Abstract:
The preferred embodiments of the present invention are directed to high bandwidth positioning systems such as fast tool servos (FTS). The applications of this invention include, for example, diamond turning of mold with structured surface for mass production of films for brightness enhancement and controlled reflectivity, diamond turning of molds for contact lens and micro-optical positioning devices. Preferred embodiments of the fast tool servo can have a closed-loop bandwidth of approximately 20±5 kHz, with acceleration of up to approximately 1000 G or more. The resolution or position error is approximately 1 nm root mean square (RMS). In a preferred embodiment, the full stroke of 50 μm can be achieved up tol kHz operation.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This patent application claims the benefit of U.S. Provisional Patent Application 60/517,216, having a filing date of Oct. 31, 2003 and U.S. Provisional Patent Application 60/619,183, having a filing date of Oct. 15, 2004, these applications being incorporated herein by reference in their entirety. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     Fast Tool Servo (FTS) technology can enable precise positioning or manufacturing of complicated sculptured surfaces having nanometer-scale resolution requirements. Such surfaces are used in a wide range of products, including films for brightness enhancement and controlled reflectivity, sine wave ring mirrors used in carbon dioxide (CO 2 ) laser resonators, molds for contact lenses, as well as in micro-optical devices such as Fresnel lenses, multi-focal lenses and microlens arrays. The limits on stroke, bandwidth, acceleration, and position noise of the FTS impose limits on the types, quality, and rate at which the intended surfaces can be produced. The requirements for obtaining high throughput for an FTS include high bandwidth, high acceleration, and high accuracy.  
         [0003]     FTS actuators can be categorized as four types: piezoelectric actuators, magnetostrictive actuators, Lorentz force motors (including linear and rotary) and variable reluctance actuators. According to moving strokes, short stroke can be defined as being less than 100 μm, intermediate as being between 100 μm and 1 mm and long stroke as being above 1 mm.  
         [0004]     Most of the high bandwidth, short stroke FTS&#39;s are based on piezoelectric actuators. Piezoelectric FTS&#39;s have the advantage that they can readily achieve bandwidths on the order of several kHz and high acceleration on the order of hundreds of G&#39;s, are capable of nanometer resolution of positioning, and can achieve high stiffness (usually greater than 50 N/μm in the typical sizes used).  
         [0005]     However, piezoelectrically actuated FTS&#39;s also have significant disadvantages. When the piezo materials undergo deformation, heat is generated by hysteresis loss, especially in high bandwidth and high acceleration applications. In addition, it may be difficult to couple the piezoelectric material to a moving payload in such a way as to not introduce parasitic strains in the actuator. Furthermore, piezoelectric FTS&#39;s require large and expensive high-voltage, high current amplifiers to drive these devices. Still another shortcoming associated with piezoelectrically activated FTS&#39;s is that the structural resonance modes of the PZT stacks limit working frequency ranges, because operation near the internal resonances can cause local tensile failure of PZT ceramics. Piezoelectric actuators can also be used in other high-bandwidth, short-stroke applications such as electric engraving, mirror positioning and scanning and micropositioning, but have the same disadvantages.  
         [0006]     However, electromagnetic actuators do not have such problems and thus are a promising alternative. Variable reluctance actuators in FTS&#39;s have not been developed extensively, because of the difficulty of controlling these devices in the presence of the inherent non-linearities. There still remains a need for developing an electromagnetically driven actuator as a replacement for widely used piezoelectrically actuated systems.  
       SUMMARY OF THE INVENTION  
       [0007]     The preferred embodiments of the present invention are directed to high bandwidth fast positioning systems such as fast tool servos (FTS). The system includes an armature assembly having a cutting tool mounted thereon, an actuator that applies a force to a working surface of the armature and a bias actuator that delivers bias flux to a biased surface of the armature. By applying bias flux to a separate region of the armature surface, a more efficient linear response is achieved at high operating frequencies. In a preferred embodiment, the bias flux is directed through a surface that is orthogonal to the surfaces receiving the working flux. For example, a preferred embodiment directs the bias flux through the outer radial surface of a disk shaped armature, and uses permanent magnets as the bias flux excitation source.  
         [0008]     Preferred embodiments of the invention utilize this system for both rotary and linear reciprocating positioning systems. The applications of this invention include, for example, fast tool servos for diamond turning of molds with structured surfaces for mass production of films for brightness enhancement and controlled reflectivity, diamond turning of molds for contact lens and positioning systems such as micro-optical devices, optical tracking and pointing systems using fine mirror steering, engravers for cutting printing plates, and so on.  
