Abstract:
A method for compensating for bias and scale factor errors in vibrating structure gyroscopes. Certain embodiments utilize the functional relationship that bias and scale factor errors have with resonant frequency of vibration in the main vibrating body. Other embodiments utilize the functional relationships that other drive parameters of vibrating structure gyroscopes, such as drive voltage, have with bias and scale factor errors. The various methods may be used repeatedly during normal gyroscope operation in order to continually compensate for the bias and scale factor errors.

Description:
RELATED APPLICATIONS 
     The present application claims the benefit of U.S. Provisional Application No. 60/975,629, filed Sep. 27, 2007, which is incorporated by reference herein in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present disclosure relates generally to instruments and methods for determination of rate of rotation. More specifically this disclosure relates to methods for temperature compensation in angular-rate gyroscopes. 
     BACKGROUND OF INVENTION 
     Gyroscopes have found application in the sensing of angular rotation rate. The design and packaging of gyroscopes has evolved as new applications for their rate-sensing capabilities have been realized. For instance, gyroscopes have been utilized in airplane navigation systems, weapon navigation systems, and boat stabilization systems. More recently, gyroscopes have been utilized in applications such as stabilizing a camera lens and in providing real time feedback for interactive game consoles indicating when a control device has been moved. 
     Inertial rate gyroscopes include vibrating elements referred to herein as “gyro resonators.” These gyro resonators may take on one of many forms, including tuning fork, cylinder and planar ring structures. Many inertial rate gyroscopes utilize Coriolis forces to detect the angular rate of rotation of the gyro resonator about a sensitive axis. Inertial rate gyroscopes may be constructed from a variety of materials, including but not limited to piezoelectric, ceramic and quartz. 
     In some applications (e.g. aeronautics), the gyroscope may be subject to a range of operating temperatures. Temperature may affect the vibrational characteristics of the resonating element, which in turn may cause a change in the zero bias and scale factor of the gyroscope. The changes in bias and scale factor are herein collectively referred to as “temperature drift” which may be manifested as an error in the detected magnitude of angular rotation. 
     One solution for handling temperature drift is to utilize a temperature sensing device such as a thermistor or thermocouple that senses the temperature of the gyro resonator. Knowing the temperature of the gyro resonator enables some correction of the effects of temperature drift. Unfortunately, the temperature sensing device may significantly lead or lag the change in temperature of the gyro resonator, causing a transient error in the temperature determination. Moreover, the presence and configuration of the temperature sensing device may load the temperature measurement in a way that cannot be simulated during calibration, leading to a potential for steady state error in the temperature determination. Such transient and steady state errors in the temperature determination may lead to insufficient precision in the detection of rotational rates. 
     Installation of the temperature measuring device into the gyroscope assembly may increase the complexity and quality assurance requirements in the manufacture of the gyro resonator. For instance, the welds of the thermistor mounts may require inspection and testing to ensure connectivity to the resonating body for temperature detection. Even welds of highest quality may introduce asymmetries in the structure that affect the propagation of the vibration pattern of the gyro resonator in operation. The heightened complexity and quality assurance requirements may increase costs and reduce manufacturing output. 
     For silicon ring gyro resonators, the technique of inferring temperature from the resonant frequency of the gyro resonator, as well as from secondary indicia such as drive voltage level and quadrature sense signal level, is known. U.S. Pat. No. 7,120,548 to Malvern et al. (Malvern) discloses a method for implementing bias and scale factor corrections utilizing measurements of the resonant frequency from the silicon ring resonator. The technique is disclosed as being applicable to silicon ring gyro resonators having a substantially linear variation in resonant frequency with temperature of −0.4 Hz/Celsius in the vicinity of −40 Celsius. Such an approach eliminates the need for installation of the temperature measuring device and attendant quality assurance complexities. 
