Sensorless controller for electrostatic machine

A variable speed drive for an electrostatic motor provides feedback control according to rotor position and/or rotor rotational rate deduced from back currents (back-MMF). Extraction of the back currents is performed by a modeling of the stator and the development of isolated stator voltages from plate voltage measurements.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH FOR DEVELOPMENT

CROSS-REFERENCE TO RELATED APPLICATIONS

BACKGROUND OF THE INVENTION

The present invention relates to electrostatic machines (motors and generators) and, in particular, to a motor drive system sensing rotor position and/or velocity without the need for a separate resolver, or the like, mechanically attached to the rotor.

Electrostatic machines provide an alternative to electromagnetic machines which exploit electrically induced electrical fields and change in capacitance to provide a motivating force. Electrostatic machines have a number of advantages over conventional electromagnetic rotating electrical machines including the elimination of magnets and costly rare earth materials, reduction of the significant weight of ferrous materials, and reduced reliance on costly high-current copper windings.

Another significant advantage of electrostatic machines is their ability to hold a torque or position without substantial current flow or resistive heating losses of a type that occur in the electromagnetic coils of conventional electromagnetic machines. This feature makes electrostatic machines attractive for high-torque, low-speed operation and positioning.

Electrostatic machines used for low-speed or positioning applications can employ a large number of electrical poles. For example, in contrast to electromagnetic motors which typically have a limited number of poles (e.g., 8), an electrostatic motor may include as many as 96 poles or more. Precise position control within an electrical cycle of an electrostatic motor having 96 poles requires mechanical resolution of the resolver that is an order of magnitude higher than that required for electromagnetic motors and exceeds the capabilities of a standard 12-bit encoder. As a result, expensive 15-bit encoders or higher may be required for electrostatic machines in such applications.

SUMMARY OF THE INVENTION

It is recognized that electrostatic motors provide a “back-current” or back-MMF (magnetomotive force) roughly analogous to the back EMF (electromotive force) of a standard electromagnetic motor. The measure of MMF, also called the back current, will generally be a vector having phase and magnitude, either or both of which may provide information to deduce position and or speed. The present invention provides a method of extracting measurements of the MMF from an electrostatic motor when the electrostatic motor is advantageously powered by a current drive, for example, of a type described in U.S. Pat. No. 9,979,323 naming co-inventor, Ludois, and hereby incorporated by reference. Importantly, the invention permits tractable voltage sampling at the motor terminals without the need for bulky current transformers or the like. At modest speeds, this MMF value may be used to deduce position and/or motor speed without the need for a resolver at the necessary resolution. At low or zero speeds, when there is insufficient/insignificant MMF, position and/or velocity may be sensed by injecting a current in either the rotor or stator to serve in place of the MMF measurement. On the other hand, at high speeds injecting a current distinguishable from the driving current can be difficult making MMF sensing preferable.

Specifically, then, in one embodiment, the invention provides an electrostatic motor drive for an electrostatic motor which includes a set of current-source drives adapted to connect to the multiple stator electrodes. A back-current monitor circuit detects a back-current value from the electrostatic motor proportional to rotor speed, and a back-current conditioning circuit receives the detected back-current value to provide at least one of an estimated rotor position and rotor speed which is provided to a comparison circuit which receives the at least one of estimated rotor position and rotor speed, and a motor control value and compares the two to produce an error output to the set of current-source drives. The back-current monitoring circuit may take voltage measurements at the connections between the current-source drives and corresponding stator electrodes.

It is thus a feature of at least one embodiment of the invention to provide position and/or velocity measurements of the motor shaft of the type for high-pole-number electrostatic motors for low-speed and high-torque applications using simple voltage monitoring eliminating the need for direct output back-current sensing.

The current-source drives may provide a set of electrical switches in series with a current source implemented by an inductance serving to modulate current to the stator electrodes and regulate voltage.

It is thus a feature of at least one embodiment of the invention to provide a resolver-less position/rotational rate sensor compatible with current-source drives of a type advantageous for electrostatic motors.

The back-current monitoring circuit may compare the voltage measurements to a common voltage to extract stator voltages isolated from common mode voltage.

It is thus a feature of at least one embodiment of the invention to eliminate the effects of highly variable common mode voltages on the calculation of back-current.

The monitoring circuit may model an impedance of the stator circuit to deduce current through each stator electrode and may compare that deduced current to the drive current from the current-source drive associated with the stator electrode to deduce back current.

It is thus a feature of at least one embodiment of the invention to deduce forward current into the stator, as necessary to compute the back current from a voltage measurement.

The back-current conditioning circuit may further measure a peak of the back current to provide a velocity signal, and the comparison circuit may further use the velocity signal to provide the error output.

It is thus a feature of at least one embodiment of the invention to provide an independent measurement of velocity useful for, for example, velocity control of the motor.

The back-current conditioning circuit may extract the estimated rotor position dependent on variations in the back current.

It is thus a feature of at least one embodiment of the invention to deduce position from position dependent changes in the back current.

The electrostatic motor drive may further include a signal generator providing an injection signal to one of the rotor and stator;

an extraction circuit monitoring at least one of the rotor and stator to extract a resulting signal indicating at least one of capacitive coupling between the rotor and stator and changing effective capacitance of at least one of the rotor and stator from saliency and spatial alignment; and

a conditioning circuit receiving the resulting signal to provide an estimated rotor position;

wherein the comparison circuit also receives the estimated rotor position signal from the saliency and spatial alignment conditioning circuit to develop the error output.

