Abstract:
A radial position sensor includes a rotating element configured to rotate about an axis of rotation, which subject to displacement. The displacement from a first position to a second position can be represented by polar coordinates, e.g., (ρ, φ), where ρ is a distance and φ is an angle. The sensor also includes a non-rotating emitting element configured to provide a plurality of electromagnetic fields and a non-rotating receiving element configured to receive the plurality of electromagnetic fields. The plurality of electromagnetic fields are electromagnetically coupled to the non-rotating receiving element through the rotating element. The electromagnetic coupling varies in dependence on the radial position of the axis of rotation of the rotating element. The non-rotating receiving element produces an output signal in response to the amount of coupling of the plurality of electromagnetic fields, and so the output signal is an indication of the radial position of the axis of rotation.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     The present invention is related to U.S. Pat. No. 5,872,408, Feb. 16, 1999 and U.S. Pat. No. 6,101,084, Aug. 8, 2000, both of which are fully incorporated herein by reference for all purposes. The present invention is also related to commonly owned U.S. Pat. No. 7,282,878, filed Apr. 28, 2006 and pending U.S. application Ser. No. 11/724,951, filed Mar. 15, 2007, both of which are fully incorporated herein by reference for all purposes. 
     BACKGROUND OF THE INVENTION 
     The present invention is directed generally to the detection of radial position, and in particular to the use of reactance sensors, to indicate the radial position of the rotary elements of rotational devices. 
     Control of rotational electromechanical devices, such as electrical motors, typically requires knowledge of the position and/or speed of their rotors, and may further require information about the position of their axes of rotation. There are several ways to determine such parameters. First, the position of the rotor may be determined by an array of photo-transistors and a special shutter coupled to the rotor shaft, or by using Hall-effect sensors. Such systems are described in T. Kenjo, Electrical Motors and Their Controls, Oxford University Press (1994), pp 176 and following. Second, the speed informative signal may be obtained by using a small permanent magnet tachometer generator, attached to the shaft, or by using magnetic or optical sensors for generating pulses for each angular increment of the rotor. Such systems are described in W. Leonhard, Control of Electrical Drives, 2nd ed., Springer Verlag (2001), pp 420 and following. Third, a resolver may be used to determine the position of the rotor by a two-phase (sine/cosine) signal at a carrier frequency modulated sinusoidally by the rotation of the rotor. Such a system is described in J. R. Hendershot, Jr. and T. Miller, Design of Brushless Permanent-Magnet Motors, Magna Physics Publishing (1994), pp 1-19. All these methods require precise mechanical placement of sensors, or galvanic contact between moving parts. 
     Conventionally, the moveable element of a rotary device is the informative element that indicates rotational (angular) position; i.e., the information signal (an electrical signal) is generated on the moveable element. It is therefore necessary to have some means for transferring the information signal from this moveable element to external processing circuitry. This is usually accomplished by the use of rings and brushes, flexible connectors, and so on. The use of brushes can introduce noise into the information signal. Brushless solutions exist, but they suffer from low signal to noise ratios, and can be mechanically cumbersome. More significantly, brushes create problems with reliability and require constant maintenance. It is highly desirable to form and deliver signals to and from the rotating parts of mechanical or electromechanical devices without the use of mechanical or galvanic contact and a complex sensor supporting system. 
     Conventional motor drive technology using mechanical bearings suffers from many limitations. For example, mechanical bearings require lubrication, which can lead to high maintenance cost. Additionally, mechanical bearings tend to wear out and need to be replaced. As motor drive technology evolves, magnetic bearings and bearingless drives have been introduced to reduce the need for bearing lubrication and bearing replacement. Such systems are described in A. Chiba et al., Magnetic Bearings and Bearingless Drives, Newnes, Elsevier, (2005).  FIG. 1  is a diagram illustrating a conventional motor system  100  including magnetic bearings. The motor  104  is located between electromagnetic bearings  102  and  106 . Each electromagnetic bearing  102  and  106  have coils to generate radial forces in two perpendicular radial axes (e.g., X-Y coordinates shown in the figure). A feedback control mechanism is used to maintain the axis of rotation at the center of the stator core. Accordingly, the X-Y position of the axis of rotation must be provided to the control system to control the strength of the magnetic forces generated by the bearings  102 ,  106  in order to maintain the proper positioning of the axis of rotation. 
     In conventional magnetic bearings and bearingless drives systems, Cartesian coordinates are usually used to control the radial position of the axis of rotation. As shown in  FIG. 1 , electromagnetic bearing  102  is controlled in two radial axis coordinates x 1  and y 1 , and electromagnetic bearing  106  is controlled in two radial axis coordinates x 2  and y 2 . Even though this technique may be adequate in certain applications, there are many limitations as discussed below. 
     Accordingly, it is desirable to have improved methods and systems for sensing the radial displacement of a rotating element in an electromechanical device, and more specifically in devices having magnetic bearings and bearingless drives. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention is directed to reactance (capacitive and inductive) sensors for mechanical and electromechanical devices. More particularly, this invention provides a method and system including reactance (capacitive and inductive) sensors indicative of the radial position of a rotational device, specifically the position of the axis of rotation of one of its rotating parts. Merely by way of example, the invention has been applied to sensing radial position of rotors of electrical motors of different types having magnetic bearings, and bearingless drives. But it would be recognized that the invention has a much broader range of applicability. For example, the invention can be applied to electromechanical motion devices in general. 