         [0009]     Preferred embodiments of the fast tool servo can have a closed-loop bandwidth of approximately 20±5 kHz, with an acceleration of a cutting tool up to approximately 1000 G or more. The resolution or position error is approximately 1 nm root mean square (RMS). In a preferred embodiment, the full stroke of 50 μm can be achieved up to 3 kHz operation.  
         [0010]     In accordance with a preferred embodiment, a servo tool device for fabricating a three-dimensional surface, includes an armature assembly having a front end and a rear end with a cutting tool provided at the front end, a shaft, such as a carbon fiber tube, and an armature actuated by a pair of solenoids. At least one flexure attaches the moving armature assembly to a frame. The flexure guides a tool tip along one degree of freedom in the axial direction of the shaft or tube. The pair of solenoids can be circular E-type solenoids in a preferred embodiment. The device further includes coil windings provided into a plurality of slots of the solenoids, and a linear power amplifier or switching amplifier to drive the coils. The device further includes a capacitance probe provided in the rear end of the device to sense the motion of the armature. The armature and solenoids are made of high frequency, soft magnetic materials, for example, ferrite, silicon steel lamination, nickel-steel, cobalt-steel, powder sintered iron and metallic glass.  
         [0011]     In accordance with another aspect of the present invention, the device further includes a controller. The controller comprises a dynamic non-linear compensator, an adaptive-feed forward compensator and a lead-lag (frequency shaping) controller. The controller can include digital processing integrated circuits in a preferred embodiment. The controller can include a programmable computer. Position sensing can be performed with capacitance sensors, inductive sensors, optical sensors or with a glass scale.  
         [0012]     In accordance with yet another aspect of the invention, a servo tool device for fabricating a three-dimensional surface is provided. The servo tool devices include a frame and an armature assembly moveably disposed within the frame. The armature assembly has a front end and a back end and the shaft moves along a defined axis, and has an armature attached to the back end. The servo tool device also includes a cutting tool which is mounted on the front end of the shaft so that it can engage a workpiece along the defined axis. A flexure is mounted to the frame in a manner allowing the shaft to pass therethrough. The flexure provides both axial and rotational stiffness to the shaft as it moves along the axis while the cutting tool engages a workpiece. An elastomeric material such as a rubber-pad or laminated rubber bearing provides further motion guiding for the armature assembly along the defined axis. The servo tool device may also include a controller, power amplifier, position sensor and user interface for facilitating operation on the workpiece.  
         [0013]     The foregoing and other features and advantages of the system and method for high bandwidth variable reluctance fast tool servos will be apparent from the following more particular description of preferred embodiments of the system and method as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]      FIG. 1  illustrates a schematic representation of a fast tool servo based system in accordance with embodiments of the invention;  
         [0015]      FIGS. 2A-2E  illustrate various views of an embodiment of a fast tool servo in accordance with an aspect of the invention;  
         [0016]      FIG. 3  illustrates a sectional view of a fast tool servo;  
         [0017]      FIG. 4  illustrates an assembly of a fast tool servo including an armature, moving backbone and tool insert;  
         [0018]      FIG. 5  illustrates an embodiment of a front core for use in a fast tool servo;  
         [0019]      FIG. 6  illustrates the front core of  FIG. 5  along with coils for carrying alternating current;  
         [0020]      FIG. 7  illustrates a middle assembly of a fast tool servo in accordance with an embodiment of the invention;  
         [0021]      FIG. 8  illustrates an embodiment of a front flexure, or bearing;  
         [0022]      FIG. 9A  illustrates various flux paths associated with an embodiment of a fast tool servo;  
         [0023]      FIG. 9B  illustrates various acceleration curves as a function of frequency for magnetic materials used in an embodiment of an armature;  
         [0024]      FIG. 10  illustrates an embodiment of an ultra fast rotary, motor that can be used for operating a cutting tool;  
         [0025]      FIG. 11  illustrates an alternative embodiment of an ultra fast rotary motor having a substantially square housing;  
         [0026]      FIG. 12  illustrates a front body assembly having an armature in accordance with a preferred embodiment of the invention;  
         [0027]      FIG. 13A  illustrates a schematic representation of an embodiment of a fast tool servo and a controller;  
         [0028]      FIG. 13B  illustrates a perspective view of the armature assembly with the flexure system in accordance with a preferred embodiment of the invention.  
