , i a02 ,˜i d01 , i d02  from excitation current signals i a1 , i a2 ,˜i d1 , i d2  from current detectors  36   a ,  36 ′ a ˜ 36   d ,  36 ′ d.    
     The average calculators  44   x  and  44   y  average the x-direction gap deviation signals Δg xa1 , Δg xa2 , Δg xd1 , Δg xd2 , and the y-direction gap deviation signals Δg ya1 , Δg ya2 ,˜Δg yd1 , Δg yd2 respectively, and output the calculated x-direction gap deviation signals Δx a ˜Δx d , and the calculated y-direction gap deviation signals Δy a ˜Δy d . 
     The gap deviation coordinate transformation circuit  45  calculates y-direction variation Δy of the center of the movable unit  4  on the basis of the y-direction gap deviation signals Δy a ˜Δy d , x-direction variation Δx of the center of the movable unit  4  on the basis of the x-direction gap deviation signals Δx a ˜ΔΔx d , a rotation angle Δθ in the θ-direction (rolling direction) of the center of the movable unit  4 , a rotation angle Δξ in the ξ-direction(pitching direction) of the movable unit  4 , and a rotation angled Δφ in the φ-direction (yawing direction) of the movable unit  4 , by the use of the formula 33. 
     The current deviation coordinate transformation circuit  46  calculates a current deviation Δi y  regarding y-direction movement of the center of the movable unit  4 , a current deviation Δi x  regarding x-direction movement of the center of the movable unit  4 , a current deviation Δi θ  regarding a rolling around the center of the movable unit  4 , a current deviation Δi ξ  regarding a pitching around the center of the movable unit  4 , a current deviation Δi φ  in regarding a yawing around the center of the movable unit  4 , and current deviations Δi ζ , Δi γ  and Δi γ  regarding ζ, δ and γ stressing the movable unit  4 , on the basis of the current deviation signals Δi a1 , Δi a2 ,˜Δi d1 , Δi d2  by using the formula 34. 
     The controlling voltage calculator  47  calculates controlling voltages e y , e x , e θ , e ξ , e φ , e ζ , e δ  and e γ  for magnetically and securely levitating the movable unit  4  in each of the y, x, θ, ξ, φ, ζ, δ and γ modes on the basis of the outputs 
     Δy, Δx, Δθ, Δξ, Δφ, Δi y , Δi x , Δi θ , Δi ξ , Δi φ , Δi ζ , Δi δ  and Δi γ  of the gap deviation coordinate transformation circuit  45  and the current deviation coordinate transformation circuit  46 . The controlling voltage coordinate inverse transformation circuit  48  calculates respective exciting voltages e a1 , e a2 , e d1 , e d2  of the magnet units  15   a ˜ 15   d  on the basis of the outputs e y , e x , e θ , e ξ , e φ , e ζ , e δ  and e γ  by the use of the formula 35, and feeds back the calculated result to the power amplifiers  33   a ,  33 ′ a ˜ 33   d ,  33 ′ d.    
     The controlling voltage calculator  47  includes a back and forth mode calculator  47   a , a right and left mode calculator  47   b , a roll mode calculator  47   c , a pitch mode calculator  47   d , a yaw mode calculator  47   e , an attractive mode calculator  47   f , a torsion mode calculator  47   g , and a strain mode calculator  47   h.    
     The back and forth mode calculator  47   a  calculates an exciting voltage e y  in the y-mode on the basis of the formula  43  by using inputs Δy and Δi y . The right and left mode calculator  47   b  calculates an exciting voltage e x  in the x-mode on the basis of the formula 43 by using inputs Δx and Δi x . The roll mode calculator  47   c  calculates an exciting voltage eθ in the θ-mode on the basis of the formula 43 by using inputs Δθ and Δi θ . The pitch mode calculator  47   d  calculates an exciting voltage et in the ξ-mode on the basis of the formula 43 by using inputs Δξ and Δi ξ . The yaw mode calculator  47   e  calculates an exciting voltage e φ  in the θ-mode on the basis of the formula 43 by using inputs Δφ and Δi φ . The attractive mode calculator  47   f  calculates an exciting voltage e ζ  in the ζ-mode on the basis of the formula 45 by using input Δi ζ . The torsion mode calculator  47   g  calculates an exciting voltage  δ  in the δ-mode on the basis of the formula 45 by using input Δi δ . The strain mode calculator  47   h  calculates an exciting voltage e γ  in the γ-mode on the basis of the formula 45 by using input Δi γ . 