     In accordance with an embodiment of the present invention, a sensor includes a non-moving sensing element from which the informative signal indicative of the radial position is obtained. A passive moveable element is introduced between the non-moving sensing element and a source of electromagnetic energy. The passive element has special electromagnetic characteristics which affect the reactance coupling (i.e., electromagnetic coupling) of the electromagnetic excitation between the non-moving sensing element and the source of electromagnetic energy. 
     A sensor according to embodiments of the present invention can be capacitive or inductive, or a combination of capacitive and inductive elements. The movable passive element can be characterized by having a dielectric constant for capacitive variants, or a magnetic constant for inductive variants. Both of these variants of reactance sensors have similar constructions and similar forms of excitation and output informative signals. 
     According to a specific embodiment, the present invention provides a radial position sensor. The sensor includes a rotating element configured to rotate about an axis of rotation, which is subject to displacement. The sensor also includes a non-rotating emitting element configured to provide a plurality of electromagnetic fields and a non-rotating receiving element configured to receive the plurality of electromagnetic fields. The rotating element is disposed in juxtaposition to the non-rotating emitting element and to the non-rotating signal receiving element. The plurality of electromagnetic fields produced by the non-rotating emitting element is electromagnetically coupled to the non-rotating receiving element through the rotating element. The electromagnetic coupling of the plurality of electromagnetic fields between the non-rotating emitting element and the non-rotating receiving element varies as the axis of rotation of the rotating element is displaced from a first position to a second position. In the sensor, the non-rotating receiving element produces an output signal in response to exposure to the plurality of electromagnetic fields, and the output signal varies depending on the direction and amount of displacement of the axis of rotation. 
     In a specific embodiment, the displacement is characterized by a combination of an angular component and a radial component; the displacement can be said to be represented by polar coordinates, e.g., (ρ, φ) where φ is distance from the first position to the second position and φ is an angle subtended between reference line and a line connecting the first position and the second position. When the output signal is a time-varying signal, then a phase of the output signal is associated with the angular component (φ) of the displacement and a magnitude of the output signal is associated with the radial component (ρ) of the displacement. In an embodiment, the non-rotating emitting element comprises a plurality of electrically isolated emitters, each emitter emitting one of the electromagnetic fields. 
     According to another embodiment of the present invention, a radial position sensor is provided. The sensor includes a plurality of emitters, which are electrically isolated from each other. Each of the plurality of emitters is configured to receive a respective one of a corresponding plurality of time-varying input electrical signals. The sensor also includes a receiving element disposed in juxtaposition to each of the plurality of emitters. The receiving element is coupled to each of the plurality of emitters by a respective electrical reactance. Additionally, the sensor includes a rotating element disposed between the emitters and the receiving element. The rotating element is configured to rotate about an axis of rotation, the axis of rotation being subject to displacement. The sensor also has an output terminal coupled to the receiving element for providing a time-varying output signal. A phase of the time-varying output signal is related to an angular component of the displacement, and a magnitude of the time-varying output signal is related to a radial component of the displacement. In a specific embodiment, the plurality of time-varying input electrical signals include N time-varying electrical signals that are 360°/N out of phase from one another, where N is an integer. 
     According to yet another embodiment of the present invention, a radial position sensor includes a emitting element which has a plurality of electrically isolated emitters. Each emitter is configured to produce a magnetic field when it is energized, thereby producing a plurality of magnetic fields when two or more of the emitters are energized. The sensor also includes a receiving element and a rotating element disposed in juxtaposition to the emitting element and to the receiving element. The rotating element is configured to rotate about an axis of rotation which is subject to displacement. The displacement can cause a change in electromagnetic coupling between the plurality of magnetic fields and the receiving element when the emitters are energized. In the sensor, the receiving element produces a single output signal when the plurality of magnetic fields are electromagnetically coupled thereto by the rotating element, characteristics of the single output signal depending on the displacement. 
     In a specific embodiment, each emitter includes an electromagnet and the receiving element includes a coil. The plurality of magnetic fields produced by the emitters are coupled to the coil thus inducing a flow of current in the coil. In the sensor, the single output signal is a measure of the flow of current. In an embodiment, the rotating element is substantially coplanar with the emitting element. The rotating element is connected to a shaft, and the receiving element is disposed about the shaft. In an embodiment, the characteristics of the single output signal includes a phase and a magnitude. The phase of the single output signal corresponds to an angular component of the displacement, and the magnitude of the single output signal corresponds to a radial component of the displacement. 
     According to an alternative embodiment, the invention provides a radial position sensor. The sensor includes a emitting element which has a plurality of electrically isolated emitters. Each emitter is configured to produce an electric field when it is energized, thereby producing a plurality of electric fields when two or more of the emitters are energized. The sensor also includes a receiving element and a rotating element disposed in juxtaposition to the emitting element and to the receiving element. The rotating element is configured to rotate about an axis of rotation, which is subject to displacement. The displacement causes a change in electromagnetic coupling between the plurality of electric fields and the receiving element when the plurality of emitters are energized. Additionally, the receiving element produces a single output signal when the plurality of electric fields are electromagnetically coupled thereto by the rotating element. The characteristics of the single output signal are dependent on the displacement. 
     In a specific embodiment, each emitter includes a conductive region and the receiving element includes a conducting plate. The plurality of electric fields produced by the emitters are coupled to the conducting plate thus inducing a voltage in the conducting plate. The single output signal is a measure of the voltage. In an embodiment, the characteristics of the single output signal include a phase and a magnitude. The phase of the single output signal corresponds to an angular component of the displacement, and the magnitude of the single output signal corresponds to a radial component of the displacement. 