     However, the use of a silicon ring gyro resonator does not eliminate the effects of lead or lag in the sensing of temperature. The gyro resonator of a silicon ring gyroscope comprises a continuous silicon ring suspended from a support structure on thin silicon filaments. Drive and sense components, typically magnetic or capacitive in nature, are operatively coupled to the filaments and ring. In steady state operation, the temperature of the silicon ring is typically is elevated from the magnetic or capacitive drive/sense components due to flexure heating (i.e. dissipation of vibrational energy). The magnetic or capacitive drive/sense components respond more quickly to external temperature changes because they are more closely coupled to the external case of the gyroscope package than the silicon ring, which is isolated by the thin silicon filaments. Accordingly, with silicon ring resonators, there often remains a lead or lag in the ring temperature with respect to the magnetic or capacitive drive/sense components in response to external temperature changes. Malvern characterizes this lead or lag as an “apparent hysteresis” in the time domain. Malvern further discloses a method for correction that implements a power series expansion utilizing the resonant frequency of the gyro resonator, the drive voltage required to maintain a fixed vibration amplitude at the antinode of the oscillation pattern, and quadrature sense signal levels to correct for the effects of lead or lag on the bias. 
     In addition, many silicon ring gyro resonators have limited life cycles and durability issues. While the ring and filaments are made of silicon, the support structure is typically a composite structure of a glass or quartz material. As such, silicon ring gyro resonators are prone to failure due to delamination between the silicon and the glass or other dissimilar components. Fatigue of the thin silicon filaments is also a frequent mode of failure. 
     A device and method that can effectively compensate for the bias and scale factor errors associated with temperature drift while reducing the complexities associated with sensing the temperature of the gyro resonator in a more durable configuration would be welcome. 
     SUMMARY OF THE INVENTION 
     Various embodiments of the invention are presented that include a monolithic vibrating structure such as a piezoelectric resonator and that utilizes the temperature dependency of the resonant frequency of the resonator to determine the temperature of the resonator. The use of monolithic vibrating structures can improve reliability and durability of the gyro resonator because they are not composite structures. Some embodiments of the invention utilize changes in attendant operating characteristics of the gyro resonator other than resonant frequency, such as drive signal, to correlate with and compensate for the temperature drift of the gyroscope. Certain embodiments further utilize alternative configurations other than the ring gyro resonator, such as a cup (cylindrical or hemispherical) or fork geometry that are less prone to lead or lag between the resonator and the drive and/or sense components in response to external temperature changes. Accordingly, the various embodiments of the invention can eliminate or reduce the vagrancies associated with silicon ring gyro resonators. 
     Much of the present disclosure is directed to piezoelectric gyro resonators. Piezoelectric resonators are in some instances preferred because they offer a monolithic alternative to silicon ring gyro resonators, thus avoiding the problems of delamination associated with silicon ring gyro resonators. Furthermore, it has been discovered that the power series expansion technique of Malvern, as described above, does not account for changes in the scale factor due to the thermal lead or lag. Certain piezoelectric resonator geometries, for example the piezoelectric cup, can be constructed so that all of the operating components are mounted on the resonating element itself. In this way, the magnitude of the lead or lag between the resonating element and the drive or sense components can be greatly reduced relative to the silicon ring gyro resonator. In addition, the sensing elements in piezoelectric resonators may also be more closely and firmly coupled to the resonator at or near the resonance node for improved shock and vibration rejection. This is in contrast to the use of flexible filaments used to soft mount silicon ring structures. 
     The use of piezoelectric gyro resonators pose unique challenges to inferring temperature from the operating characteristics. One notable difference is a substantially greater sensitivity of the scale factor to temperature change vis-à-vis silicon ring gyro resonators. For example, the scale factor of some silicon ring gyro resonators are known to vary less than ±1.5% over the range from −40 to +80 Celsius, or a change of only ±0.0125% per Celsius. Piezoelectric resonators, on the other hand, are known to vary greater than 10% over the range from just +20 to +80 Celsius, for a change of 0.17% per Celsius, which is greater than a ten-fold increase. 
     Furthermore, while the variation in both the bias and the scale factor with temperature are generally linear for silicon ring gyro resonators, the temperature dependency of the bias and scale factors of piezoelectric gyro resonators can be substantially non-linear. Unlike silicon ring gyro resonators which comprise a homogenous, single crystalline resonating structure, a piezoelectric ceramic resonator may be comprised of a sintered polycrystalline material. The different elements in the polycrystalline structure generally have differing thermal expansion coefficients, as well as differing directionality in the thermal expansion. As a result, piezoelectric gyro resonators are typically characterized as having non-linear operational properties, unlike their silicon counterparts. For example, the resonant frequency vs. temperature relationship, which is generally linear for silicon-based resonators, is substantially non-linear for piezoelectric resonators. 