         [0029]      FIG. 14  illustrates a schematic representation of a fast tool servo based diamond turning machine;  
         [0030]      FIGS. 15A-15C  illustrate exemplary control algorithms useful for operating embodiments of a fast tool servo;  
         [0031]      FIGS. 16A and 16B  illustrate the closed loop frequency response, magnitude and phase, respectively, with respect to frequency in accordance with an embodiment of the invention;  
         [0032]      FIG. 16C  illustrates a small signal closed loop step response in accordance with a preferred embodiment of a fast tool servo;  
         [0033]      FIG. 16D  illustrates tabulated results illustrating the performance of an adaptive feed forward control algorithm;  
         [0034]      FIGS. 17A and 17B  illustrate embodiments of a controller that can be used for operating a fast tool servo;  
         [0035]      FIGS. 18A through 18C  illustrate schematic representations of embodiments of a power amplifier that can be used when practicing embodiments of a fast tool servo;  
         [0036]      FIG. 19A  illustrates the static performance of the actuator in accordance with a preferred embodiment of the present invention, in particular, a plot of force (N) versus current (A);  
         [0037]      FIGS. 19B and 19C  illustrate the dynamic performance of the actuator in accordance with a preferred embodiment of the present invention;  
         [0038]      FIG. 19D  illustrates the acceleration of the fast tool servo when tracking a 9 μm peak-to-valley 3 kHz sine wave in accordance with a preferred embodiment of the present invention;  
         [0039]      FIG. 19E  illustrates the full stroke of 50 μm that is achieved at 1 kHz operation of a fast tool servo in accordance with a preferred embodiment of the present invention;  
         [0040]      FIG. 19F  illustrates graphically a 1.2 nm RMS error when the spindle is off in accordance with a preferred embodiment of the present invention;  
         [0041]      FIG. 19G  graphically illustrates the error in tracking a 10 μm, 1 kHz sinusoidal signal in accordance with a preferred embodiment of the present invention;  
         [0042]      FIG. 20A  illustrates a diamond turned part provided by the electromagnetically driven FTS in accordance with a preferred embodiment of the present invention; and  
         [0043]      FIG. 20B  graphically illustrates a profile, expanded in the circumference, to show a half sinusoidal wave of the diamond turned part illustrated in  FIG. 20A  wherein the peak-to-valley amplitude of the sine wave is 20 μm in accordance with a preferred embodiment of the present invention.  
         [0044]      FIGS. 20C-20H  illustrate preferred embodiments of positioning systems in accordance with the invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0045]      FIG. 1  illustrates a schematic representation of a system  10  consisting of linear fast tool servo (linear FTS)  12  having a shaft  14  and tool  16 , a tool tip position sensor  18  having a position sensor interface  20  and a position sensor control and processing module  22 , a controller  24  and a power amplifier  26 . FTS  12  is an electromagnetic device that operates at very high speeds while allowing extremely precise control of tool tip  16 . In fact, embodiments of FTS can operate at speeds on the order of 20 kHz while providing tool position accuracies on the order of 1 nanometer (nm).  
         [0046]     Position sensor  18  is communicatively coupled to shaft  14  in a manner allowing the position of tool  16  to be monitored with respect to a reference. The reference may be a face  34  of a housing  32  surrounding components making up FTS  12 , or the reference may be a gap between magnetic components, a point located external to housing  32 , etc. Position sensor  18  may also include an interface  20  and control module  22  for coupling sensor  18  to controller  24 .  
         [0047]     Interface  20  may be coupled to position sensor processing module  22  using a cable  28 . Cable  28  may consist of a single electrical or electromagnetic medium such as a wire or optical fiber, or it may consist of multiple wires and/or fibers. Cable  28  may carry power, data and/or control signals.  
         [0048]     Processing module  22  is coupled to controller  24 . Controller  24  may consist of a general purpose and/or application specific processor executing machine-readable instructions for controlling the operation of FTS  12 . A power amplifier  26  is used to drive shaft  14  at a desired frequency and with a desired excursion or amplitude. Power amplifier  26  may be coupled to FTS  12  using one or more wires  30 .  