     According to embodiments of the present invention, those elements of the radial position sensor that require an electrical connection do not rotate. This is a significant advantage because it obviates the need for brushes or the like which would be used to provide electrical contact to rotating surfaces and the disadvantages of having to use such brushes. In various embodiments, these sensors are characterized by uniformity of the information signal, high reliability and low maintenance costs because of absence of contacts or brushes, and simple construction that allowed them to be practically implemented using modern methods of mass production. Another benefit is in the simplification of further signal processing. Depending upon the embodiment, one or more of these benefits may be achieved. These and other benefits will be described in more detail throughout the present specification and more particularly below. 
     Various additional objects, features and advantages of the present invention can be more fully appreciated with reference to the detailed description and accompanying drawings that follow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view diagram illustrating a conventional motor system including magnetic bearings; 
         FIG. 2  is a view diagram illustrating a conventional method for radial position sensing; 
         FIGS. 3A-3B  are simplified view diagrams illustrating a method for a radial position sensor that uses polar rather than Cartesian system of coordinates according to an embodiment of the present invention; 
         FIG. 4A  is a simplified perspective view diagram illustrating a radial position sensor  400  according to an embodiment of the present invention; 
         FIG. 4B  is a simplified cross-sectional view diagram illustrating a radial position sensor system  410  according to an embodiment of the present invention; 
         FIGS. 5A-5C  are simplified diagrams showing additional details of the sensor  410  viewed along respective view lines  5 A- 5 A′,  5 B- 5 B′, and  5 C- 5 C′ shown in  FIG. 4 ; 
         FIG. 6  is a simplified schematic diagram of the sensor  410  shown in  FIG. 4  according to an embodiment of the present invention; 
         FIG. 7  is a simplified diagram illustrating signal waveforms produced in the circuit of  FIG. 6 ; 
         FIG. 8  is a simplified schematic diagram illustrating a capacitive sensor of radial position according to an embodiment of the present invention; 
         FIG. 9  is a simplified schematic diagram illustrating a reactance sensor of radial position according to an embodiment of the present invention; 
         FIG. 10  is a simplified schematic diagram illustrating an inductive sensor of radial position according to an alternative embodiment of the present invention; 
         FIG. 11  is a simplified diagram illustrating an inductive sensor of radial position according to an alternative embodiment of the present invention; 
         FIG. 12  simplified perspective view diagram illustrating additional details of the sensor of  FIG. 1 ; and 
         FIG. 13  is a simplified view diagram illustrating a method for radial position sensing and correction according to another embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is directed to reactance (capacitive and inductive) sensors for mechanical and electromechanical devices. More particularly, this invention is directed to reactance sensors to sense the radial position of rotational devices. Still more particularly, this invention provides a method and systems for reactance sensors that sense the displacement of the position of an axis of rotation of a rotational device. Merely by way of example, the invention has been applied to sensing the radial position (relative to a reference position) of rotors of electrical motors of different types having magnetic bearings, and bearingless drives. But it would be recognized that the invention has a much broader range of applicability. For example, the invention can be applied to electromechanical motion devices in general to sense the position of an axis of rotation of the device with respect to a reference position. 
     As discussed above in connection with  FIG. 1 , in conventional magnetic bearings and bearingless drives systems, radial axis coordinates are used to control the radial position of the axis of rotation. That is, conventional sensors of radial position use Cartesian coordinates: (x, y). An x-direction sensor provides position signals for positions x 1  and x 2  along the X coordinate, and a y-direction sensor provides position signals for positions y 1  and y 2  along the Y-coordinate. The actual position of the rotor is calculated as a function of differences between respective position signals of the four sensors; e.g., x 1 -x 01 , y 1 -y 01 , x 2 -x 02 , and y 2 -y 02 , where x 1 , y 1  and x 2 , y 2  are actual and x 01 , y 01 , and x 02 , y 02  are reference (central) coordinates of the axes, respectively. 
       FIG. 2  is a view diagram illustrating a conventional method for radial position sensing. As shown, drawing  202  illustrates the x and y components of the Cartesian coordinates based sensor signals. Drawing  204  illustrates the geometry of a torque-producing part of electromechanical devices (e.g., a stator). For example, the stator may have a polyphase construction that is driven by suitable polyphase driving signals. Drawing  206  illustrates a combination of the Cartesian coordinates based sensing and the rotational property of the electromechanical device. This system is rather complicated and its accuracy seems to be limited. A limitation is that such a sensor system is not topologically compatible with the geometry of the torque-producing part of electromechanical devices. As a consequence, the system of sensors, bearings, and torque-producing parts, such as shown in  206 , tends to be rather complicated, clumsy, and expensive in fabrication. 
     Accordingly, it is desirable to have an improved radial position sensor, for example, to determine a the position of rotor axis with respect to the stator axis. Such sensors would be useful in applications of electromagnetic devices such as magnetic bearings and bearingless drives. 
       FIG. 3A  is a simplified view diagram illustrating a method for sensing radial position in polar coordinates according to an embodiment of the present invention. This diagram is merely an example and should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize other variations, modifications, and alternatives. As shown, an emitting element  302  includes three electrically isolated pads or signal sources A, B, and C. The center O S  of the emitting element  302  is aligned to an initial center axis of a rotational system, such as a motor; for example, the initial center axis position can be the longitudinal axis of the stator element of a motor. 