     Also unlike silicon ring gyro resonators, the power required to maintain a piezoelectric gyro resonator at a fixed vibration amplitude at the antinode of the oscillation pattern may be substantially non-linear. Moreover, the temperature represented by a given power parameter such as drive voltage may be non-unique in some instances. That is, a given power metric (e.g. drive voltage, current or impedance) could be indicative of more than one operating temperature across certain ranges. 
     Ways to overcome these challenges are presented in the ensuing portions of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a schematic of a representative inertial rate gyroscope and control system in a first embodiment of the invention; 
         FIG. 1B  is a schematic of a representative inertial rate gyroscope and control system in a second embodiment of the invention; 
         FIG. 2  is a representative rotational rate bias versus temperature graph in an embodiment of the invention; 
         FIG. 3  is a representative scale factor change versus temperature graph in an embodiment of the invention; 
         FIG. 4  is a representative resonant frequency of oscillation of a vibrating gyroscope versus temperature graph in an embodiment of the invention; 
         FIG. 5  is a representative bias error versus resonant frequency graph in an embodiment of the invention; 
         FIG. 6  is a representative scale factor change versus resonant frequency graph in an embodiment of the invention; 
         FIG. 7  is a representative drive voltage versus temperature graph in an embodiment of the invention; 
         FIG. 8  is a representative bias error versus drive voltage graph in an embodiment of invention; and 
         FIG. 9  is a representative scale factor change versus drive voltage graph in an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIGS. 1A and 1B , a gyroscope system  20 A or  20 B is depicted in an embodiment of the invention. The gyroscope system  20 A may include a piezoelectric gyro resonator  22 , a drive control loop  24 , a phase reference connection  25  for demodulating the rotation rate signal, and an output processor  26 . The piezoelectric gyro resonator  22  may include at least one drive element  32  for generating a vibration pattern on the piezoelectric gyro resonator  22  and at least one sensing element  34  positioned on the piezoelectric gyro resonator  22  at a location of the node of the vibration pattern for detecting a minimum or near-minimum signal when the piezoelectric gyro resonator  22  is being driven (vibrated) but is rotationally at rest. 
     The gyroscope system  20 A may further include a dedicated feedback element  36  (as depicted) that is substantially distanced from any node locations of the at-rest vibration pattern for detection of the amplitude of the oscillation pattern. The drive control loop  24  may include a drive source  44  such as a voltage source or drive amplifier that is controlled by a controller  46  to output a drive signal  48  to the drive element(s)  32 . The controller  46  may include digitally controlled potentiometers, an automatic gain control (AGC) amplifier and/or a phase locked loop for altering the drive signal  48 . 
     The dedicated feedback element  36 , when implemented, can provide a control feedback signal  50  to the controller  46  having a set point  52 . The set point  52  may be the reference level for a controller that implements an AGC amplifier. It is noted that the magnitude of the drive signal  48  required to maintain the feedback signal  50  at the set point  52  generally depends on the temperature of the piezoelectric gyro resonator  22 , as described below in more detail. 
     The gyroscope system  20 B of  FIG. 1B  may include many of the same components as described for the gyroscope system  20 A of  FIG. 1A . However, the sensing elements  34  may comprise the feedback element that generates the control feedback signal  50 . The sensing elements  34  in this embodiment may be proximate to but not directly at the node locations of the at-rest vibration pattern in an arrangement that senses a component of the amplitude of the vibration of the piezoelectric gyro resonator  22 . Such sensing elements  34  are arranged so that they sense both the drive amplitude and the rotation rate of the piezoelectric gyro resonator  22 , thus negating the need for a “dedicated” feedback element. Examples of such an embodiment are disclosed in co-pending U.S. Patent Application Publication No. 2007/0256495 to Watson, assigned to the assignee of the instant application, the disclosure of which is hereby incorporated by reference herein except for express definitions contained therein. Such embodiments may eliminate the need for a dedicated feedback element  36 . 