         [0049]      FIG. 2A  illustrates an embodiment of FTS  12  showing probe  18 , cables  30  and housing  32 .  FIG. 2B  illustrates a cutaway view of the FTS  12  illustrated in  FIG. 2A .  FIG. 2B  illustrates FTS  12  along with a front solenoid  36  ( FIG. 2C ), shaft  14  (here carbon fiber tube), a front flexure, or bearing  40 , a front body  42 , an adjustment washer  44 , an armature  46 , a rear body  48 , a rear solenoid  50 , a rear flexure  52  and position sensor  18  (here shown as a capacitance probe). Front solenoid  36  and rear solenoid  50  ( FIG. 2E ) provide a pushing force, displacing (extending) tool  16  away from front face  34 , and a pulling force, displacing (retracting) tool  16  toward face  34 . Front and rear solenoids  36 ,  50  apply force to armature  46  which is attached to shaft  14 .  FIG. 2D  illustrates an embodiment of armature  46  and carbon fiber tube  14 . As shown in  FIG. 2D , a distal end of carbon fiber tube  14  is coupled to armature  46  and a proximal end  56  is available for mounting to a base of tool  16 . Armature  46  and carbon fiber tube  14  together make a moving assembly  58  which is suspended to housing  32  using front flexure  40  and rear flexure  52 . Flexures  40 ,  52  may be fabricated from nonmagnetic or magnetic materials such as spring steel.  
         [0050]     Flexures  40 ,  52  guide assembly  58  allowing it to move in only one direction, for example, along axis  60  ( FIG. 2B ). Thus flexures  40 ,  52  allow tool  16  to have one degree of freedom. Front solenoid  36  and rear solenoid  50  together provide a push-pull drive to assembly  58 . In a preferred embodiment, circular E-type solenoids are employed having respective air gaps on the order of 100 micrometers (μm). If desired, air gaps can be reduced to improve efficiency of operation.  FIG. 2C  illustrates an embodiment of front solenoid  36  and  FIG. 2E  illustrates an embodiment of rear solenoid  50 .  
         [0051]      FIG. 3  illustrates an embodiment of front solenoid as having a first front core  70  and a front winding set  76 . In addition, rear solenoid includes a rear core  78 , and a rear winding set  84 . Front and rear solenoids may be mounted in a front housing  86  and rear housing  88 , respectively. And, a middle housing  90  may include a middle core  92 , a permanent magnet  96 , a middle bearing  100 . Armature  46  may be slideably associated with the middle bearing  100 .  
         [0052]     Permanent magnet  96  generates a DC biasing flux which facilitates generation of a force that is linear with respect to both the air gap and excitation current. This linearity results, at least in part, from the fact that the permeability of the permanent magnets is near that of air, and therefore the DC bias flux does not change significantly with the armature position.  
         [0053]      FIG. 3  also illustrates an alternative preferred embodiment for mounting a cutting tool to FTS  12 . In particular,  FIG. 3  illustrates a hollow shaft  14  having position sensor  18  passing into an open inner volume of shaft  14 . At the distal end of shaft  14 , a tool insert  104  is coupled to shaft  14  and to tool holder  106 . Tool holder  106  is in turn releasably coupled to tool tip  108 . For example, tool tip  108  may be attached to tool holder  106  using threaded fasteners or a machined recess adapted for holding tool tip  108 . Bias is directed through the biasing surface  105  which corresponds to the outer radial surface of the armature  46  on which the middle bearing  100  is secured. The biasing surface faces the bias actuator surface  107  of magnet  96 . The force applied to the armature  46  by magnetic front and rear cores  70  and  78  is directed through the working surface,  109  on the front and rear sides of the armature. Preferred embodiments of the invention separate the working surface  109  and the bias receiving surface  105  completely or provide at most a 10-20 percent overlap of these surfaces. In this embodiment, these two surfaces are positioned at an orthogonal angle relative to each other.  
         [0054]     In an embodiment, front core  70  and rear core  78  have gaps approximately 2 millimeters (mm) wide and 20 mm deep into which windings consisting of 4 strands of #30 AWG self-bonding wire are wound. The use of multi-strand self-bonding wire reduces the skin-depth effect in the copper conductor at high frequencies. The mass of armature  46  and shaft  14  can be reduced in order to maximize acceleration and minimize the reaction force associated with assembly  58 . Eddy currents along magnetic flux paths may be reduced by utilizing sintered soft magnetic materials made from iron particles having a diameter on the order of 100 μm.  
         [0055]     Alternative embodiments can employ different magnetic materials suitable for high frequency applications such as, for example, but not limited to, ferrite, laminated nickel iron, silicon iron, powder sintered iron and laminated metallic glass. Desirable magnetic materials have high saturation, high resistivity, high permeability and mechanical strength.  