     A rotating element  304  has an axis of rotation O R  which is originally aligned with O S , but is subject to a radial displacement.  FIG. 3A  shows the rotating element having been displaced radially to a new position off of center O S . The original radial position of the rotating element  304  will be referred to herein variously as the reference position, initial radial position, starting position, the original radial position, and so on. It is understood that the rotating element  304  can have any initial position and need not be aligned with O S . As will become clear, the invention is directed to sensing displacement of the radial position of the rotating element  304  from its original radial position, so its initial radial position is not relevant to the basic teachings of the present invention. 
     In an embodiment of the present invention, a displacement vector from O S  to O R  is characterized by a radial component ρ and an angular component φ. The angle φ is an angle subtended between a line connecting O S  and O R  and a reference line. In the particular embodiment shown in  FIG. 3A , the reference line is the seam  312  between the signal source pad C and the signal source pad A. 
       FIG. 3B  is a simplified view diagram illustrating a method for a radial position sensor that uses a polar coordinate system rather than a Cartesian system of coordinates, according to another embodiment of the present invention. As shown in drawing  312 , the sensor is based on polar coordinates and provides multiphase sensing signals. Drawing  314  illustrates the rotation of the electromechanical device. Drawing  316  illustrates a combination of the polar coordinates based sensor and the rotational device. The radial position sensor is configured to indicate radial position relative to a reference radial position, e.g. deflection of rotor axis from the desirable position relative to the stator axis. A benefit of this approach stems from the fact that sensors, bearings, and torque-producing parts of electromechanical devices can utilize the identical basic polyphase topology. As a result, a complete system presenting an organic combination of these component parts tends to be constructively simple and easy in fabrication. 
     In a specific embodiment of the invention, a polyphase system includes a number of phase-shifted voltages U i  (i=1, 2, . . . ) and corresponding reactances X i . Such a system is balanced under the condition that all voltages and all reactances are equal. Under this balanced condition, the current through the load resistance R L  and the voltage on R L  are equal to zero. When the axis of rotation of the rotating element is displaced from its initial reference position, the output signal of the sensor has the following form:
 
 U   OUT   =U   m (sin ω t +φ)  EQN 1
 
This equation relates the output signal to the displacement illustrated in  FIG. 3A . The phase component φ is related to the direction of displacement φ and the magnitude component U m  is related to the magnitude of displacement ρ. This vector form of output, where just one signal contains information about character of deflection, makes further processing simple and promises better accuracy of positioning than the existing multiple sensors based on Cartesian coordinates. Moreover, this approach significantly simplifies the overall construction of the system and technology of its production. Further details of the invention are found throughout the present specification and more particularly below.
 
       FIG. 4A  is a simplified perspective view diagram illustrating a radial position sensor  400  according to an embodiment of the present invention. This diagram is merely an example and should not unduly limit the scope of the claims herein. The sensor includes a rotating element  404 , a non-rotating emitting element  402 , and a non-rotating receiving element  406 . In this particular embodiment, the rotating element  404  is disposed in juxtaposition between the emitting element  402  and the receiving element  406 . The rotating element  404  is spaced apart from the emitting element  402  and from the receiving element  406 . One of ordinary skill will readily appreciate that other configurations may be equally suitable. The emitting element  402  and the receiving element  406  are of conductive material. As discussed below, the rotating element  404  can include a suitable dielectric material. Together, these components constitute a capacitive sensor device. That is, the radial displacement of the rotating element  404  can cause a change in the capacitance of the system. In an example, the rotating element  404  can be coupled to a moveable element of a rotary device through shaft  408 . The position of the moveable element of the rotary device can then be determined from the change in capacitance caused by the displacement of the rotating element  404 . Further details of the operation of the sensor are discussed below. 
       FIG. 4B  is a simplified cross-sectional view diagram illustrating a radial position sensor system  410  according to an embodiment of the present invention. This diagram is merely an example and should not unduly limit the scope of the claims herein. One of ordinary skill in the art would recognize other variations, modifications, and alternatives. In this particular embodiment, the sensor system  410  includes a capacitive sensor having a planar construction, and in particular a disk-shaped construction. In other embodiments, the sensor can have a cylindrical, tubular, or interleaving construction. Examples of various constructions are described in U.S. Pat. No. 5,872,408, Feb. 16, 1999 and pending U.S. application Ser. No. 11/724,951, filed Mar. 15, 2007, both of which are fully incorporated herein by reference for all purposes. The sensor system  410  includes a rotating element  404 , a non-rotating emitting element  402 , and a non-rotating receiving element  406 . In this particular embodiment, the rotating element  404  is disposed in juxtaposition between the emitting element  402  and the receiving element  406 . The rotating element  404  is spaced apart from the emitting element  402  and from the receiving element  406 . One of ordinary skill will readily appreciate that other configurations may be equally suitable. The emitting element  402  and the receiving element  406  are of conductive material. As discussed below, the rotating element  404  can include a suitable dielectric material. Together, these components constitute a capacitive sensor device. 