     The output processor  26  of the gyroscope system  20 A may include a signal conditioner  62 , an analog-to-digital (A/D) converter  64 , a microprocessor  66 , and an electronic data storage medium  68 . In the depicted embodiment, the signal conditioner  62  is operatively coupled with an analog output or outputs  74  from the sensing element(s)  34  to output a conditioned signal or signals  76 . The drive signal  48  may also be in communication with the signal conditioner  62 . The conditioned signals  76  may provide an amplitude output or outputs  78  of the vibration sensed by the sensing element(s)  34  and a resonant frequency output  80  of the piezoelectric gyro resonator  22 , as well as an indication of the magnitude of the drive signal  82 . The conditioned signals  76  may be routed to the A/D converter  64  for digitization and subsequent processing by the microprocessor  66 . The microprocessor  66  may access the electronic data storage medium  68  to convert the digitized data into a rotation rate  84 . Alternatively, the output processor  26  may incorporate circuitry  70  such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA) operatively coupled to the A/D converter ( FIG. 1B ). 
     The phase reference connection  25 , which is taken from the drive signal  48 , provides an indication of the magnitude (e.g., voltage) of drive signal. The phase reference connection  25  may also carry a waveform to the signal conditioner  62  that has the same frequency as the resonant frequency of the piezoelectric gyro resonator  22 . Hence, either of the phase reference connection  25  or the analog output or outputs  74  from the sensing element(s)  34  can provide an indication of the magnitude of the drive signal  48  as well as the resonant frequency of the piezoelectric gyro resonator  22 . 
     The piezoelectric gyro resonator  22  may be configured in one of a variety of gyro resonators, including but not limited to a tuning fork resonator, a triangular prism resonator or a cylindrical or cup resonator. It is further understood that the drive control loop  24  and the output processor  26  may be located proximate the piezoelectric gyro resonator  22  to provide a unitary or compact assembly. 
     In operation, the drive signal  48  when applied to the drive element(s)  32  causes the piezoelectric gyro resonator  22  to vibrate at a resonant frequency. In certain embodiments (e.g.,  FIG. 1A ), the dedicated feedback element  36  picks up the magnitude of the vibration for feedback to the controller  46 . In other embodiments (e.g.,  FIG. 1B ), the drive sensing element  34  picks up the magnitude of the vibration for feedback to the controller  46 . In either case, the controller  46  may be utilized to adjust the drive signal  48  output by the drive source  44  so that the magnitude of the vibration as communicated by the feedback signal  50  is controlled to within an acceptable tolerance of a set point  52 . 
     Vibration of the gyro resonator  22  generally causes the sensing element(s)  34  to output a substantially sinusoidal signal at the resonant frequency and characterized by an amplitude. The resonant frequency and amplitude of the sinusoidal signal may be isolated by the signal conditioner  62  before being digitized by the A/D converter  64  ( FIG. 1A ). 
     The resonant frequency of the piezoelectric gyro resonator  22  can be generally temperature dependent, as will be described below. The ensuing discussion is directed to piezoelectric gyro resonators of the various configurations limned above (e.g. a tuning fork, triangular prism, cylindrical cup or hemispherical cup). However, it is noted that the techniques described herein are generally applicable to gyro resonators that exhibit non-linear, temperature dependent characteristics. 
     Referring to  FIGS. 2 and 3 , respective examples of a temperature vs. an error function such as a bias function or relationship  90  ( FIG. 2 ) or a scale factor function or relationship  92  ( FIG. 3 ) are graphed versus temperature  94  for the piezoelectric gyro resonator  22  in the embodiment of  FIGS. 1A and 1B . For purposes of this application, “temperature bias” is defined as the effect that temperature has on the measured voltage when the gyroscope is not rotating about its sensitive axis. The “scale factor” as used herein is defined as the constant of proportionality between the actual gyroscope rotation rate about its sensitive axis and the output signal of the gyroscope. The temperature vs. bias relationship  90  may be presented in terms of a false rotation rate or rotation rate bias  96  versus an operating temperature  94 , as depicted in  FIG. 2 . The scale factor may be presented in terms of a percent change in the scale factor  102  relative to a calibration reference temperature  104  versus the operating temperature  94 , as depicted in  FIG. 3 . 
     Functionally, the temperature vs. bias relationship  90  of  FIG. 2  illustrates that the rotation rate bias  96  may generate a false component of rotation that adds to or subtracts from the true rotation rate as the temperature  94  changes or shifts away from the temperature of calibration. The temperature dependency of the temperature vs. scale factor relationship  92  illustrates that the proportionality of a signal from the piezoelectric gyro resonator  22  may also change with temperature, thus affecting the slope or gain of a given calibration curve. 
