RELATED APPLICATION The present disclosure claims priority to United States Provisional Patent

Application Serial No. 63/186,169, filed May 9, 2021, and further claims priority to United States Patent Application Serial No. 17/568,248, filed January 4, 2022, both of which are incorporated by reference herein in their entireties. FIELD OF DISCLOSURE

The present disclosure relates in general to methods, apparatuses, or implementations for monitoring loads with complex impedances. Embodiments set forth herein may also disclose improvements to how a displacement of a haptic actuator or other electromechanical load may be sensed and/or improvements to how a complex impedance is monitored.

BACKGROUND

Vibro-haptic transducers, for example linear resonant actuators (LRAs), are widely used in portable devices such as mobile phones to generate vibrational feedback to a user. Vibro-haptic feedback in various forms creates different feelings of touch to a user’s skin and may play increasing roles in human-machine interactions for modem devices.

An LRA may be modelled as a mass-spring electro-mechanical vibration system. When driven with appropriately designed or controlled driving signals, an LRA may generate certain desired forms of vibrations. For example, a sharp and clear- cut vibration pattern on a user’s finger may be used to create a sensation that mimics a mechanical button click. This clear-cut vibration may then be used as a virtual switch to replace mechanical buttons.

FIGURE 1 illustrates an example of a vibro-haptic system in a device 100. Device 100 may comprise a controller 101 configured to control a signal applied to an amplifier 102. Amplifier 102 may then drive a vibrational actuator (e.g., haptic transducer) 103 based on the signal. Controller 101 may be triggered by a trigger to output to the signal. The trigger may, for example, comprise a pressure or force sensor on a screen or virtual button of device 100.

Among the various forms of vibro-haptic feedback, tonal vibrations of sustained duration may play an important role to notify the user of the device of certain predefined events, such as incoming calls or messages, emergency alerts, and timer warnings, etc. In order to generate tonal vibration notifications efficiently, it may be desirable to operate the haptic actuator at its resonance frequency.

The resonance frequency fo of a haptic transducer may be approximately estimated as: where C is the compliance of the spring system, and M is the equivalent moving mass, which may be determined based on both the actual moving part in the haptic transducer and the mass of the portable device holding the haptic transducer.

Due to sample-to-sample variations in individual haptic transducers, mobile device assembly variations, temporal component changes caused by aging, and use conditions such as various different strengths of a user gripping of the device, the vibration resonance of the haptic transducer may vary from time to time.

FIGURE 2 illustrates an example of a linear resonant actuator (LRA) modelled as a linear system. LRAs are non-linear components that may behave differently depending on, for example, the voltage levels applied, the operating temperature, and the frequency of operation. However, these components may be modelled as linear components within certain conditions. In this example, the LRA is modelled as a third order system having electrical and mechanical elements. In particular, Re and Le are the DC resistance and coil inductance of the coil-magnet system, respectively; and Bl is the magnetic force factor of the coil. The driving amplifier outputs the voltage waveform V (t) with the output impedance Ro. The terminal voltage V _T (t) may be sensed across the terminals of the haptic transducer. The mass-spring system 201 moves with velocity u(t).

A haptic system may require precise control of movements of the haptic transducer. Such control may rely on the magnetic force factor Bl, which may also be known as the electromagnetic transfer function of the haptic transducer. In an ideal case, magnetic force factor Bl can be given by the product B . l, where B is magnetic flux density and / is a total length of electrical conductor within a magnetic field. Both magnetic flux density B and length / should remain constant in an ideal case with motion occurring along a single axis.

In generating haptic vibration, an LRA may undergo displacement. In order to protect an LRA from damage, such displacement may be limited. Accordingly, accurate measurement of displacement may be crucial in optimizing LRA displacement protection algorithms. Accurate measurement of displacement may also enable increased drive levels of the LRA. While existing approaches measure displacement, such approaches have disadvantages. For example, displacement may be measured using a Hall sensor, but Hall sensors are often costly to implement.

SUMMARY

In accordance with the teachings of the present disclosure, the disadvantages and problems associated with existing approaches for monitoring a complex impedance may be reduced or eliminated. In accordance with embodiments of the present disclosure, a system may include an electromagnetic actuator and a processing subsystem configured to apply a low-frequency actuation signal on an actuation coil of the electromagnetic actuator to drive mechanical displacement of the electromagnetic actuator, apply high-frequency electrical stimulus to a sensing coil of the electromagnetic actuator, and sense a change in high-frequency impedance of the sensing coil in response to the high-frequency electrical stimulus over a full cycle of oscillation of the electromagnetic actuator.