     In a specific embodiment, the rotating element  404  is attached to a shaft  408 . Rotation of the shaft  408  about its axis of rotation causes the rotating element  404  to rotate. An opening is provided through a center portion of non-rotating emitting element  402 , through which the shaft  408  passes. This allows the shaft  408  to be mechanically connected to a device for which detection of its radial position is desired. For example, the shaft can be connected to the rotor of a motor having magnetic bearings, or bearingless drives, whose operation requires knowledge of the radial position of its rotor. Of course, any suitable configuration that allows for rotation of the rotating element  404  that does not require rotating the emitting element  402  or the receiving element  406  is appropriate. With respect to  FIG. 4B , “radial position” refers to the displacement of the axis of rotation of the rotating element  404  in the radial direction. 
       FIG. 4B  also shows a multiphase signal generator  422  for providing two or more input signals to the emitting element  402 . Recall in  FIG. 3A  that the emitting element  302  comprises three electrically isolated signal source pads A, B, C. In this particular embodiment, the signal generator  422 , or other suitable source of signals, is configured to provide three input signals U A , U B , and U C  respectively to the isolated pads A, B, and C of the emitting element  402  of  FIG. 4B . The receiving element  406  provides a single output signal U OUT , resulting from the electromagnetic coupling of input signals U A , U B , and U C  between the emitting element  402  and the receiving element  406 , through the dielectric material of the rotating element  404 . Of course, one of ordinary skills in the art would recognize other variations, modifications, and alternatives. 
       FIGS. 5A-5C  are simplified diagrams showing additional details of the sensor  410  viewed along respective view lines  5 A- 5 A′,  5 B- 5 B′, and  5 C- 5 C′ shown in  FIG. 4B .  FIG. 5A  is a face-on view (viewed along view lines  5 A- 5 A′), showing further detail of emitting element  402 . In accordance with the present invention, the emitting element  402  is configured to emit a plurality of electromagnetic fields during operation of the sensor  410 . The specifically disclosed embodiment of the emitting element  402  is a disk-shaped element comprising three electrically isolated emitting regions. It will be understood, however, that the emitting element  402  is not necessarily disk-shaped and can comprise more than three such emitting elements, or as few as two emitting elements. For purposes of explanation, the discussions which follow will assume a three-element configuration and three-phase excitation. 
     As shown in  FIG. 5A , the emitting element  402  comprises an underlying disk-shaped substrate  522  of nonconductive material. In a specific embodiment, disposed on the substrate  522  are three separate electrically conductive regions  524 ,  526 , and  528 , which divide the disk into equal areas and constitute the emitting elements in this particular embodiment of the invention. Each conductive region is substantially a 120° sector. The three electrically conductive regions  524 ,  526 , and  528  are electrically isolated from each other. Each of the input signals U A , U B , and U C  produced by the signal generator  522  is provided respectively to one of the electrically conductive regions  524 ,  526 , and  528 , for example, by way of a wire connection. It will be appreciated that other implementations of the emitting elements are possible. For example, in an alternative embodiment, the sensor can have N time-varying electrical signals that are 360°/N out of phase from one another, where N is an integer. 
       FIG. 5B  shows a face-on view (viewed along view lines  5 B- 5 B′) of the receiving element  406 . In accordance with the present invention, the receiving element  406  is configured to output a single output signal. The particular implementation of the receiving element  406  shown in  FIG. 5B  illustrates a single disk-shaped element of electrically conductive material  562 . The electrically conductive material  562  can be disposed on a substrate (not shown) for mechanical stiffness. Although the shape of receiving element  406  is shown to match the shape of the emitting element  402 , it will be apparent that the present invention does not impose such a restriction of matching shapes. 
     Since the emitting element  402  and the receiving element  406  do not rotate, it is a simple matter to provide electrical connections to these elements to energize the emitter regions of the emitting element  402  and to measure or otherwise sense the single output signal U OUT  on the receiving element  406 . For example,  FIG. 5A  shows wires  502   a ,  502   b ,  502   c  soldered or otherwise electrically connected respectively to the conductive regions  524 ,  526 , and  528 . In this way, a source of signals such as signal generator  422  can provide individual signals respectively to the conductive regions  524 ,  526 , and  528  without the need for brushes as compared to conventional devices where the emitting element is a moving part. 
       FIG. 5B  similarly shows a wire  502   d  soldered or otherwise electrically connected to the electrically conductive material  562 . In this way, the output signal U OUT  that appears on receiving element  406  can be measured or otherwise detected by a suitable detection device (not shown) without the need for brushes as compared to conventional devices where the receiving element is a moving part. In a practical application of the present invention, the output signal can be fed into a controller (not shown) which would then perform control functions based on the measured output signal. As discussed above and further explained below, the output signal has information pertaining to the radial displacement of the rotating element  404 . The magnitude U M  is proportional to the distance ρ of the rotating element  404  from its initial radial position. The phase φ is the phase difference between U OUT  and the signal that is output from the receiving element  406  when the rotating element  404  is positioned in the initial radial position. In a specific embodiment, the phase φ is proportional to the subtended angle φ described above. 
       FIG. 5C  shows a face-on view (viewed along view lines  5 C- 5 C′) of rotating element  404 . The shaft  408  connected to the rotating element  404  can be seen in cross-section. In a specific embodiment, the rotating element includes a dielectric material characterized by a dielectric constant ∈ 1 . Practically, the dielectric constant should be sufficiently greater than that of air which is defined by the constant of the air, ∈ 0 . In other embodiments, the rotating element  404  can include combinations of materials having different dielectric constants. For example, the rotating element  404  can comprise three or more portions each having a different constant. 