     FIG. 7 shows in detail each of the calculators  47   a ˜ 47   e.    
     Each of the calculators  47   a ˜ 47   e  includes a differentiator  60  calculating time change rate Δy′, Δx′, Δθ′, Δξ′ or Δφ′ on the basis of each of the variations Δy, Δx, Δθ, Δξ and Δφ, gain compensators  62  multiplying each of the variations Δy˜Δφ, each of the time change rates Δy′˜Δφ′ and each of the current deviations Δi y ˜Δi φ , by an appropriate feedback gain respectively, a current deviation setter  63 , a subtractor  64  subtracting each of the current deviations Δi y ˜Δi φ  from a reference value output by the current deviation setter  63 , an integral compensator  65  integrating the output of the subtractor  64  and multiplying the integrated result by an appropriate feed back gain, an adder  66  calculating the sum of the outputs of the gain compensators  62 , and a subtractor  67  subtracting the output of the adder  66  from the output of the integral compensator  65 , and outputting the exciting voltage e y , e x , e θ , e ξ  or e φ , of the respective y, x, θ, ξ and φ modes. 
     FIG. 8 shows components in common among the calculators  47   f ˜ 47   h.    
     Each of the calculators  47   f ˜ 47   h  is composed of a gain compensator  71  multiplying the current deviation Δi ζ , Δi δ  or Δi y  by an appropriate feedback gain, a current deviation setter  72 , a subtractor  73  subtracting the current deviation Δi ζ , Δi δ  or Δi γ  from a reference value output by the current deviation setter  72 , an integral compensator  74  integrating the output of the subtractor  73  and multiplying the integrated result by an appropriate feedback gain, and a subtractor  75  subtracting the output of the gain compensator  71  from the output of the integral compensator  74  and outputting an exciting voltage e ζ , e δ  or e γ  of the respective ζ, δ and γ modes. 
     The following is an operation of the above described elevator magnetic guide unit of the first embodiment of the present invention. 
     Any of the ends of the center cores  16  of the magnet units  15   a ˜ 15   d , or the ends of the electromagnets  18  and  18 ′ of the magnet units  15   a ˜ 15   d  adsorb to facing surfaces of the guide rails  2  and  2 ′ through the solid lubricating materials  22  at a stopping state of the magnetic guide system. At this time, an upward and downward movement of the movable unit  4  is not impeded because of the effect of the solid lubricating materials  22 . 