In accordance with these and other embodiments of the present disclosure, a method may include applying a low-frequency actuation signal on an actuation coil of the electromagnetic actuator to drive mechanical displacement of the electromagnetic actuator, applying high-frequency electrical stimulus to a sensing coil of the electromagnetic actuator, and sensing a change in high-frequency impedance of the sensing coil in response to the high-frequency electrical stimulus over a full cycle of oscillation of the electromagnetic actuator.

In accordance with these and other embodiments of the present disclosure, an integrated circuit may include one or more outputs configured to apply a low- frequency actuation signal on an actuation coil of the electromagnetic actuator to drive mechanical displacement of the electromagnetic actuator and apply high-frequency electrical stimulus to a sensing coil of the electromagnetic actuator, and sensing circuitry configured to sense a change in high-frequency impedance of the sensing coil in response to the high-frequency electrical stimulus over a full cycle of oscillation of the electromagnetic actuator.

Technical advantages of the present disclosure may be readily apparent to one having ordinary skill in the art from the figures, description and claims included herein. The objects and advantages of the embodiments will be realized and achieved at least by the elements, features, and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are examples and explanatory and are not restrictive of the claims set forth in this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings, in which like reference numbers indicate like features, and wherein:

FIGURE 1 illustrates an example of a vibro-haptic system in a device, as is known in the art;

FIGURE 2 illustrates an example of a Linear Resonant Actuator (LRA) modelled as a linear system, as is known in the art;

FIGURE 3 illustrates selected components of an example host device, in accordance with embodiments of the present disclosure;

FIGURE 4 illustrates selected components of an example impedance measurement subsystem, in accordance with embodiments of the present disclosure;

FIGURE 5 illustrates an example graph of high-frequency coil impedance of two electromagnetic coils versus a displacement x of a moving mass of an electromagnetic actuator, in accordance with embodiments of the present disclosure;

FIGURE 6 illustrates an example graph of high-frequency coil impedance of two electromagnetic coils versus a displacement x of a moving mass of an electromagnetic actuator, including excursion ranges of the two electromagnetic coils, in accordance with embodiments of the present disclosure;

FIGURE 7 illustrates an example graph of combined position-sensing impedance function of high-frequency coil impedance of two electromagnetic coils versus a displacement x of a moving mass of an electromagnetic actuator, in accordance with embodiments of the present disclosure;

FIGURE 8 illustrates an example graph of example sensing trajectories for a position-sensing impedance function of high-frequency coil impedance of two electromagnetic coils versus a displacement x of a moving mass of an electromagnetic actuator, in accordance with embodiments of the present disclosure;

FIGURE 9 illustrates a flow chart of an example method for calibration, in which calibration may be performed with simultaneous driving of actuation signals on two electromagnetic coils and simultaneous driving of pilot/test signals for sensing on both electromagnetic coils, in accordance with embodiments of the present disclosure;

FIGURE 10 illustrates a flow chart of an example method for calibration, in which calibration may be performed with time-multiplexed driving of actuation signals between two electromagnetic coils and simultaneous driving of pilot/test signals for sensing on both electromagnetic coils, in accordance with embodiments of the present disclosure; and

FIGURE 11 illustrates a flow chart of an example method for calibration, in which calibration may be performed with time-multiplexed driving of actuation signals between two electromagnetic coils and time-multiplexed driving of pilot/test signals for sensing between the electromagnetic coils, in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

The description below sets forth example embodiments according to this disclosure. Further example embodiments and implementations will be apparent to those having ordinary skill in the art. Further, those having ordinary skill in the art will recognize that various equivalent techniques may be applied in lieu of, or in conjunction with, the embodiment discussed below, and all such equivalents should be deemed as being encompassed by the present disclosure.

Various electronic devices or smart devices may have transducers, speakers, and acoustic output transducers, for example any transducer for converting a suitable electrical driving signal into an acoustic output such as a sonic pressure wave or mechanical vibration. For example, many electronic devices may include one or more speakers or loudspeakers for sound generation, for example, for playback of audio content, voice communications and/or for providing audible notifications.