         [0056]      FIG. 4  illustrates an embodiment of moving assembly  58  coupled to tool insert  104 . Shaft  14  is rectangular in shape along its long axis  120  and has a substantially square cross section  122 . Shaft  14  is made from a material with high stiffness and low weight such as a metal matrix composite ceramic carbon fiber, aluminum oxide, silicon carbide or silicon nitride. Armature  46  has an inner surface  124  and outer surface  126 . Inner surface  124  conforms to the outer dimensions of cross section  122 . The sides of armature  46  making up outer surface  126  may take on substantially any shape that facilitates desired operation in conjunction with the magnetic components of front housing  86 , middle housing  90  and rear housing  88 .  
         [0057]      FIG. 5  illustrates a preferred embodiment of front core assembly  128  consisting of a first front core section  70 , second front core section  72 , third front core section  71  and fourth front core section  73 . Front core assembly  128  has an inner volume  130  shaped to enclose shaft  14  with a determined clearance around each side of shaft  14 .  FIG. 6  illustrates front core assembly  128  along with a front winding assembly  132 .  
         [0058]      FIG. 7  illustrates a middle assembly  140  consisting of middle core  92 , middle housing  90 , a rear bearing  142 , and first, second, third and fourth permanent magnetics  96 ,  98 ,  97 ,  99 , respectively.  
         [0059]      FIG. 8  illustrates an embodiment of front flexure, or bearing,  110 . Front flexure  110  is substantially planar in shape and cut so as to encircle shaft  14  using inner surfaces  144  while mounted to front housing  86 . Front flexure  110  can be fitted with mounting holes  146 . Front flexure  110  provides lateral stiffness and rotational stiffness to the armature and the shaft  14 .  
         [0060]      FIG. 9A  illustrates flux paths associated with FTS  12 . The direct current (DC), or steady state flux  150  is generated by permanent magnet  96 . The arrow tips indicate the direction of magnetic induction fields. If the alternating current (AC), or varying, flux generated by coils  74  and  76  flows as shown, the magnetic induction field generated by the excitation current flows as shown by loop  154 . The magnitude of the net force is proportional to the current inside the coil windings. If the current directions through the coils are reversed, the net force will be directed in the opposite direction. As such, bi-directional motion of the tool tip  108  is generated by reversing the current directions through the coils.  
         [0061]     An elastic material can be positioned in the gap between the bias receiving surface  105  and the bias actuator surface  107 .  
         [0062]     The embodiment of  FIG. 9A  produces an actuating force that is a linear function of both the exciting current and armature displacement. Moving assembly  58  ( FIG. 2D ) consists of an armature  46  and motion backbone (shaft)  14  having high specific stiffness. The configuration of  FIG. 9A  allows the entire normal area of armature  56  to generate normal force since the flux bias is brought in through the radial faces of the armature  56 . Moreover, the excitation coils  74 ,  76  are fully enclosed by the armature pole faces. Thus, more coil area can be accommodated while significantly reducing leakage flux.  
         [0063]     The actuating force F is a linear function of exciting current I and the armature position X, which greatly simplifies the associated control laws. By normalizing these variables with F o , I o , and X o , the force relation can be formulated as: f=ηλ, λ=I+ηx where f, η, λ, I, and x are normalized force, permanent magnet biasing strength, flux, and excitation current as defined below: 
    f=F/F o , i=I/I o , q=B pm /B o , x−X/X o , F o =A e B sat   2 /2μ o , B o =B sat /2, B pm =B r A pm /2A e , I o =2X o B o /μ o N. 
 
 Here X o  is the air gap at neutral position, B sat  is the saturation flux of the armature, B r  is the remanence flux of the permanent magnet, A e  is the effective armature pole face area, A pm  is the pole face area of permanent magnet, and N is the turn number of excitation coil winding. From this result, it is clear that the actuating force f is more directly related to flux λ than to exciting current i. By using a flux feedback method as shown later, we can thus achieve better linearity than using current control alone. 
   
 
         [0065]      FIG. 9B  shows calculated maximum accelerations over frequency for various materials employed in embodiments of armature  46  having a thickness of 3 mm.  
         [0066]      FIG. 10  illustrates a rotary embodiment  169  of FTS  12  which employs the principles discussed in conjunction with  FIG. 9A . Rotary embodiment  169  includes a moving backbone  172  coupled to an armature  170 . A rotary core  190  houses permanent magnets  174 ,  176 ,  178 ,  180 , respectively. Each magnet includes a winding set having an AC current flow as shown. For example, magnet  174  has a winding employing a current flow  182  out of the page, magnet  176  has current flow  184  into the page, magnet  178  has current flow  186  out of the page, and magnet  180  has current flow  188  into the page. Moving backbone  172  may be fabricated out of lightweight material such as silicon carbide. Armature  170  and magnetic core  190  can be made from nanocrystalline laminations or other soft magnetic material. A supporting bearing can be rubber or laminated rubber and fitted between magnets  174 ,  176 ,  178 ,  180  and armature  190 . As with the linear tool system, the bias is directed through the outer radial surfaces of the armature to achieve efficient linear high frequency operation.  