     Once the guide system is activated at the stopping state, fluxes of the electromagnets  18  and  18 ′, which possesses the same or opposite direction of fluxes generated by the permanent magnets  17  and  17 ′, are controlled by the guide controller  50  of the controller  30 . The guide controller  50  controls excitation currents to the coils  20  and  20 ′ in order to keep a predetermined gap between the magnet units  15   a ˜ 15   d  and guide rails  2  and  2 ′. Consequently, as shown in FIGS. 4 and 5, a magnetic circuit Mcb is formed with a path of the permanent magnet  17 ˜the L-shaped core  19 ˜the core plate  21 ˜the gap Gb˜the guide rail  2 ′˜the gap Gb″˜the center core  16 ˜the permanent magnet  17 , a magnetic circuit Mcb′ is formed with a path of the permanent magnet  17 ′˜the L-shaped core  19 ′˜the core plate  21 ′˜the gap Gb′˜the guide rail  2 ′˜the gap Gb″˜the center core  16 ˜the permanent magnet  17 ′. The gaps Gb, Gb′ and Gb″, or other gaps formed with the magnet units  15   a ,  15   c  and  15   d , are set to certain distances so that magnetic attractive forces of the magnet units  15   a ˜ 15   d  generated by the permanent magnets  17  and  17 ′ balance with a force in the y-direction (back and force direction) acting on the center of the movable unit  4 , a force in the x-direction(right and left direction), and torques acting around the x, y and x-axis passing on the center of the movable unit  4 . When some external forces operate on the movable unit  4 , the controller  30  controls excitation currents flowing into the electromagnets  18  and  18 ′ of the respective magnet units  15   a ˜ 15   d  in order to keep such balance, thereby achieving the so-called zero power control 
     Even if a shake of the movable unit  4  is made due to movements of passengers or irregularities on the guide rails  2  and  2 ′ while the movable unit  4 , which is controlled to be guided with no contact by the zero power control, is moved upwardly by a hoisting machine (not shown), the shake may be restrained by promptly controlling attractive forces generated by the magnet units  15   a ˜ 15   d  by excitation of the electromagnets  18  and  18 ′, since the magnet units  15   a ˜ 15   d  possess the permanent magnets  17  and  17 ′ having common magnetic paths with the electromagnets  18  and  18 ′ within the gaps Gb, Gb′ and Gb″. 
     Further, even if the gaps Gb, Gb′ and Gb″ are set large, the quality of no contact guide control does not become worse, because permanent magnets having a large residual magnetic flux density and coersive force are adopted. As a result, the guide system may obtain a large stroke and low rigidity for the guide control, and achieve a comfortable ride. 
     Moreover, since each of the magnet units  15   a ˜ 15   d  is disposed so that magnetic poles face each other putting the guide rail  2  or  2 ′ between the magnetic poles, attractive forces, which are generated by the magnetic poles, operating on the guide rail  2  or  2 ′, are cancelled entirely or in part, whereby a large attractive force does not operate on the guide rails  2  and  2 ′. Accordingly, since a large attractive force in the only one direction caused by the magnet unit does not operate on the guide rails  2  and  2 ′, an installed position of the guide rail  2  or  2 ′ is difficult to be shifted, and a difference in level at the joint  80  of the guide rails  2  and  2 ′, and a straight performance of the guide rail  2  or  2 ′ do not get worse. As a result, strength for installation of the guide rails  2  and  2 ′ maybe reduced, thereby reducing a cost of an elevator system. 
     In case the magnetic guide system stops working, current deviation setters  62  for they-mode and the x-mode set reference values from zero to minus values gradually, whereby the movable unit  4  gradually moves in the y and x-directions. At last, any of the ends of the center cores  16  of the magnet units  15   a ˜ 15   d , or the ends of the electromagnets  18  and  18 ′ of the magnet units  15   a ˜ 15   d  adsorb to facing surfaces of the guide rails  2  and  2 ′ through the solid lubricating materials  22 . If the magnetic guide system is stopped at this state, a reference value of the current deviation setter  62  is reset to zero, and the movable unit  4  adsorbs to the guide rails  2  and  2 ′. 
     In the first embodiment, although the zero power control, which controls to settle an excitation current for an electromagnet to zero at a steady state, is adopted for no contact guide control, various other control methods for controlling attractive forces of the magnet units  15   a ˜ 15   d  may be used. For example, a control method, which controls to keep the gaps constant, may be adopted, if the magnet units is required to follow the guide rails  2  and  2 ′ more strictly. 
     A magnetic guide system of a second embodiment of the present invention is described on the basis of FIGS. 9 and 10. 