Such speakers or loudspeakers may comprise an electromagnetic actuator, for example a voice coil motor, which is mechanically coupled to a flexible diaphragm, for example a conventional loudspeaker cone, or which is mechanically coupled to a surface of a device, for example the glass screen of a mobile device. Some electronic devices may also include acoustic output transducers capable of generating ultrasonic waves, for example for use in proximity detection-type applications and/or machine- to-machine communication.

Many electronic devices may additionally or alternatively include more specialized acoustic output transducers, for example, haptic transducers, tailored for generating vibrations for haptic control feedback or notifications to a user. Additionally or alternatively, an electronic device may have a connector, e.g., a socket, for making a removable mating connection with a corresponding connector of an accessory apparatus, and may be arranged to provide a driving signal to the connector so as to drive a transducer, of one or more of the types mentioned above, of the accessory apparatus when connected. Such an electronic device will thus comprise driving circuitry for driving the transducer of the host device or connected accessory with a suitable driving signal. For acoustic or haptic transducers, the driving signal may generally be an analog time varying voltage signal, for example, a time varying waveform.

To accurately sense displacement of an electromagnetic load, methods and systems of the present disclosure may determine an impedance of the electromagnetic load, and then convert the impedance to a position signal, as described in greater detail below. Further, to measure impedance of an electromagnetic load, methods and systems of the present disclosure may utilize either a phase measurement approach and/or a high-frequency pilot-tone driven approach, as also described in greater detail below.

To illustrate, an electromagnetic load may be driven by a driving signal V (t) to generate a sensed terminal voltage V _T (t) across a coil of the electromagnetic load. Sensed terminal voltage V _T (t) may be given by:

V _T (t) = Z _COIL I(t) + V _B (t ) wherein /(t) is a sensed current through the electromagnetic load, ZCOIL is an impedance of the electromagnetic load, and V _B (t ) is the back-electromotive force (back-EMF) associated with the electromagnetic load.

As used herein, to “drive” an electromagnetic load means to generate and communicate an actuation signal to the electromagnetic load to cause displacement of a movable mass of the electromagnetic load. Further, to “drive” an electromagnetic load may also mean driving of a pilot signal or other test signal to the electromagnetic load from which electrical parameters of the electromagnetic load may be measured.

Because back-EMF voltage V _B (t) may be proportional to velocity of the moving mass of the electromagnetic load, back-EMF voltage V _B (t) may in turn provide an estimate of such velocity. Thus, velocity of the moving mass may be recovered from sensed terminal voltage V _T (t) and sensed current I(t) provided that either: (a) sensed current I(t) is equal to zero, in which case V _B (t) = V _T (t); or (b) coil impedance ZCOIL is known or is accurately estimated.

Position of the moving mass may be related to an impedance of the electromagnetic load, including a coil inductance LCOIL of the electromagnetic load. At high frequencies significantly above the bandwidth of the electromagnetic load, back-EMF voltage V _B (t) may become negligible and inductance may dominate the coil impedance Z _COIL . Sensed terminal voltage V _T@HF (t) at high frequencies may be estimated by: An inductance component of coil impedance ZCOIL may be indicative of a position or a displacement of the moving mass of the electromagnetic load. To illustrate, such inductance may be a nominal value when the moving mass is at rest. When the mass moves, the magnetic field strength may be modulated by the position of the mass which leads to a small alternating-current (AC) modulation signal of the inductance that is a function of the mass position.

Hence, at high frequencies, the position of the moving mass of the electromagnetic load may be recovered from sensed terminal voltage V _T (t) and sensed current /(t) by: (a) estimating the coil impedance at high frequency as Z _C0IL@HF = R _@HF + L _@HF . S, where R@HF is the resistive part of the coil impedance at high frequency, L@HF is the coil inductance at high frequency, and s is the Laplace transform; and (b) converting the measured inductance to a position signal. Velocity and/or position may be used to control vibration of the moving mass of the electromagnetic load.

FIGURE 3 illustrates selected components of an example host device 300 having an electromagnetic actuator 304. Host device 300 may include, without limitation, a mobile device, home application, vehicle, and/or any other system, device, or apparatus that includes a human-machine interface. Electromagnetic actuator 304 may include any suitable load with a complex impedance, including without limitation a haptic transducer, a loudspeaker, a microspeaker, a voice-coil actuator, a solenoid, or other suitable transducer.

In operation, a signal generator 324 of a processing subsystem 305 of host device 300 may generate a raw transducer driving signal x'(t) (which, in some embodiments, may be a waveform signal, such as a haptic waveform signal or audio signal). Raw transducer driving signal x'(t) may be generated based on a desired playback waveform received by signal generator 324.

