BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
       [0001]    The present disclosure relates to rotating machinery, and more particularly to determining the rotational position of rotating components in rotating machinery. 
       2. Description of Related Art 
       [0002]    Resolvers are commonly used to determine the rotational position of rotating components in rotating machinery. For example, resolvers are oftentimes associated with starter motor generators and actuators in aircraft to provide feedback regarding the state of the actuator, e.g., whether the actuator is open, partially open, or closed. A typical resolver includes an excitation coil carried by a rotating component and rotatable relative to first and second secondary coils positioned 90-degrees out of phase with one another. A sinusoidal excitation signal supplied to the excitation coil induces corresponding output signals in the first and second secondary coils. By comparing the phase of the excitation signal to the phase of the output signals, the orientation or position of the excitation coil can be determined. 
         [0003]    In some applications, such as in high speed rotating machinery, the resolver output signals need to be sampled at rates that can approach the excitation frequency of the resolver. Since many resolver algorithms require a full sinusoid of the waveform to determine the shaft position or additional filtering as in full wave rectification, rotational position determination may be delayed or erroneous when rotational speed changes. 
         [0004]    Such conventional methods and systems for determining rotational position have generally been considered satisfactory for their intended purpose. However, there is still a need in the art for improved resolvers, resolver interfaces, and methods of determining position using resolvers. The present disclosure provides a solution for this need. 
       SUMMARY OF THE INVENTION 
       [0005]    A resolver system includes a rotatable primary winding, a secondary winding fixed relative to the primary, and an analog-to-digital converter (ADC) electrically connected to the secondary winding. A control module is operatively connected to the ADC and is responsive to instructions to apply an excitation voltage with an oscillating waveform to the primary winding, induce a secondary voltage using the secondary winding using the excitation voltage, and acquire a plurality of voltage measurements from the secondary winding separated by a time interval corresponding to π/3 of the excitation voltage oscillating waveform. 
         [0006]    In certain embodiments, the control module can acquire secondary voltage measurements in synchronization with the period of the excitation voltage periodic waveform. The secondary voltage periodic waveform can be phase shifted relative to the excitation voltage periodic waveform. The control module can determine an RMS voltage of the secondary waveform between acquisition of the third secondary voltage measurement and end of the waveform period, such as with only three secondary waveform voltage measurements. 
         [0007]    It is also contemplated that, in accordance with certain embodiments, the resolver system can include an excitation module electrically connected to the primary winding. An excitation module input lead can connect the control module to the excitation module. The control module can be operatively connected to the excitation module through the excitation module input lead to apply a sinusoidal voltage waveform to the primary winding. An ADC input lead can connect the control module to the ADC. The control module can be operatively connected to the ADC through the ADC input lead. A buffer can connect between the secondary winding and the ADC. 
         [0008]    It is also contemplated that, in accordance with certain embodiments, the secondary winding can be a first secondary winding, and a second secondary winding can be fixed relative to the primary winding. The control module can be configured to acquire a three or more secondary voltage measurements separated by time intervals corresponding to π/3 of the excitation voltage periodic waveform from the second secondary winding. The ADC can be a first ADC, and a second ADC converter can be electromagnetically coupled between the primary winding and the control module. The primary winding can be fixed to a rotating component of a rotorcraft. 
         [0009]    A method of determining rotational position of a rotating component includes applying an excitation voltage having a periodic waveform to a primary winding, inducing a secondary voltage having the same periodic waveform in a secondary winding using the excitation voltage, and acquiring a three or more secondary voltage measurements from the secondary winding. The voltage measurements are separated by time intervals corresponding to π/3 of the periodic waveform of the excitation voltage. 
         [0010]    In certain embodiments, the secondary winding voltage measurements can be acquired in synchronization with the period of the excitation voltage periodic waveform. The periodic waveform of the secondary voltage is phase shifted relative to the periodic waveform of the excitation voltage. An RMS voltage of the secondary waveform can be determined between acquisition of the third secondary voltage measurement and end of the waveform period. The RMS voltage can be determined using only three measurement of the secondary waveform within one-half the period of the secondary waveform. These and other features of the systems and methods of the subject disclosure will become more readily apparent to those skilled in the art from the following detailed description of the preferred embodiments taken in conjunction with the drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    So that those skilled in the art to which the subject disclosure appertains will readily understand how to make and use the devices and methods of the subject disclosure without undue experimentation, embodiments thereof will be described in detail herein below with reference to certain figures, wherein: 
           [0012]      FIG. 1  is a schematic block diagram of an exemplary embodiment of a resolver system constructed in accordance with the present disclosure, showing a resolver coupled to a control module through a resolver interface; and 