         [0067]      FIG. 11  illustrates an alternative implementation for a rotary configuration of FTS. Rotary assembly  200  includes a magnetic core  202  retained in a housing  204 . Within magnetic cores  202  are permanent magnets  210 ,  212 ,  214 ,  216  having respective windings with current directions  224 ,  218 ,  220 ,  222 , respectively. Rotary assembly  200  also includes an armature  206  and moving backbone  208 .  
         [0068]      FIG. 12  illustrates a front body  229  containing an armature  46  and the flexure supporting the armature disk.  
         [0069]      FIG. 13A  illustrates a schematic representation of a system  230  for precisely operating tool tip  108 . System  230  includes FTS  12 , position sensor processor  18  implemented using a differential amplifier  22 , power amplifier  26  and controller  24 , including an analog-to-digital converter (A/D)  232  for receiving the position sensor signal, a digital-to-analog converter (D/A)  236  for producing an analog input signal to power amplifier  26 , a digital controller  234  for executing machine-readable instructions necessary to control FTS  12  and a DSPACE digital control system for providing a user interface as well as machine-readable instructions to digital controller  234 . The armature assembly  45  includes an armature  46  having flexures  40 ,  52  that provide lateral stiffness ( FIG. 13B ). The assembly also includes a tool holder  57  on the distal end of shaft  14 .  
         [0070]      FIG. 14  illustrates a system  250  for machining a workpiece in accordance with teachings herein. In particular, system  250  is a diamond turning machine (DTM). The DTM  250  is composed of three main parts: a machine base  252 , a Z stage  254 , and an X stage  256 . The machine base  252  is made from concrete or granite, and is isolated from ground vibration by air legs and/or active vibration isolation systems. The X and Z stages are supported by a hydrostatic bearing system on the machine base  252 , so that they can move along X and Z directions as shown in  FIG. 14 , respectively. The X stage  256  and Z stage  254  may be driven by linear motors.  
         [0071]     On top of the X stage  256  is installed the spindle  272 , which is supported by an air bearing. The workpiece  276 , to be machined, is installed in the front end of spindle  272 . A spindle encoder  274  is mounted at the back end of spindle  272  to measure the spindle rotation angle. FTS  12  is installed on Z stage  254  via FTS housing bearing  258 , which guides the FTS housing to move only in Z direction relative to Z stage  254 . FTS housing sensor  266  measures the position of the FTS  12  relative to Z stage  254 . Tool tip  108  is installed in the front end of FTS  12 . Z stage laser scale  270  measures the motion of Z stage  254  in the Z direction, while the X stage laser scale  268  measures that of X stage  256  in X direction. All position signals are fed into real-time computer  24  via signal conditioning modules  266  and  264 , respectively. Real-time computer  24  outputs control signals to the linear power amplifier  26 , which in turn drives the coils inside the FTS  12 . A host computer  260  may communicate with real-time computer  24  to display the working status of system  250 , and to receive commands from an operator. With appropriate motion coordination of X stage  256 , Z stage  254 , the spindle  272 , and the FTS  12 , arbitrarily shaped surfaces can be machined on workpiece  276  with high precision.  
         [0072]      FIG. 15A  illustrates an exemplary control algorithm  280  that can be utilized in conjunction with FTS  12  and DTM  250 . Electromagnetically driven actuators can be difficult to control in the sense that the actuating force is proportional to the current squared and inversely proportional to the air gap squared. Moreover, the force decreases with frequency because the magnetic field cannot penetrate the magnetic material at high frequencies. In order to compensate for these non-linear and frequency dependent characteristics, a dynamic non-linear compensation (DNC) control method  280  as shown in  FIG. 15A  is applied. Here K(x)  282  represents the relation between current and magnetic field, D(s)  284  the eddy current effect, and the “Square” block  286  relates the magnetic flux to the actuating force. This DNC control method uses a compensator  298  to partially compensate the non-linearity of the actuator, but is not expected to linearize the actuator completely because it is a feed-forward model-based method and modeling errors may exist. The whole position control loop is compensated with a lead-lag controller (including notch or resonant elements) and low-frequency integrator.  