Raw transducer driving signal x'(t) may be received by waveform preprocessor 326 which may modify raw transducer driving signal x'(t) based on parameters received from impedance measurement subsystem 308 and/or based on any other factor in order to generate processed transducer driving signals x _t (t) and x ₂ (t) . For example, such modification may include control of processed transducer driving signals x ₁ (t) and x ₂ (t) in order to prevent overexcursion of electromagnetic actuator 304 that could lead to damage. Processed transducer driving signal x ₁ (t) may in turn be amplified by amplifier 306a to generate a driving signal V ₁ (t) for driving electromagnetic load 301a. Similarly, processed transducer driving signal x ₂ (t) may in turn be amplified by amplifier 306b to generate a driving signal V ₂ (t ) for driving electromagnetic load 301b. Accordingly, host device 300 may operate such that electromagnetic actuator 304 is altematingly driven by driving signal V ₁ (t) and driving signal V ₂ (t).

Accordingly, host device 300 may operate in a series of alternating phases: a first phase in which driving signal V _t (t) driven to electromagnetic load 301a drives electromagnetic actuator 304 and electromagnetic load 301b is used to measure a displacement of electromagnetic actuator 304, and a second phase in which driving signal V ₂ (t) driven to electromagnetic load 301b drives electromagnetic actuator 304 and electromagnetic load 301a is used to measure a displacement of electromagnetic actuator 304.

A sensed terminal voltage V _T1 (t) of electromagnetic load 301a may be sensed by impedance measurement subsystem 308 (e.g., using a volt-meter). Similarly, sensed current I _t (t) through electromagnetic load 301a may be sensed by impedance measurement subsystem 308. For example, current I ₁ (t) may be sensed by a sense voltage V _S1 ( t ) across a shunt resistor 302a having resistance R _s coupled to a terminal of electromagnetic load 301a. Likewise, a sensed terminal voltage V _T2 (t) of electromagnetic load 301b may be sensed by impedance measurement subsystem 308 (e.g., using a volt-meter). Similarly, sensed current / ₂ (t) through electromagnetic load 301b may be sensed by impedance measurement subsystem 308. For example, current / ₂ (t) may be sensed by a sense voltage V _S2 ( t ) across a shunt resistor 302b having resistance R _s coupled to a terminal of electromagnetic load 301b.

As shown in FIGURE 3, and as described in greater detail below, processing subsystem 305 may include an impedance measurement subsystem 308 that may estimate respective coil inductances LCOIL of electromagnetic loads 301a and 301b. From such estimated coil inductance LCOIL _, impedance measurement subsystem 308 may determine a displacement associated with electromagnetic load 304. Based on such determined displacement, impedance measurement subsystem 308 may communicate one or more parameters to waveform preprocessor 326 (including, without limitation, the value of such displacement), which may cause waveform preprocessor 326 to modify raw transducer driving signal x (t). In some embodiments, such displacement may also be indicative of a human interaction (e.g., applied force) to electromagnetic actuator 304.

In operation, to estimate impedance ZCOIL, impedance measurement subsystem 308 may measure impedance in any suitable manner, including without limitation using the approaches set forth in U.S. Patent. Appl. No. 17/497,110 filed October 8, 2021, which is incorporated in its entirety by reference herein.

As a particular example, in order to estimate coil impedance ZCOIL, waveform preprocessor 326 may generate a processed transducer driving signal x ₁ (t) or x ₂ (t) (depending on which electromagnetic coil 301 is the actuating coil used to drive movement of electromagnetic load 304 and which electromagnetic coil 301 is used for sensing) comprising a high-frequency stimulus for driving the sensing coil. Such high- frequency stimulus may be a tone or a carrier signal (e.g., pulse-width modulation carrier for an amplifier 306). In response, impedance measurement system 308 may measure impedance of the sensing coil. FIGURE 4 illustrates selected components of an example impedance measurement subsystem 308, in accordance with embodiments of the present disclosure. As shown in FIGURE 4, sensed terminal voltage V _T1 (t) of electromagnetic load 301a may be converted to a digital representation by an analog-to-digital converter (ADC) 403a. Similarly, sensed voltage V _s1 (t), indicative of current / ₁ (t), may be converted to a digital representation by an ADC 404a. Likewise, sensed terminal voltage V _T2 (t) of electromagnetic load 301b may converted to a digital representation by an ADC 403b and sensed voltage V _S2 (t) , indicative of current I ₂ (t) , may be converted to a digital representation by an ADC 404b.