           [0013]      FIG. 2  is a schematic diagram of a method of determining rotational speed of a rotating component, showing the steps of the method. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0014]    Reference will now be made to the drawings wherein like reference numerals identify similar structural features or aspects of the subject disclosure. For purposes of explanation and illustration, and not limitation, a partial view of an exemplary embodiment of a resolver in accordance with the disclosure is shown in  FIG. 1  and is designated generally by reference character  10 . Other embodiments of resolvers in accordance with the disclosure, or aspects thereof, are provided in  FIG. 2 , as will be described. The systems and methods described herein can be used for determining linear position or rotational position of a rotating shaft, such as in linearly variable differential transfer (LVDT) or rotary variable differential transformer (RVDT) devices, though the present disclosure is not limited to LVDT or RVDT devices. 
         [0015]    Referring to  FIG. 1 , an exemplary embodiment of an RVDT device, e.g., resolver  10 , is shown. Resolver  10  includes an excitation module  12 , a winding module  14 , an interface module  16 , and a control module  100 . Winding module  12  includes a primary winding  18 , a first secondary winding  20 , and a second secondary winding  22 . Primary winding  18  is fixed to a rotating component  2 , which may be a shaft for an electric motor, and is electrically connected to excitation module  12 . First secondary winding  20  and second secondary winding  22  are fixed relative to primary winding  18 , and are electromagnetically coupled to primary winding  18 . First secondary winding  20  and second secondary winding  22  are both connected to interface module  16 . 
         [0016]    Excitation module  12  is electrically connected primary winding  18  and is configured and adapted to generate an excitation voltage of oscillating magnitude and period defined by control module  100 . The frequency of the oscillating excitation voltage is determined by an input received from control module  100  through an excitation module input lead  24 , which connects control module  100  with excitation module  12 . In the illustrated exemplary embodiment excitation module  12  applies an excitation voltage to primary winding with a waveform A having a sinusoidal shape. The excitation voltage with waveform A induces a first secondary voltage with a corresponding waveform B in first secondary winding  20 . The excitation voltage with waveform A also induces a second secondary voltage with a corresponding waveform C in second secondary winding  22 . In the illustrated exemplary embodiment waveform B is a SINE waveform that may be offset in phase relative to waveform A. Waveform C is a COSINE waveform which is offset by 90-degrees from waveform B. 
         [0017]    Interface module  16  includes a first buffer  26 , a first analog-to-digital converter (ADC)  28 , a second buffer  30 , and a second ADC  32 . First buffer  26  is electrically connected to first secondary winding  20  through a first buffer lead, and receives voltage waveform B therethrough. First buffer  26  is connected to first ADC  28 , and provides voltage waveform B therethrough to first ADC  28 , which acquires periodic voltage measurements therefrom according to a sampling scheme defined by control module  100 . 
         [0018]    Second buffer  30  is similar to first buffer  26  with the difference that second buffer  30  is connected to second secondary winding  22  through a second buffer lead, receives a voltage waveform C therethrough, and provides voltage waveform C to second ADC  32  through a second buffer output lead. Second ADC  32  acquires periodic voltage measurements voltage waveform C, also according to a sampling scheme defined by control module  100 . 
         [0019]    First ADC  28  is connected to control module  100  through an output lead  40  and an input lead  42 . Based on a sampling scheme received from control module  100  through input lead  42 , first ADC provides periodic voltage measurements D to control module  100  through output lead  40 . Second ADC  32  is similar to first ADC  28  with the difference that second ADC  32  is connected to control module  100  through an output lead  44  and an input lead  46 . Based the sampling scheme received from control module  100  through input lead  46 , second ADC  32  also provides periodic voltage measurements E to control module  100  through output lead  44 . Control module  100  receives the voltage measurements D and voltage measurements E, and provides to an output lead  48  an RMS voltage F that corresponds to the rotational position, e.g., according to rotational speed R, of shaft  2 . 
         [0020]    The sampling scheme applied by control module  100  causes first ADC  28  and second ADC  32  to acquire at least three voltage measurements of voltage waveform B within one-half the period of waveform A. Each of the at least three voltage measurements is offset from another of the at least three voltage measurements by π/3 radians of one-half the period of waveform A. In this respect a first voltage measurement (i) occurs π/3 radians prior to a second voltage measurement (ii), and second voltage measurement (iii) occurs π/3 radians after second voltage measurement (ii). The sampling of waveform B by first ADC  28  is synchronized with waveform A. The sampling of waveform C by second ADC  32  is also synchronized with waveform B, and may further be simultaneous with sample of waveform B. Sampling the sinusoidal shape of waveform B at π/3 radians intervals allows for exact calculation of the RMS voltage of waveform B. The sampling is also accomplished prior to completion of the waveform period, allowing for rapid determination of the RMS voltage—advantageously allowing for both accurate and rapid determination of rotational position of shaft  2  during time intervals when the rotational speed of shaft  2  changes. 
         [0021]    Acquiring at least three voltage measurements by π/3 radians of one-half the period of waveform A from waveform B and waveform C also has the advantage that the RMS voltage determination is insensitive to any initial phase offset of waveform B and waveform C relative to waveform A. This is because of several key trigonometric identifies that occur over intervals of π/3 radians, which render three-point RMS voltage determinations phase independent. In particular, the RMS voltage of waveform D and waveform E is given by Equation 1: 
         [0000]    
       