     Referring to  FIG. 4 , an example resonant frequency vs. temperature function or relationship  110  for the piezoelectric gyro resonator  22  is illustrated in an embodiment of the invention. A resonant frequency  112  of the piezoelectric gyro resonator  22  is presented over a range of temperatures  114 . The temperature dependency of the resonant frequency  112  may be caused by changes in the material stiffness, thermal stresses and/or dimensional changes of the gyro resonator  22 . The functional relationship  110  between the resonant frequency  112  and the temperature  114  of the piezoelectric gyro resonator  22  may be established through a calibration process. 
     Referring to  FIGS. 5 and 6 , respective examples of a resonant frequency vs. bias relationship  120  and a resonant frequency vs. scale factor relationship  122  are presented in an embodiment of the invention. The relationships  120  and  122  may be obtained by transforming the temperature vs. bias relationship  90  and the temperature vs. scale factor relationship  92  functional relationships of  FIGS. 2 and 3  into functions of resonant frequency  112 . Alternatively, the frequency, bias and scale factor error functions could be recorded directly in the process of temperature testing. In one embodiment, the temperature vs. resonant frequency relationship  110  of  FIG. 4  is utilized to assign or map the resonant frequency  112  to each temperature  94  of  FIGS. 2 and 3 . In the depiction of  FIG. 4 , the mapping provides a unique resonant frequency for each temperature. The mapping enables transformation of the resonant frequency  112  as an indication of the rotation rate bias  96  ( FIG. 5 ) and the change in the rotation rate  102  ( FIG. 6 ). 
     The technique of mapping and transformation from the temperature domain to the frequency domain can be useful in situations where the temperature dependent relationships  90 ,  92  and  110  are obtained independently. For example, for systems that implement previously known temperature correction techniques may already possess calibration data from which the temperature vs. bias relationship  90  and the temperature vs. scale factor relationship  92  can be defined. One could then acquire temperature vs. resonant frequency data via calibration to construct the temperature vs. resonant frequency relationship  110 , implementing the transformation to the resonant frequency vs. bias relationship  120  and the resonant frequency vs. scale factor relationship  122  thereafter. In other instances, the temperature dependent characteristics of all the key parameters (resonant frequency, bias and scale factor) for a given gyro resonator may be available from prior calibrations. 
     Alternatively, the resonant frequency vs. bias relationship  120  and the resonant frequency vs. scale factor relationship  122  can be obtained directly by calibration, thus eliminating the need for the foregoing mapping and transformation. The calibration comprises measuring the resonant frequency, bias and scale factors of the piezoelectric gyro resonator  22  over a series of substantially steady state temperatures. The data thus obtained can be utilized to construct the relationships  120  and  122  directly. 
     In operation, the resonant frequency  112  of the subject piezoelectric gyro resonator (e.g. piezoelectric gyro resonator of  FIGS. 1A and 1B ) may be utilized to infer the attendant bias  96  and the scale factor  102  from  FIGS. 5 and 6 , respectively, as well as the representative temperature  114  of the gyro resonator from  FIG. 4 . In the example gyroscope system  20 B of  FIG. 1B , the resonant frequency  112  is sensed by the sensing elements  34 . Ergo, this approach enables inference of the bias  96 , scale factor  102  and representative temperature  114  without resort to a temperature sensor or other additional components. The need for additional quality assurance attendant to the installation of a separate temperature sensor is thereby eliminated. Furthermore, utilizing the resonant frequency  112  as a measure of operating temperature may reduce the lag between the measured temperature and the actual temperature of the piezoelectric gyro resonator  22 , thus enhancing the performance of the gyroscope. 
     The electronic data storage medium  68  ( FIG. 1A ) may provide calibration data to the microprocessor  66  for converting the digitized signals to the rotation rate  84 . The calibration data may be in the form of a lookup table, a polynomial expansion, or other forms suitable for implementation with conversion techniques known to the artisan. The electronic data storage medium  68  may also contain instructions executable by the microprocessor for implementing the calibration data (e.g. lookup table and/or polynomial expansion algorithms) to execute the various bias and scale factor corrections outlined above, based on the various outputs  78 ,  80  and  82 . In embodiments implementing circuitry  70  such as an ASIC or an FPGA ( FIG. 1B ), the circuitry  70  may be adapted to be configured to implement these functions. 
     In some embodiments, the analog outputs  74  from the sensing element(s)  34  may be treated with analog conditioning electronics (not depicted) for conversion the analog outputs  74  into a rotation rate, including the correction of the temperature drift effects. 