As further shown in FIGURE 4, the digital representations of sensed terminal voltage V _T1 (t) and sensed terminal voltage V _T2 (t) may be received by a multiplexer 406, which may select one of such digital representations based on a control signal SENSE_SELECT. Control signal SENSE_SELECT may indicate whether host device 300 is in a first phase (e.g., electromagnetic load 301a is used to drive electromagnetic actuator 304 and electromagnetic load 301b is used for measurement) or a second phase (e.g., electromagnetic load 301b is used to drive electromagnetic actuator 304 and electromagnetic load 301a is used for measurement). Accordingly, multiplexer 406 may select the digital representation of the sensed terminal voltage of the electromagnetic load actively being used to perform sensing. In some embodiments, multiplexer 406 may periodically duty cycle selection between electromagnetic load 301a and electromagnetic load 301b.

Similarly, the digital representations of sensed voltage V _s1 (t ) and sensed voltage V _S2 (t) may be received by a multiplexer 408, which may select one of such digital representations based on a control signal SENSE_SELECT. Accordingly, multiplexer 408 will select the digital representation of the current through the electromagnetic load actively being used to perform sensing.

Although FIGURE 4 contemplates duty-cycled selection between processing sensed voltage V _S1 (t) and sensed voltage V _S2 (t) and between processing sensed terminal voltage V _T1 ( t) and sensed terminal voltage V _T2 ( t), in some embodiments, impedance measurement subsystem 308 may perform parallel estimates of impedance based on sensed voltage V _S1 (t) , sensed voltage V _S2 (t) , sensed terminal voltage V _T1 ( t ) , and sensed terminal voltage V _T2 (t) .

Based on the selected measured current and voltage signals, an inductance estimator 410 may estimate inductance L of the electromagnetic load actively being used to perform sensing. For example, inductance estimator 410 may calculate inductance based on magnitudes of the selected measured current and voltage signals and/or a phase difference between the selected measured current and voltage signals. As mentioned above, inductance estimator 410 may estimate impedance in any suitable manner, including without limitation using the approaches set forth in U.S. Patent. Appl. No. 17/497,110. Based on the estimated inductance L, a displacement estimator 412 may estimate a displacement D of electromagnetic actuator 304.

In operation, impedance measurement subsystem 308 may experience transient effects when switching between the electromagnetic loads actively being used to perform sensing, as indicated by a change of control signal SENSE_SELECT. Such transient effects may occur due to path delays present in inductance estimator 410, including one or more filters (e.g., low-pass filters) used within inductance estimator 410 to smooth and/or otherwise condition estimation of inductance L. To illustrate, at the beginning of a phase, immediately after control signal SENSE_SELECT changes, the valid displacement information may be delayed from the start of the phase until the one or more filters of inductance estimator 410 have fully settled. This may create a dead-zone in which no displacement information is valid around the phase boundaries. For example, when the electromagnetic load actively being used to perform sensing switches from electromagnetic load 301a to electromagnetic load 301b, the sensed inductance value may abruptly change, which may cause filtering artifacts, in turn leading to distorted position estimation. Such delay may lead to latency between an event that triggers an actuation and the start of the actuation period. In some applications, such as where electromagnetic transducer 304 is a haptic actuator, it may be critical that latency be minimized to ensure the actuator response is perceived as a mechanical button response to a human interaction. To reduce or eliminate such challenges, reverse inductance estimator 414 may be configured to receive the estimated displacement D from displacement estimator 412 and based thereon, calculate expected state variables (e.g., filter coefficients) associated with the sensing-inactive electromagnetic load (e.g., the electromagnetic load other than the electromagnetic load actively being used to perform sensing). Thus, displacement information estimated from the electromagnetic load actively being used to perform sensing prior to switching between phases may be used to estimate expected values of state variables of the inductance estimator 410 if the inactive load were hypothetically actively sensing. Accordingly, in response to switching of control signal SENSE_SELECT, inductance estimator 410 may update its state variables based on estimations from reverse inductance estimator 414, to reflect the then-current displacement estimate. Further, to reduce lag between a haptic or other triggering event and start of actuation, state variables of inductance estimator 410 may be updated to reflect the correct displacement estimate.