     In the first embodiment, although no contact guide control is achieved by adopting the E-shaped magnet units  15   a ˜ 15   d  as guide units  5   a ˜ 5   d , it is not limited to the above described system. As shown in FIGS. 9 and 10, two U-shaped combined magnets  141  and  141 ′ are disposed so that magnetic poles of the combined magnets  141  and  141 ′ face to the guide rails  2  and  2 ′ in part, and the same poles of the combined magnets  141  and  141 ′ face one another putting the guide rails  2  and  2 ′ between the magnetic poles. The U-shaped combined magnet  141  includes two permanent magnets  117 - 1  and  117 - 2 , and an electromagnet  118 . Likewise, the U-shaped combined magnet  141 ′ includes two permanent magnets  117 - 1 ′ and  117 - 2 ′, and an electromagnet  118 ′. The U-shaped combined magnets  141  and  141 ′ constitute respective magnet units  115   a ˜ 115   d . In the following explanation, the same numerals are suffixed to common components with the first embodiment for convenience. 
     The magnet unit  115   b  shown in FIGS. 9 and 10 includes a pair of combined magnets  141  and  141 ′, and a base  142  made of non-magnetic materials in the shape of an H for installing the combined magnets  141  and  141 ′ on a base  12  in order for the coils  20  and  20 ′ not to interfere with the base  12 , and in order for the same poles of the combined magnets  141  and  141 ′ to be disposed to face one another. 
     The combined magnet  141  includes a U-shaped electromagnet  118  formed with two symmetrical L-shaped cores  143 - 1  and  143 - 2  putting the coil  20  therebetween, and permanent magnets  117 - 1  and  117 - 2  adhered to the opposite ends of the respective magnetic poles of the electromagnet  118 . Likewise, the combined magnet  141 ′ includes a U-shaped electromagnet  118 ′ formed with two symmetrical L-shaped cores  143 - 1 ′ and  143 - 2 ′ putting the coil  20 ′ therebetween, and permanent magnets  117 - 1 ′ and  117 - 2 ′ adhered to the opposite ends of the respective magnetic poles of the electromagnet  118 ′. The permanent magnets  117 - 1  and  117 - 2  adhered to the opposite ends of the respective magnetic poles of the electromagnet  118  so that one of the magnetic poles of the combined magnet  141  become the other magnetic pole one another. In the same way as the first embodiment, the ends of the magnet unit  115   b , that is, the ends of the permanent magnets  117 - 1  and  117 - 2  include the solid lubricating materials  22 . The magnet unit  115  butilizes a magnetic allying force operating on the guide rail  2  as a guiding force in the x-direction. 
     With respect to the magnet unit  115   b  of the second embodiment, a magnetic attractive force in the x-direction operating to peeling of the guide rail  2  from a hoistway wall is smaller than that of the E-shaped magnet unit  15   b . Further, in the same way as the first embodiment, since magnetic poles of the combined magnets  141  and  141 ′ face each other putting the guide rail  2  or  2 ′ between the magnetic poles, attractive forces, which are generated by the magnetic poles, operating on the guide rail  2  or  2 ′, are cancelled entirely or in part, whereby a large attractive force does not operate on the guide rails  2  and  2 ′. Accordingly, since a large attractive force in the only one direction caused by the magnet unit does not operate on the guide rails  2  and  2 ′, an installed position of the guide rail  2  or  2 ′ is difficult to be shifted, and a difference in level at the joint  80  of the guide rails  2  and  2 ′, and a straight performance of the guide rail  2  or  2 ′ do not get worse. As a result, strength for installation of the guide rails  2  and  2 ′ may be reduced, thereby reducing a cost of an elevator system. 
     A magnetic guide system of a third embodiment of the present invention is described on the basis of FIG.  11 . 
     In the first and second embodiments, a horizontal sectional form of the guide rails  2  or  2 ′ is formed in the shape of an I, while each of guide rails  202  and  202 ′ possesses a portion having an H-shaped horizontal sectional form, facing one of magnet units  215   a ˜ 215   d  (only  215   b  is shown in FIG.  11 ), and the portion is formed with projecting portions facing magnetic poles of the magnet units  215   a ˜ 215   d  in the third embodiment shown in FIG.  11 . 