         
           
             RMS 
             = 
             
               
                 
                   
                     
                       ( 
                       
                         V 
                         · 
                         
                           sin 
                            
                           
                             ( 
                             φ 
                             ) 
                           
                         
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         V 
                         · 
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 π 
                                 3 
                               
                               + 
                               φ 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                     2 
                   
                   + 
                   
                     
                       ( 
                       
                         V 
                         · 
                         
                           sin 
                           ( 
                           
                             
                               
                                 2 
                                  
                                 π 
                               
                               3 
                             
                             + 
                             φ 
                           
                           ) 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 3 
               
             
           
         
       
     
         [0000]    where RMS is root-mean-square, V is voltage, and φ is phase shift. 
         [0022]    Factoring out V gives Equation 2. 
         [0000]    
       
         
           
             RMS 
             = 
             
               V 
                
               
                 
                   
                     
                       
                         ( 
                         
                           sin 
                            
                           
                             ( 
                             φ 
                             ) 
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           sin 
                           ( 
                           
                             
                               π 
                               3 
                             
                             + 
                             φ 
                           
                           ) 
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           sin 
                           ( 
                           
                             
                               
                                 2 
                                 · 
                                 π 
                               
                               3 
                             
                             + 
                             φ 
                           
                           ) 
                         
                         ) 
                       
                       2 
                     
                   
                   3 
                 
               
             
           
         
       
     
         [0023]    Using Equation 3 
         [0000]      sin( x ) 2 =½·(1−cos(2 x ))
 
         [0024]    gives Equation 4 
         [0000]    
       
         
           
             RMS 
             = 
             
               V 
                
               
                 
                   
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 φ 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   2 
                                   · 
                                   π 
                                 
                                 3 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           1 
                           - 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   4 
                                   · 
                                   π 
                                 
                                 3 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   3 
                 
               
             
           
         
       
     
         [0000]    which simplifies to Equation 5 
         [0000]    
       
         
           
             RMS 
             = 
             
               V 
                
               
                 
                   
                     
                       3 
                       2 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           
                             cos 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 φ 
                               
                               ) 
                             
                           
                           + 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   2 
                                   · 
                                   π 
                                 
                                 3 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                           + 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   4 
                                   · 
                                   π 
                                 
                                 3 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   3 
                 
               
             
           
         
       
     
         [0025]    Since one complete revolution of shaft  2  relative to cosine of a 2π scale is according to Equation 6: 
         [0000]      cos(2·π+ x )=cos( x )
 
         [0026]    Which becomes by substitution Equation 7: 
         [0000]    
       