When actuation of electromagnetic actuator 304 is first triggered (e.g., from rest), the expected state variables may be preset based on an estimate of inductance of the electromagnetic load actively being used to perform sensing following such triggering assuming a displacement D at which electromagnetic actuator 304 is in its resting position.

Such update of state variables may serve to reduce or eliminate transient effects caused by differences between impedances of electromagnetic coil 301a and electromagnetic coil 301b. Accordingly, such differences in impedances may need to be calibrated with one another, to ensure the estimation performed by reverse inductance estimator 414 remains accurate and precise. In some embodiments, a calibration procedure may involve driving a high frequency sensing tone on both coils and estimating the high frequency inductance value on both coils simultaneously while also driving a direct current on one of the coils to displace the moving mass of electromagnetic coil 301 into a fixed displacement. An inductance versus displacement function of each electromagnetic coil 301 may then be inferred such that an impedance L ₁ (x) of electromagnetic coil 301a may be mapped to an impedance L ₂ (x) of electromagnetic coil 301b for a given displacement x of the moving mass away from its resting position. However, other approaches may be used for calibration, as described in greater detail below.

FIGURE 5 illustrates an example graph of high-frequency coil impedance L ₁ (x) of electromagnetic coil 301a and high-frequency coil impedance L ₂ (x) of electromagnetic coil 301b versus a displacement x of a moving mass of electromagnetic actuator 304, in accordance with embodiments of the present disclosure. As shown in FIGURE 5, displacement x of the moving mass of electromagnetic actuator 304 may vary in a range between excursion limits xMin and xMax, and may be at rest at position x = 0. Electromagnetic coil 301a and electromagnetic coil 301b may not be matched relative to one another or relative to their position vis-a-vis the moving mass of electromagnetic actuator 304.

Driving a single electromagnetic coil 301 with an actuation signal may not achieve the full range of the moving mass of electromagnetic actuator 304. For instance, driving an actuation signal on electromagnetic coil 301a may allow for displacement x between limit xMin and a position xE while driving an actuation signal on electromagnetic coil 301b may allow for displacement x between a position xK and limit xMax, as shown in FIGURE 6.

As described above, displacement x may be estimated by driving a high- frequency pilot or test signal into a position-sensing electromagnetic coil 301, measuring a current and a voltage across the coil (or driving a voltage and sensing a current or driving a current and sensing a voltage) and estimating an impedance based on the measurements. The functions of high-frequency coil impedance L ₁ (x) and high- frequency coil impedance L ₂ (x) thus define a mapping between the sensed high- frequency inductance on each electromagnetic coil 301 and displacement x of the moving mass of electromagnetic actuator 304.

Impedance measurement system 308 may estimate displacement x based on sensing of a single electromagnetic coil 301 or based on sensing of both electromagnetic coil 301a and electromagnetic coil 301b alternately or simultaneously. Using both electromagnetic coil 301a and electromagnetic coil 301b for sensing may allow for selecting the position-sensing electromagnetic coil 301 based on a region in which high-frequency coil impedance L ₁ (x) or high-frequency coil impedance L ₂ (x) has the greater measurement sensitivity. In some applications, advantages may exist in driving an actuation signal on one electromagnetic coil 301 and position sensing on the other electromagnetic coil 301 in order to simplify or improve detection of the sensed signal. This may be particularly true as the sensing requirements for the position-sense signal and the actuation signal may be very different. For instance, the pilot or test signal driven for position sensing may be small relative to the actuation signal, requiring a high level of amplification.

Assuming that position sensing is performed using two electromagnetic coils 301, in some embodiments, the resting position x = 0 may be used as a boundary between sensing regions for sensing on one coil versus the other. Such an approach would result in a single position-to-impedance function L(x) that may have a discontinuity at x = 0, as shown in FIGURE 7. Because function L(x) is not a bijection, mapping impedance to position may require additional states that are updated from a trajectory history of the moving mass of electromagnetic actuator 304.

In other embodiments, sensing regions may be defined differently than that depicted in FIGURE 7. For instance, one sensing region may cover a larger excursion range of the selected regions and may change based on history of the trajectory. For example, with reference to FIGURE 8, some examples of sensing trajectories over one cycle of mass excursion (e.g., from limit xMin to limit xMax and back again to limit xMin) may include:

• Sensing on electromagnetic coil 301a for points A through D, switching over to sensing on electromagnetic coil 301b for points J through G and G through J, again switching over to sensing on electromagnetic coil 301a for points D through A.