     In operation, the input signals U A , U B , and U C  produced by the signal generator  422 , or other suitable source of signals, are applied respectively to the conductive regions  524 ,  526 , and  528  of the emitting element  402 . For example,  FIG. 5A  shows that input signal U A  is applied to conductive region  524 , input signal U B  is applied to conductive region  526 , and input signal U C  is applied to conductive region  528 . Since the conductive regions  524 ,  526 , and  528  are electrically isolated from each other, three separate electromagnetic fields will emanate from the emitting element  402 . 
       FIG. 6  is a simplified schematic diagram for sensor system  600  shown according to an embodiment of the present invention. The notation used in this figure is conventional notation used in describing multiphase systems. An example of sensor system  600  is discussed above in connection the sensor system  410  shown in  FIGS. 4 and 5 . Referring to  FIGS. 4 and 5 , schematic diagram in  FIG. 6  illustrates components for driving the emitting element  402  and measuring the single output signal U OUT  of the receiving element  406 . As shown, the rotating element  404  is disposed in juxtaposition to the non-rotating emitting element  402  and to the non-rotating signal receiving element  406 . In a specific embodiment, the output signal is used to derive information related to the radial position of the rotating element  404 . Reference numeral  422  identifies a general representation of a multiphase signal source, in this case a three-phase source. Each phase serves as one of the input signals U A , U B , and U C . The output signal U OUT  is usually measured as a voltage across a load resistance R L . 
     The specific embodiment in  FIG. 6  is a capacitive sensor, so the electromagnetic fields are electric in nature, and are also referred to as electric fields. The presence of the three electric fields emanating from the emitting element  402  causes charge variations on the conductive material  562  of the receiving element  406 . Since the electric fields are time-varying, the receiving element  406  will experience harmonic variations in charge. These variations in the charge can be measured to produce the single output signal U OUT  by measuring the voltage potential of the conductive material  562 . Since the input signals U A , U B , and U C  are time-varying signals, each of the three electric fields emanating from emitting element  402  is time-varying. The output signal U OUT  of the receiving element  406  is therefore a single time-varying voltage that is the result of the combined effect of the three electric fields on the conductive material  562 . An example of the output signal U OUT  of the receiving element  406  is discussed in more detail below. 
       FIG. 7  is a simplified diagram illustrating electrical waveforms produced in the sensor system  600  of  FIG. 6  according to an embodiment of the present invention. In this particular embodiment, the input signals U A , U B , and U C  are harmonic signals which are 120° out of phase with respect to each other. Input signal U B  is seen to be shifted in phase by 120° relative to input signal U A . Input signal U C  is 120° phase shifted relative to input signal U B . Thus, emitting element  402  can be said to be driven by a polyphase excitation signal, and in this particular embodiment by a three-phase excitation signal, where each phase is defined as follows:
 
 U   A   =U  sin ω t  
 
 U   B   =U  sin(ω t+ 120°)
 
 U   A   =U  sin(ω t+ 240°)  EQN 2
 
where U is a predetermined amplitude. However in alternative embodiments, emitting element  402  can include N emitter regions that are driven by an N-phase input signal. In other words, the sensor can have N time-varying electrical signals that are 360°/N out of phase from one another, where N is an integer.
 
     In a capacitor, the dielectric material affects the rate of variation of charge. In accordance with a specific embodiment of the present invention, the rotating element  404  includes dielectric material. The initial position of the axis of rotation can be determined when all excitation, rotating, and receiving elements are concentrically aligned. This produces a zero output on the load resistor which serves as a nice reference output. However, the initial position can be some non-concentric alignment of the elements. This would produce a non-zero output as a reference output; however, the important thing is that deviations from this initial position can still be detected because the output will still vary from the reference output. 
     During operation the axis of rotation of the rotating element  404  may be displaced from an initial central position which can be used as a reference point. The displacement of the radial position of the dielectric material of the rotating element  404  between the conductive regions  524 ,  526 , and  528  of the emitting element  402  and the electrically single conductive material  562  of the receiving element  406  will therefore change. Consequently, the capacitance between the emitting element  402  and the receiving element  406  will change as the rotating element  404  is radially displaced from the reference position. The effect created by the radial displacement of the rotating element  404  can be seen as changes in magnitude and phase in the output signal U OUT  of the receiving element  406 . 
     As discussed above in connection with  FIG. 3 , when the axis of rotation of the rotating element is displaced from its initial reference position, the output signal of the sensor is defined by interaction of exciting signals (EQN 2) and variable capacitors formed by the exciting, rotating, and receiving elements. This interaction relates the output signal to the radial displacement of the axis of rotation described in  FIG. 3A , as discussed below. 
     In accordance with an embodiment of the present invention, there is a one-to-one correspondence between the physical radial displacement of the rotating element  404  and the output signal U OUT  with respect to one of the input signals U A , U B , or U C  serving as a reference signal. The phase and magnitude components of the output signal can be used to determine the direction and magnitude of the displacement of the axis of rotation. This can be accomplished simply by monitoring changes in the output signal U OUT . At a given reference radial position of the rotating element  404 , there will be corresponding change in the output signal U OUT . In a specific embodiment, the phase component φ is related to the direction of displacement φ and the magnitude component U m  is related to the magnitude of displacement ρ. 
     It is understood, of course, that in practice commonly known signal processing techniques may be required to obtain a usable signal. For example, A/D conversion may be needed to obtain a digital signal that a digital data processor can understand. There may be filtering of the measured output signal U OUT  to filter out noise and amplification to improve the signal-to-noise ratio. These signal processing steps are commonly performed on any measured signal in order to obtain a usable signal. It is noted that these signal obtaining steps are not performed for the purpose of determining radial position, but only for the purpose of obtaining a usable signal. In accordance with a specific embodiment of the present invention, the usable signal thus obtained requires no additional signal manipulations beyond being compared to a reference signal in order to ascertain a radial position. 