     The magnet unit  215   b  being guided by the guide rail  202 ′ is fixed to a base  242  made of non-magnetic materials and formed in the shape of a U. Magnetic poles of a U-shaped combined magnet  241  face the respective same magnetic poles of a U-shaped combined magnet  241 ′ putting the projecting portions of the guide rail  2  between the respective magnetic poles. Each center of the magnetic poles of the combined magnet  241  or  241 ′ is off each center of the projecting portions of the guide rail  2  or  2 ′ in order to obtain a guiding force in the x-direction. 
     The combined magnet  241  includes two electromagnets  218 - 1  and  218 - 2 , and a permanent magnet  217  disposed between the electro magnets  218 - 1  and  218 - 2 . Likewise, the combined magnet  241 ′ includes two electromagnets  218 - 1 ′ and  218 - 2 ′, and a permanent magnet  217 ′ disposed between the electromagnets  218 - 1 ′ and  218 - 2 ′. The electromagnets  218 - 1 ,  218 - 2 ,  218 - 1 ′ and  218 - 2 ′ include coils  220 - 1 ,  220 - 2 ,  220 - 1 ′ and  220 - 2 ′ respectively. The respective two coils  220 - 1  and  220 - 2 , or  220 - 1 ′ and  220 - 2 ′ of the combined magnets  241  and  241 ′ are made a circuit so as to increase or decrease fluxes generated by the permanent magnets  217  and  217 ′ by excitation. 
     The magnet units  215   a ˜ 215   d  of the third embodiment possesses a stronger guiding force in the x-direction compared with the magnet unit  115   a ˜ 115   d  of the second embodiment shown in FIGS. 9 and 10. 
     Structure of a magnet unit is not limited to the above described embodiments. A magnet unit having at least magnetic poles facing each other putting a guide rail therebetween may be adopted. Moreover, a sectional form of a guide rail is not limited to the above described embodiments. A guide rail having any one of horizontal sectional forms of a round shape, an elliptic shape and a rectangular shape may be adopted. 
     In the above embodiments, although a condition of the magnetic circuit formed with the magnet unit and the guide rail is detected by measuring a gap calculated by an average of outputs of gap sensors, and an excitation current detected by current detectors, a method of measuring a gap, a use of a gap sensor and a use of a current detector are not limited. Other methods, which may detect a condition of the magnetic circuit formed with the magnet unit and the guide rail, may be adopted. 
     Further, in the above embodiments, although a controller for a magnetic levitation control is described as an analog control, either analog control or digital control maybe adopted. Furthermore, a power amplification system is not limited likewise, a current type system, or a PWM type system may be adopted. 
     According to the magnetic guide system of the present invention, since the magnet unit is provided with the permanent magnet having a common magnetic path with the electromagnet at the gap formed with the magnet unit and the guide rail, partial differential terms ∂f/∂x and ∂f/∂i do not become zero where f is an attractive force of the magnet unit, x is a gap, and i is an excitation current, even if an excitation current is made zero when a guiding force is not needed at a steady state of the movable unit, thereby enabling to design a linear control system. 
     Since a common magnetic path of the permanent magnet and the electromagnet is formed at the gap, a guide system possessing a high control performance and a low rigidity can be achieved. 
     Further, since magnetic poles of the magnet unit face each other putting the guide rail between the magnetic poles, attractive forces, which are generated by the magnetic poles, operating on the guide rail, are cancelled entirely or in part, whereby a large attractive force does not operate on the guide rail. Accordingly, since a large attractive force in the only one direction caused by the magnet unit does not operate on the guide rail, an installed position of the guide rail is difficult to be shifted, and a difference in level at the joint of the guide rail, and a straight performance of the guide rail do not get worse. As a result, the strength for installation of the guide rail maybe reduced, thereby reducing a cost of an elevator system. 
     Various modifications and variations are possible in light of the above teachings. Therefore, it is to be understood that within the scope of the appended claims, the present invention may be practiced otherwise than as specifically described herein.