• Sensing on electromagnetic coil 301a for points A through E, switching over to sensing on electromagnetic coil 301b for points H through G and G through H, again switching over to sensing on electromagnetic coil 301a for points E through A. • Sensing on electromagnetic coil 301a for points A through E, switching over to sensing on electromagnetic coil 301b for points H through G and G through K, again switching over to sensing on electromagnetic coil 301a for points B through A.

In actual practice, high-frequency coil impedance function L ₁ (x) or high- frequency coil impedance function L ₂ (x) may not be known with a physical position sensor. However, displacement x may be proportional to the current of a direct-current component of an actuation signal and displacement x may also be proportional to a phase ph of an alternating-current component of the actuation signal. Thus, high- frequency coil impedance function L ₁ (ph) and high-frequency coil impedance function L ₂ (ph) may be proxies for high-frequency coil impedance function L ₁ (x) and high- frequency coil impedance function L ₂ (x), respectively, within an amplitude factor, and may be sufficient for controlling excursion of the moving mass of electromagnetic actuator 304 using a closed-loop system.

As previously mentioned, calibration between high-frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (x) relative to one another may be required to realize practical operation of a two-coil sensing system. Accordingly, prior to operation, processing subsystem 305 may need to sense the high- frequency inductance of each of electromagnetic coil 301a and electromagnetic coil 301b when they are driven by the same actuation signal on the same coil. In other words, during calibration the actuation signal may be driven independently on each of electromagnetic coil 301a and electromagnetic coil 301b but position sensing may need to occur for both of electromagnetic coil 301a and electromagnetic coil 301b for the same actuation excitation in order to allow for accurate calibration.

For example, FIGURE 9 illustrates a flow chart of an example method 900 for calibration, in which calibration may be performed with simultaneous driving of actuation signals on both of electromagnetic coil 301a and electromagnetic coil 301b and simultaneous driving of pilot/test signals for sensing on both of electromagnetic coil 301a and electromagnetic coil 301b, in accordance with embodiments of the present disclosure. At step 902, waveform preprocessor 326 may drive low-frequency actuation signals and high-frequency pilot/test signals on both of electromagnetic coil 301a and electromagnetic coil 301b. At step 904, displacement x may oscillate between limits xMin and xMax, and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 906, impedance measurement system 308 may sense high- frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (X) over at least one oscillation cycle and create a mapping function between high- frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (X) over the range from limit xMin to limit xMax. After completion of step 906, method 900 may end.

Steps 902 through 906 described above are merely exemplary, and some embodiments may include more or fewer steps than those described above with reference to method 900.

As another example, FIGURE 10 illustrates a flow chart of an example method 1000 for calibration, in which calibration may be performed with time-multiplexed driving of actuation signals between electromagnetic coil 301a and electromagnetic coil 301b and simultaneous driving of pilot/test signals for sensing on both of electromagnetic coil 301a and electromagnetic coil 301b, in accordance with embodiments of the present disclosure. At step 1002, waveform preprocessor 326 may drive a low-frequency actuation signal on electromagnetic coil 301a and drive high-frequency pilot/test signals on both of electromagnetic coil 301a and electromagnetic coil 301b. At step 1004, displacement x may oscillate between limit xMin and position xE (see FIGURE 6), and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1006, impedance measurement system 308 may sense high-frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (x) over at least one oscillation cycle and create a mapping function Ml between high- frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (X) valid for the range from limit xMin to position xE. At step 1008, waveform preprocessor 326 may drive a low-frequency actuation signal on electromagnetic coil 301b and drive high-frequency pilot/test signals on both of electromagnetic coil 301a and electromagnetic coil 301b. At step 1010, displacement x may oscillate between position xK (see FIGURE 6) and limit xMax, and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1012, impedance measurement system 308 may sense high-frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (x) over at least one oscillation cycle and create a mapping function M2 between high- frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (X) valid for the range from position xK to limit xMax.

At step 1014, impedance measurement system 308 may merge mapping functions Ml and M2 into a single mapping function M valid for the range from limit xMin to limit xMax. After completion of step 1014, method 1000 may end.

Steps 1002 through 1014 described above are merely exemplary, and some embodiments may include more or fewer steps than those described above with reference to method 1000.

As a further example, FIGURE 11 illustrates a flow chart of an example method 1100 for calibration, in which calibration may be performed with time- multiplexed driving of actuation signals between electromagnetic coil 301a and electromagnetic coil 301b and time-multiplexed driving of pilot/test signals for sensing between electromagnetic coil 301a and electromagnetic coil 301b, in accordance with embodiments of the present disclosure.