       FIG. 8  is a simplified schematic diagram illustrating an equivalent circuit for a capacitive sensor system  800  of radial position according to an embodiment of the present invention. An example of a capacitive sensor is shown above in connection to  FIGS. 4 and 5 . Here the equivalent circuit in  FIG. 8  is discussed with reference to  FIGS. 4 and 5 . As shown, the three emitter regions A, B, and C, which comprise the emitting element  402  and the electrically single conductive material  562  of the receiving element  406  are coupled by three variable capacitors C A , C B , and C C  connected in a star configuration to a common point U OUT . The signal generator  422  produces input signals U A , U B , and U C  as defined by equation EQN 2 given above. Each capacitor is driven by a different excitation source. The capacitors C A , C B , and C C  are variable due to the changing location of the dielectric material of the rotating element  404  as its axis of rotation is displaced during rotation. In the example discussed above, the sensor uses capacitive coupling to determine a change in radial position of the axis of rotation. 
       FIG. 9  is a simplified schematic diagram illustrating a reactance sensor  900  according to an embodiment of the present invention. As shown, sensor  900  is substantially similar to sensor  800  of  FIG. 8 , with the variable capacitors C A , C B , and C C  replaced by variable reactances X A , X B , and X C , respectively. In a specific embodiment, the phase component φ of output signal U OUT  is related to the direction of displacement φ, and the magnitude component U m  of output signal U OUT  is related to the magnitude of displacement ρ. Depending on the embodiment, the reactance X can be a capacitance, an inductance, or a combination of capacitance and inductance. 
       FIG. 10  is a simplified schematic diagram illustrating an inductive sensor  1000  according to an embodiment of the present invention. As shown, sensor  1000  is substantially similar to sensor  900  of  FIG. 9 , with the variable capacitor reactances X A , X B , and X C  replaced by variable inductors L A , L B , and L C , respectively. In a specific embodiment, the phase component φ of output signal U OUT  is related to the direction of displacement φ, and the magnitude component U m  of output signal U OUT  is related to the magnitude of displacement ρ. To illustrate an application of this embodiment, a specific example of an inductive sensor for radial position is discussed below. 
       FIG. 11  is a simplified top view diagram illustrating an example of an inductive sensor of radial position  1100  in accordance with an alternative embodiment of the present invention. A three-phase sensor will be described; however, it will be apparent that the present invention can be embodied in an N-phase sensor. The sensor  1100  comprises three emitters  1102   a ,  1102   b , and  1102   c , which collectively constitute the non-rotating emitting element of the sensor. In this embodiment of the present invention, the emitters  1102   a ,  1102   b , and  1102   c  are electromagnets. Each emitter  1102   a ,  1102   b , and  1102   c  comprises a ferromagnetic core about which a coil is wound. The harmonic multi-phase input signals U A , U B , and U C  discussed above are respectively provided to the coils of emitters  1102   a ,  1102   b , and  1102   c . The resulting electromagnetic fields are magnetic in nature, and can also be referred to simply as magnetic fields. 
     The rotating element  1104  is shown in  FIG. 11  and is configured for rotation about an axis of rotation which extends perpendicularly with respect to the drawing sheet. As shown, the rotating element  1104  is connected to a shaft  1108 , which in turn can be connected to a rotating device for which knowledge of its radial position is desired. The rotating element  1104  and the shaft  1108  each is of a material that is characterized by a magnetic permeability μ that may or may not be equal to each other, thus providing a path of magnetic flux between the rotating element and the shaft. 
       FIG. 12  is a simplified perspective view diagram illustrating a portion of sensor  1100  according to an embodiment of the invention. As shown, the non-rotating receiving element  1106  comprises a stationary bobbin  1116  about which a coil of wire  1126  is wound. The bobbin  1116  is disposed around and spaced apart from shaft  1108 , allowing the shaft to rotate while the bobbin remains stationary. An induced current flow through the coil of wire  1126  can be measured and used to provide the single output signal U OUT . 
     Operation of the inductive sensor  1100  is similar to operation of capacitive sensor  410  discussed above. When the coils of the emitters  1102   a ,  1102   b , and  1102   c  of sensor  1100  are respectively energized by the time-varying multiphase input signals U A , U B , and U C , each emitter element will emit an electromagnetic field. In the case of inductive sensor  1100 , the electromagnetic fields are magnetic in nature. As the rotating element  1104  rotates in proximity to each of the emitters  1102   a ,  1102   b ,  1102   c , the magnetic fields emanating from the emitters will be coupled by magnetic induction to the rotating element. This creates a magnetic field in the rotating element  1104  and in the shaft  1108 . Since the input signals U A , U B , and U C  are time-varying signals, the magnetic field created in the rotating element  1104  and the shaft  1108  likewise is time-varying. The varying magnetic field emanating from the shaft  1108  induces a current in the coil of the receiving element  1106 . The resulting current flow in the coil is measured as the single output signal U OUT . 