         [0073]     Different details of the system controller in accordance with a preferred embodiment of the present invention are shown in  FIGS. 15B  and C. At the spindle rotational frequency and its higher harmonics, a plug-in type adaptive-feed forward-compensation (AFC) controller  320  is used to improve the rejection of spindle-generated disturbance and to improve the spindle-synchronized trajectory tracking performance. The lead-lag controller  322  and the DNC  324  control provides the control mechanism for the FTS actuators  326 . The position of the actuator provides the feed back control input into the control system  319 .  
         [0074]     In one preferred embodiment, the controller is implemented with a DSPACE  1103  board, for example, wherein all the digital controllers are in the discrete domain. The full stroke of 50 μm can be achieved up to 1 kHz operation. The maximum acceleration is 160 G&#39;s when tracking a 9 μm peak-to-valley 3 kHz sine wave. For a sampling frequency of 100 kHz, the closed-loop frequency response is shown in  FIGS. 16A and 16B . The small signal bandwidth can be as high as 10 kHz. For a sampling frequency of 83 kHz, the closed loop bandwidth is 8 kHz. The 100 nm closed-loop step response is shown in  FIG. 16C .  
         [0075]     The position error is approximately 1.2 nm RMS when the spindle is turned off. After the spindle is turned on, the error degrades to 3.5 nm RMS because of the pulse width modulation (PWM) noise from the spindle amplifier. To evaluate the tracking performance, a 10 μm peak-to-valley 1 kHz sine wave trajectory may be applied to drive the fast tool servo. When the AFC is not included in the control loop, the tracking error is approximately 1.048 μm RMS. When the first harmonic AFC is applied, the error is reduced to approximately 0.0214 μm RMS. The tracking error reduces to approximately 0.0148 μm RMS when the second harmonic AFC is further applied and to approximately 0.0073 μm RMS when the third harmonic is also added. This illustrates that the non-linearity of the actuator and the power amplifier introduces disturbance forces of second and higher order harmonics, and the AFC of poles at multiple harmonic frequencies can significantly improve the tracking error.  FIG. 16D  illustrates tabulated results showing the performance of the adaptive feed forward control in accordance with a preferred embodiment.  
         [0076]     In accordance with an alternate preferred embodiment, the controller  300  includes at least three digital signal processing (DSP) integrated circuit chips such as, for example, TS 101 chips provided by Analog Devices. These may be multiple DSP chips. The bandwidth of the FTS can be increased to approximately 20±5 kHz using the DSP chips. In an embodiment of controller  380  a computation power on the order of 5.4 G FLOPS is achieved using three DSP&#39;s  382 A-C operating in parallel at speeds of 300 MHz. This embodiment produces a 1 MHz control loop having a delay on the order of 1.8 μs. Total harmonic distortion for A/D  392  and D/A  398  is less than −88 dB up to 50 kHz. Therefore, embodiments of system  10  can operate with tool speeds on the order of 50 kHz.  FIG. 17A  illustrates a schematic diagram of the control system  350  in accordance with a preferred embodiment of the present invention using the DSP integrated circuits  356 . The input  352  is indicative of the position information of the actuators. In a preferred embodiment, the signal  352  is the output from the capacitance probe  18 . The input signal is digitized by the analog to digital (A/D) converter circuit  354 , the output of which forms the input to the DSP control circuit  356 . The output of the DSP circuit is then converted to an analog signal by the D/A converter circuit  358  and the output of which forms the input to the power amplifier  360 . The output of the power amplifier is provided to the solenoids. An oscilloscope or display unit  362  can be used in the control loop in a preferred embodiment. Additionally a central processing unit  366  or a computing device such as, for example, a high-speed real time computer can be included in the control loop to monitor the control system. Memory units can also be added in preferred embodiments. Flux feedback and sensing elements can also be incorporated in the preferred embodiment FTS.  
         [0077]      FIG. 17B  is a schematic block diagram of the real time computer  380 . Computer  380  includes three digital signal processors (DSP  382 A, DSP  382 B, and DSP  382 C), which share a common cluster bus  384  with the synchronous dynamic random access memory (SDRAM)  386 , the field programmable gate array (FPGA)  388 , and the electrically-erasable read only memory (FLASH)  390 . Through the FPGA  388 , three processors  382 A-C can read/write  392  peripheral resources, such as 16-bit analog-to-digital converters (ADC), 16-bit digital-to-analog converters (DAC)  394 , quadrature encoder interfaces  396 , digital inputs/outputs (I/O)  398 , and RS-232 serial port  400 . The tool tip sensor  18  and the FTS housing sensor  266  are fed into the ADC of the real-time computer. The Z-stage laser scale  270 , the X-stage laser scale  268  and the spindle encoder  274  connect to encoder interfaces of the real-time computer. The DACs  394  output control signals to the linear power amplifier  26 . The real-time computer communicates with host computer  260  via RS-232 serial port  400 .  