At step 1102, waveform preprocessor 326 may drive a low-frequency actuation signal on electromagnetic coil 301a and drive a high-frequency pilot/test signal on electromagnetic coil 301a. At step 1104, displacement x may oscillate between limit xMin and position xE (see FIGURE 6), and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1106, impedance measurement system 308 may sense high-frequency coil impedance function L ₁ (x) over at least one oscillation cycle. At step 1108, waveform preprocessor 326 may continue to drive the low- frequency actuation signal on electromagnetic coil 301a, cease driving the high- frequency pilot/test signal on electromagnetic coil 301a, and begin driving a high- frequency pilot/test signal on electromagnetic coil 301b. At step 1110, displacement x may oscillate between limit xMin and position xE (see FIGURE 6), and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1112, impedance measurement system 308 may sense high-frequency coil impedance function L ₂ (x) over at least one oscillation cycle. At step 1114, impedance measurement system 308 may create a mapping function Ml between high-frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (x) valid for the range from limit xMin to position xE.

At step 1116, waveform preprocessor 326 may drive a low-frequency actuation signal on electromagnetic coil 301b and drive a high-frequency pilot/test signal on electromagnetic coil 301b. At step 1118, displacement x may oscillate between position xK (see FIGURE 6) and limit xMax, and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1120, impedance measurement system 308 may sense high-frequency coil impedance function L ₂ (x) over at least one oscillation cycle.

At step 1122, waveform preprocessor 326 may continue to drive the low- frequency actuation signal on electromagnetic coil 301b, cease driving the high- frequency pilot/test signal on electromagnetic coil 301b, and begin driving a high- frequency pilot/test signal on electromagnetic coil 301a. At step 1124, displacement x may oscillate between position xK (see FIGURE 6) limit xMax, and impedance measurement system 308 may wait for the oscillatory behavior to settle. At step 1126, impedance measurement system 308 may sense high-frequency coil impedance function L ₁ (x) over at least one oscillation cycle. At step 1128, impedance measurement system 308 may create a mapping function M2 between high-frequency coil impedance function L ₁ (x) and high-frequency coil impedance function L ₂ (x) valid for the range from position xK to limit xMin. At step 1130, impedance measurement system 308 may merge mapping functions Ml and M2 into a single mapping function M valid for the range from limit xMin to limit xMax. After completion of step 1130, method 1100 may end.

Steps 1102 through 1130 described above are merely exemplary, and some embodiments may include more or fewer steps than those described above with reference to method 1100.

Although the foregoing contemplates defining a function L(x) between the inductance of a coil and an actuator mass displacement, in general, such function may establish a mapping between a high-frequency impedance of the coil and the actuator mass displacement. For instance, in some cases the impedance may comprise a resistive portion and a reactive (e.g., inductive) portion.

As used herein, when two or more elements are referred to as “coupled” to one another, such term indicates that such two or more elements are in electronic communication or mechanical communication, as applicable, whether connected indirectly or directly, with or without intervening elements.

This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Similarly, where appropriate, the appended claims encompass all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Moreover, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, or component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative. Accordingly, modifications, additions, or omissions may be made to the systems, apparatuses, and methods described herein without departing from the scope of the disclosure. For example, the components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses disclosed herein may be performed by more, fewer, or other components and the methods described may include more, fewer, or other steps. Additionally, steps may be performed in any suitable order. As used in this document, “each” refers to each member of a set or each member of a subset of a set. Although exemplary embodiments are illustrated in the figures and described below, the principles of the present disclosure may be implemented using any number of techniques, whether currently known or not. The present disclosure should in no way be limited to the exemplary implementations and techniques illustrated in the drawings and described above. Unless otherwise specifically noted, articles depicted in the drawings are not necessarily drawn to scale.

All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the disclosure and the concepts contributed by the inventor to furthering the art, and are construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the present disclosure have been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the disclosure.

Although specific advantages have been enumerated above, various embodiments may include some, none, or all of the enumerated advantages.

Additionally, other technical advantages may become readily apparent to one of ordinary skill in the art after review of the foregoing figures and description.

To aid the Patent Office and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims or claim elements to invoke 35 U.S.C. § 112(f) unless the words “means for” or “step for” are explicitly used in the particular claim.