     When the axis of rotation of rotating element  1104  is displaced from a center position, the magnetic coupling of rotating element with the magnetic fields among the emitters  1102   a ,  1102   b ,  1102   c  changes. Suppose, for example, in  FIG. 11  that the center position of the rotating element  1104  is such that it is equidistant from emitters  1102   a ,  1102   b ,  1102   c ; e.g., d 1 =d 2 =d 3 . Suppose further that the rotating element  1104  is displaced from a reference position such that the distances between the rotating element  1104  and the emitters  1102   a ,  1102   b ,  1102   c  are not equal. If, as shown in the figure, the rotating element  1104  is displaced so as to be closer to emitter  1102   c  and further from emitters  1102   a  and  1102   b , then the magnetic coupling between the emitter  1102   c  and the rotating element will be increased while the magnetic coupling between the rotating element and the emitters  1102   a  and  1102   b  will be decreased. The magnetic field created in the rotating element  1104 , and hence the output signal U OUT , will include primarily of the contribution of the magnetic coupling of the magnetic field produced by emitter  1102   c , and to a lesser degree contributions from emitters  1102   a  and  1102   b . If the rotating element  1104  displaced closer to emitters  1102   a  and  1102   b  than to emitter  1102   c , then the magnetic field created in the rotating element and hence the output signal U OUT , will result from contributions from the magnetic fields of emitters  1102   a  and  1102   b , and to a lesser degree from emitter  1102   c . The radial displacement of the axis of rotation can be characterized by an angular component and a radial component; i.e., using polar coordinates. When the output signal U OUT  is a time-varying signal as discussed above, then the phase of the output signal is proportional to the angular component of the displacement, and the magnitude of the output signal is proportional to the radial component of the displacement. 
     Both the capacitive and inductive sensors disclosed above are governed by the principles of electromagnetic theory. However, differences in technical properties and construction will dictate their suitability in different areas of use. For example, the capacitive sensor is simple in construction, and lends itself to implementation using mass production techniques including microelectronic manufacturing and nanotechnology fabrication. 
     Inductive radial position sensors, on the other hand, require the manufacture of coil windings. It is well known fact, that systems with windings are not easily adapted for microelectronic manufacturing techniques. Nonetheless, inductive position sensors still find use in certain applications, including for example electromechanical devices, such as brushless DC motors and magnetic bearings motors, where radial position information is necessary for proper operation. Inductive sensors also produce a stronger output signal, and thus generally offer better signal to noise performance as compared capacitive sensors. 
       FIG. 13  is a simplified view diagram illustrating a method for radial position sensing and correction according to another embodiment of the present invention. As shown in  FIG. 13A , an emitting element  1302  includes three electrically isolated signal sources A, B, and C. The center O 1  of the emitting element  1302  is aligned to an initial reference point of the mechanical system. The rotating element  1304  has an axis of rotation O 2  which was originally aligned to O 1 , but has now displaced radially to the new position O 2 . According to an embodiment of the present invention, the displacement vector from O 1  to O 2  is characterized in polar coordinates by a radial component ρ and an angular component φ.  FIG. 13B  is a simplified vector diagram showing polyphase input signals U A , U B , and U C . In a specific embodiment, signals U A , U B , and U C  are coupled to isolated regions A, B, and C, respectively.  FIG. 13B  also includes a vector diagram of output signal U OUT  which is shown to have a magnitude U m  and a phase angle φ. As discussed above, the radial displacement can be derived from the output vector.  FIG. 13C  shows a vector diagram of a corrective force F, which can be applied to restore the rotating element to the original position of the axis of rotation. In a specific embodiment, the corrective force F is in the opposite direction of the radial displacement vector characterized by magnitude U m  and phase angle φ. 
     In a specific embodiment, the corrective force F can be determined according to the following process. 
     Step 1: 
     
         
         
           
             If U m =0, no control 
             If U m &gt;0, control start
 
Step 2:
 
             If φ=0° or 360°: increase power of U B  and U C  (U B =U C ) 
             If 0°&lt;φ&lt;60°: increase power of U C  and U B  (U C &gt;U B ) 
             If φ=60°: increase power of U C    
             If 60°&lt;φ&lt;120°: increase power of U C  and U A (U C &gt;U A ) 
             If φ=120°: increase power of U A  and U C (A=C) 
             If 120°&lt;φ&lt;180°: increase power of U A  and U C (U A &gt;U C ) 
             If φ=180°: increase power of U A    
             If 180°&lt;φ&lt;240°: increase power of U A  and U B (U A &gt;U B ) 
             If φ=240°: increase power of U A  and U B (U A =U B ) 
             If 240°&lt;φ&lt;300°: increase power of U B  and U A (U B &gt;U A ) 
             If φ=300°: increase power of U B    
             If 300°&lt;φ&lt;360°: increase power of U B  and U C (U B &gt;U C ). 
           
         
       
    
     In some applications (e.g., motors), the inductive sensor according to the present invention can simplify the design because the function of torque production and the function of obtaining an information signal indicative of angular position of the rotor use the same system of stator poles and windings. This advantageous aspect of the present invention arises from the constructional similarities between a motor and a sensor according to the present invention. Both utilize a multi-phase excitation system and have corresponding poles and windings. In this case, the sensor may not have separate poles with windings, and the general construction of a combined motor and sensor can be effectively simplified. This makes the inductive sensor of the present invention an attractive design element for use in control of electromechanical devices. 
     While the preferred embodiments of the invention have been illustrated and described, it will be clear that the invention is not limited to these embodiments only. Numerous modifications, changes, variations, substitutions and equivalents will be apparent to those skilled in the art without departing from the spirit and scope of the invention as described in the claims.