         
           
             
               cos 
               ( 
               
                 
                   
                     4 
                     · 
                     π 
                   
                   3 
                 
                 + 
                 
                   2 
                    
                   φ 
                 
               
               ) 
             
             = 
             
               
                 cos 
                 ( 
                 
                   
                     2 
                      
                     π 
                   
                   - 
                   
                     
                       2 
                        
                       π 
                     
                     3 
                   
                   + 
                   
                     2 
                      
                     φ 
                   
                 
                 ) 
               
               = 
               
                 cos 
                 ( 
                 
                   
                     - 
                     
                       
                         2 
                          
                         π 
                       
                       3 
                     
                   
                   + 
                   
                     2 
                      
                     φ 
                   
                 
                 ) 
               
             
           
         
       
     
         [0027]    RMS then becoming according to Equation 8: 
         [0000]    
       
         
           
             RMS 
             = 
             
               V 
                
               
                 
                   
                     
                       3 
                       2 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           
                             cos 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 φ 
                               
                               ) 
                             
                           
                           + 
                           
                             cos 
                             ( 
                             
                               
                                 
                                   2 
                                   · 
                                   π 
                                 
                                 3 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                           + 
                           
                             cos 
                             ( 
                             
                               
                                 - 
                                 
                                   
                                     2 
                                      
                                     π 
                                   
                                   3 
                                 
                               
                               + 
                               
                                 2 
                                  
                                 φ 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   3 
                 
               
             
           
         
       
     
         [0028]    Using Equation 9: 
         [0000]      (cos( x−y )+cos( x+y ))=2 cos( x )·cos( y )
 
         [0029]    Then Equation 10: 
         [0000]    
       
         
           
             
               ( 
               
                 
                   cos 
                   ( 
                   
                     
                       
                         2 
                         · 
                         π 
                       
                       3 
                     
                     + 
                     
                       2 
                        
                       φ 
                     
                   
                   ) 
                 
                 + 
                 
                   cos 
                   ( 
                   
                     
                       - 
                       
                         
                           2 
                            
                           π 
                         
                         3 
                       
                     
                     + 
                     
                       2 
                        
                       φ 
                     
                   
                   ) 
                 
               
               ) 
             
             = 
             
               2 
               · 
               
                 ( 
                 
                   
                     cos 
                      
                     
                       ( 
                       
                         2 
                          
                         φ 
                       
                       ) 
                     
                   
                    
                   
                     cos 
                     ( 
                     
                       
                         2 
                         · 
                         π 
                       
                       3 
                     
                     ) 
                   
                 
                 ) 
               
             
           
         
       
     
         [0030]    Which becomes Equation 11: 
         [0000]    
       
         
           
             
               ( 
               
                 
                   cos 
                   ( 
                   
                     
                       
                         2 
                         · 
                         π 
                       
                       3 
                     
                     + 
                     
                       2 
                        
                       φ 
                     
                   
                   ) 
                 
                 + 
                 
                   cos 
                   ( 
                   
                     
                       - 
                       
                         
                           2 
                            
                           π 
                         
                         3 
                       
                     
                     + 
                     
                       2 
                        
                       φ 
                     
                   
                   ) 
                 
               
               ) 
             
             = 
             
               - 
               
                 cos 
                  
                 
                   ( 
                   
                     2 
                      
                     φ 
                   
                   ) 
                 
               
             
           
         
       
     
         [0031]    Plugging Equation 11 into Equation 8 yields RMS voltage Equation 12: 
         [0000]    
       
         
           
             RMS 
             = 
             
               
                 V 
                  
                 
                   
                     
                       
                         3 
                         2 
                       
                       - 
                       
                         
                           1 
                           2 
                         
                         · 
                         
                           ( 
                           
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   φ 
                                 
                                 ) 
                               
                             
                             - 
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   φ 
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                     3 
                   
                 
               
               = 
               
                 
                   V 
                   · 
                   
                     
                       3 
                       
                         2 
                         · 
                         3 
                       
                     
                   
                 
                 = 
                 
                   V 
                   · 
                   
                     
                       1 
                       2 
                     
                   
                 
               
             
           
         
       
     