         [0078]      FIG. 18A  is a block diagram of power amplifier  26 . Magnetic cores  402  are a representation of the magnetic path composed by the front core  70 , the middle core  92 , the rear core  78 , and armature  46 . Surrounding the magnetic cores  402 , multiple-start windings are driven separately by power voltage amplifiers  406  in parallel. The current of each winding is controlled independently with separate current controllers  404 , which are driven by the same reference current signal I REF .  
         [0079]      FIG. 18B  illustrates the power amplifier circuit in greater detail. The embodiment of  FIG. 18B  produces 1 KW of output power over a linear range. Four APEX PA52A amplifiers are driven in parallel to drive the excitation coils  74 ,  76 . Using fluxing sensing coils  402 , a flux sensing circuit  409  is integrated into the current feedback path as shown in  FIG. 18B  to feed back the generated flux at high frequencies. The embodiment of  FIG. 18B  works in current mode at low frequencies, and works in flux mode at high frequencies where the current feedback signal rolls down and the flux feedback signal rolls up. The circuit includes current sensor  411  and low pass filter  405 . Consequently, better linearity can be achieved at high frequencies. Additionally, armature position x- 407  is fed back to compensate the negative spring effect of the ultra fast motor using an analog feedback loop, which maintains a higher bandwidth than a comparable digital implementation.  
         [0080]      FIG. 18C  contains a more detailed schematic diagram of power amplifier  26 .  
         [0081]      FIG. 19A  illustrates the static performance of the actuator in accordance with a preferred embodiment of the present invention, in particular, a plot of force (N) versus current (A).  FIGS. 19B and 19C  illustrate the dynamic performance of the actuator in accordance with a preferred embodiment of the present invention.  
         [0082]      FIG. 19D  illustrates the acceleration of the fast tool servo when tracking a 9 μm peak-to-valley 3 kHz sine wave in accordance with a preferred embodiment of the present invention.  FIG. 19E  illustrates the full stroke of 50 μm that is achieved at 1 kHz operation of a fast tool servo in accordance with a preferred embodiment of the present invention.  
         [0083]      FIG. 19F  illustrates graphically a 1.2 nm RMS error when the spindle is off in accordance with a preferred embodiment of the present invention.  FIG. 19G  graphically illustrates the error in tracking a 10 μm, 1 kHz sinusoidal signal in accordance with a preferred embodiment of the present invention.  
         [0084]      FIG. 20  illustrates a diamond turned part provided by a preferred embodiment of an electromagnetically driven FTS. The surface is machined by face turning. The cutting is conducted using a Moore diamond turning machine. A DSPACE  1103  board controls both the X-Z slides of the machine and the FTS as described with respect to one preferred embodiment. A multiple sampling rate system is implemented. The sampling rate for the FTS controller is 83 kHz and the sampling rate for the spindle and X-Z slides controller is 4 kHz to ensure that the slides controls achieve 100 Hz bandwidth. The spindle speed is approximately 1800 rpm.  
         [0085]      FIG. 20B  illustrates the profile, expanded in the circumference to be a half sinusoidal wave. There are 30 harmonics per spindle revolution and the peak-to-valley amplitude of the sine wave is 20 μm. The flat surface (a piece of aluminum material) was machined first and then the sinusoidal surface was cut.  
         [0086]      FIGS. 20C and 20D  illustrate micro-positioning systems  680 . A linear fast motor  682  as described herein is used to position article  686  along a longitudinal (X) axis. Alternatively, a rotary fast motor  684  is used to rotate article  686  around axis through angle 0.  
         [0087]     As shown in  FIGS. 20E and 20F , fast mirror steering  660  can be obtained using a rotary fast motor  666  as described herein to position mirror  664  to reflect light from a lamp or laser  662  along a path. Alternatively, a linear fast motor  672  can position mirror  674  along an axis.  
         [0088]     As shown in  FIGS. 20G and 20H , an engraver  690  can include a rotating drum  696  positioned relative to a linear motor  692  and tool  694  or rotary motor  697  and tool  698 .  
         [0089]     The claims should not be read as limited to the described order or elements unless stated to that effect. Therefore, all embodiments that come within the scope and spirit of the following claims and equivalents thereto are claimed as the invention.