     Referring to  FIG. 7 , a drive function  128  of the magnitude of a drive voltage  132  corresponding to the drive signal  48  required to maintain the amplitude of the vibration of the piezoelectric gyro resonator  22  at the set point  52  over a range of temperatures  130  is illustrated. The changing characteristic of the drive function  128  as the temperature  130  changes is believed to be the result of changing electromechanical properties of the piezoelectric gyro resonator  22 . As a result, a functional relationship between the drive voltage  132  and temperature  130  of the piezoelectric gyro resonator  22  may be created through known calibration processes. 
     In operation, establishment of the drive function  128  versus temperature  130  may enable the temperature of the piezoelectric gyro resonator  22  to be inferred from the magnitude of the drive signal  48 . In some embodiments the drive function  128  is characterized by a local minima or saddle point  134 . On either side of the saddle point  134 , there is a non-unique temperature  130  for a given drive voltage  132 . Accordingly, the utility of the drive function  128  may be applicable over a limited range of temperatures for piezoelectric gyro resonators, as explained below. 
     Referring to  FIGS. 8 and 9 , a temperature dependent bias vs. drive voltage relationship  140  and a temperature dependent scale factor vs. drive voltage relationship  142  are graphed, respectively, versus the drive voltage  132  of the piezoelectric gyro resonator  22  in embodiments of the invention. The relationships  140  and  142  may be constructed using methods akin to the construction of  FIGS. 5 and 6 . That is, the drive function  128  of  FIG. 7  can be utilized to assign or map the drive voltages  132  to the temperatures  130 , thus enabling transformation of the drive voltage  132  as an indication of a false rotation rate or rotation rate bias  144  and a scale factor change or error  146 . Alternatively, the temperature dependent bias vs. drive voltage relationship  140  (or other suitable indicia of the drive signal or drive power) and the temperature dependent scale factor vs. drive voltage relationship  142  may be obtained by direct calibration, thus precluding the need for the transformation. 
     The false rotation rate or rotation rate bias  144  may be presented in terms of an angular rate (e.g. degrees per second), as depicted in  FIG. 8 . The scale factor change or error  146  may be presented in terms of a percent change (as depicted in  FIG. 9 ) in relation to a calibration reference point  148 . 
     Functionally, the temperature dependent bias vs. drive voltage relationship  140  of  FIG. 8  may be utilized to correct a false component of rotation that adds to or subtracts from the true rotation rate as the drive voltage  132  changes. Likewise, the temperature dependent scale factor vs. drive voltage relationship  142  of  FIG. 9  may be implemented for correction of the scale factor as a function of drive voltage. 
     The graphs of  FIGS. 8 and 9  also illustrate the limited utility of the drive function  128  for various embodiments of the invention. For the examples of piezoelectric gyro resonators presented herein, the drive voltage vs. temperature bias function  138  is characterized by a zone of ambiguity  150  within which the drive voltage  132  is representative of more than one solution. The zone of ambiguity is also depicted on  FIG. 7  portraying the drive function  128 , from which the ambiguity is derived. For example, the drive voltage of 1 volt in  FIG. 8  is representative of both −1.1 degrees per second and +0.3 degrees per second (approximate). Accordingly, the temperature dependent bias vs. drive voltage relationship  140  and the temperature dependent scale factor vs. drive voltage relationship  142  standing alone may have a limited range of utility. In the case of the piezoelectric gyro resonators characterized in this work, using the drive voltage  132  as an input or operand is limited to gyro resonator temperatures of less than approximately −12 Celsius. 
     The foregoing descriptions present numerous specific details that provide a thorough understanding of various embodiments of the invention. It will be apparent to one skilled in the art that various embodiments, having been disclosed herein, may be practiced without some or all of these specific details. In other instances, known components have not been described in detail in order to avoid unnecessarily obscuring the present invention. It is to be understood that even though numerous characteristics and advantages of various embodiments are set forth in the foregoing description, together with details of the structure and function of various embodiments, this disclosure is illustrative only. Other embodiments may be constructed that nevertheless employ the principles and spirit of the present invention. 
     For purposes of interpreting the claims for the present invention, it is expressly intended that the provisions of Section 112, sixth paragraph of 35 U.S.C. are not to be invoked with respect to a given claim unless the specific terms “means for” or “step for” are recited in that claim.