         [0032]    It should be understood, that the above Equations can be implemented in digital logic or by a processor and involve computing in-phase and quadrature-phase resultants of the sampled resolver sine and cosine output signals of the resolver excitation signals. Further, it should also be noted that a computing device can be used to implement various functionality, such as that attributable to the method of digital demodulation and other functions performed by an FPGA. In terms of hardware architecture, such a computing device can include a processor, a memory, and one or more input and/or output (I/O) device interface(s) that are communicatively coupled via a local interface. The local interface can include, for example but not limited to, one or more buses and/or other wired or wireless connections. The local interface may have additional elements, which are omitted for simplicity, such as controllers, buffers (caches), drivers, repeaters, and receivers to enable communications. Further, the local interface may include address, control, and/or data connections to enable appropriate communications among the aforementioned components. 
         [0033]    The processor may be a hardware device for executing software, particularly software stored in memory. The processor can be a custom made or commercially available processor, a central processing unit (CPU), an auxiliary processor among several processors associated with the computing device, a semiconductor based microprocessor (in the form of a microchip or chip set) or generally any device for executing software instructions. 
         [0034]    The memory can include any one or combination of volatile memory elements (e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM, VRAM, etc.)) and/or nonvolatile memory elements (e.g., ROM, hard drive, tape, CD-ROM, etc.). Moreover, the memory may incorporate electronic, magnetic, optical, and/or other types of storage media. Note that the memory can also have a distributed architecture, where various components are situated remotely from one another, but can be accessed by the processor. 
         [0035]    The software in the memory may include one or more separate programs, each of which includes an ordered listing of executable instructions for implementing logical functions. A system component embodied as software may also be construed as a source program, executable program (object code), script, or any other entity comprising a set of instructions to be performed. When constructed as a source program, the program is translated via a compiler, assembler, interpreter, or the like, which may or may not be included within the memory. 
         [0036]    The I/O devices that may be coupled to system I/O Interface(s) may include input devices, for example but not limited to, a keyboard, mouse, scanner, microphone, camera, proximity device, etc. Further, the I/O devices may also include output devices, for example but not limited to, a printer, display, etc. Finally, the I/O devices may further include devices that communicate both as inputs and outputs, for instance but not limited to, a modulator/demodulator (modem; for accessing another device, system, or network), a radio frequency (RF) or other transceiver, a telephonic interface, a bridge, a router, etc. 
         [0037]    When the computing device is in operation, the processor can be configured to execute software stored within the memory, to communicate data to and from the memory, and to generally control operations of the computing device pursuant to the software. Software in memory, in whole or in part, is read by the processor, perhaps buffered within the processor, and then executed. 
         [0038]    With reference to  FIG. 2 , a method  200  of determining rotational position of a rotating component is shown. Method  200  includes applying  210  an excitation voltage having a periodic waveform to a primary winding, as shown with box  210 . Method  200  also includes inducing a secondary voltage having a periodic waveform in a secondary winding using the excitation voltage, as shown with box  220 . Inducing the secondary voltages can include inducing voltages in a first secondary winding, as shown with box  222 , and in a second secondary winding, as shown with box  224 . Three or more secondary voltage measurements can be acquired from the first and/or secondary windings, shown with box  230 , and an RMS voltage including positional information of the rotating element can be determined, as shown with box  240 . 
         [0039]    The methods and systems of the present disclosure, as described above and shown in the drawings, provide for resolvers with superior properties including the ability to determine the rotational position of a rotating element with one-half of the cycle of the excitation frequency of the resolver primary winding. While the apparatus and methods of the subject disclosure have been shown and described with reference to preferred embodiments, those skilled in the art will readily appreciate that changes and/or modifications may be made thereto without departing from the scope of the subject disclosure.
A resolver system includes a rotatable primary winding, a secondary winding fixed relative to the primary winding, and an analog-to-digital converter electrically connected to the secondary winding. A control module is operatively connected to analog-to-digital converter and is responsive to instructions to apply an excitation voltage with an oscillating waveform to the primary winding, induce a secondary voltage using the secondary winding using the excitation voltage, and acquire a plurality of voltage measurements from the secondary winding separated by a time interval corresponding to p/3 of the excitation voltage oscillating waveform.