It is thus a feature of at least one embodiment of the invention to accommodate the low signal-to-noise ratio of the back-current signal at low speeds for low-speed control.

The electrostatic motor drive may further include a switch for selectively communicating one of the estimated rotor position signals from the saliency conditioning circuit and the estimated rotor positioning signal from the back-current conditioning circuit for use by the comparison circuit.

It is thus a feature of at least one embodiment of the invention to provide an automatic basis for switching between back current and injection-current position sensing.

The switch may be controlled by an estimated rotor speed derived from at least one of the back-current conditioning circuit and the saliency conditioning circuit.

It is thus a feature of at least one embodiment of the invention to make use of the rotor speed derived from the sensing systems of the present invention to select between those sensing systems.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Electrostatic Motor Design

Referring now toFIG. 1, an electrostatic drive system10may include an electrostatic motor12in one example having one or more disk-shaped plates having radially-extending, circumferentially displaced stator electrodes16. The stator electrodes16interact with corresponding radially-extending, circumferentially displaced rotor electrodes20on a corresponding disk-shaped rotor18positioned adjacent to the disk-shaped stator14. For simplicity, the stator electrodes16and rotor electrodes20are shown on the visible surface of the stator14and rotor18; however, they will normally be closely proximate on opposed faces of the stator14and rotor18. This type of motor will be termed an “axial field” motor referring generally to the alignment of the electrostatic field along an axis25of rotation of the rotor18.

The present invention also contemplates operation with a “radial field” motor having an electric field extending perpendicularly to the axis25, for example, with circumferentially nested cylindrical plates or rings of axially extending pegs. Normally the number of rotor electrodes20in each of these types of motors will match the number of poles of the motor. This number of poles normally will be in excess of 16 and more typically in excess of 60 and preferably 96 or more.

Axial field and radial field motors are described in U.S. Pat. No. 9,184,676; 2016/0211775; and 2016/0344306 all assigned to the assignee of the present invention and incorporated by reference. The present invention is applicable to both types of motors.

In both of the designs of radial and axial flux motors, the rotors18may be supported for rotation on driveshafts24extending along axis25for the extraction of mechanical work. A slip ring or brushless power transfer system22(e.g., capacitive or inductive) is attached to the driveshaft24which allows electricity from a stationary rotor power supply26to be conducted to the rotating rotor electrodes20, as is generally understood in the art, to provide an electrostatic polarization of the rotor18.

Overview of Variable Speed Drive

A variable speed drive32may provide for controlled application of power to the stator electrodes16of the stator14based on the position signal generated by a position detection system30. In this regard, the variable speed drive32may receive a command signal34, for example, a position, speed, torque, or other related quantity, and determine the proper variable currents to be applied to the stator electrodes16to provide operation of the electrostatic motor12in conformance with that command signal34. As such, the output of the variable speed drive32will provide multiple phases36(also designated A, B, C, for a three phase embodiment) associated with different stator electrodes16providing sinusoidal or other continuously varying signals to those stator electrodes16necessary to control motor operation.

Referring now toFIG. 2, the instantaneous values of the output phases36required for a given command signal34can be a function of not only the command signal34but also rotor position and the characteristics of the motor12. This processing necessary to generate the output phases36may be simplified through a coordinate transformation known in conventional electromagnetic motors in which constantly varying multiple phases36are mapped to a reference frame rotating with the motor rotor18. This reference frame is termed the d-q reference frame where the d axis (the direct axis) is aligned with the positive electrode on the electrodes20and the q axis (the quadrature axis) is positioned at 90 degrees with respect to the d axis. Viewed in this reference frame, the complexity of the waveforms at the multiple phases36(termed A, B, C, for an example, in a three-phase system) devolves to a single vector that is largely unvarying for steady-state operation of the motor12. Details of this transformation in the context of electromagnetic machines are described, for example, at D. W. Novotny and T. A. Lipo, “Vector Control and Dynamics of AC Drives,” 1st edition, Oxford University Press, 1996 (including pages 88-102) with the underlying mathematics also applicable to the present invention.

Using this transformation, the present invention provides a feedback control of a current-source drive40having phases36connected to each of the stator electrodes16. In this regard, voltages from each of these phases36are measured and these measurements received by ABC-dq transformation circuit42. The ABC-dq transformation circuit42also receives a position signal44and a velocity signal45from the position detection system30to convert the received phase signals (A, B, C) into a vector in d-q space termed the “measured” d-q vector48.

The input command signal34will be converted to a similar “desired” d-q vector50by input conversion circuit52. This desired d-q vector50will generally have a different angle and different magnitude than the measured d-q vector48when the electrostatic motor12is not operating in steady-state. When the input command signal34is a torque value, the magnitude of the desired d-q vector50will be proportional to the desired torque, and the ideal angle with respect to the q-axis will depend on the type of motor12. For a non-salient machine, the angle will simply be zero degrees (a desired d-q vector50aligned with the q-axis); however, for a salient machine this calculation will be more complex as discussed U.S. Pat. No. 9,979,323 assigned to the assignee of the present invention and hereby incorporated by reference. The ideal angle is one that provides maximum torque per voltage thereby reducing motor losses. Alternatively, the command signal34may be a velocity value in which case the velocity signal45is used. More generally an arbitrary control strategy may use both the position signal44and velocity signal45.

Once the desired d-q vector50is determined, it is compared it to the measured d-q vector48to produce an error value53at comparison circuit54which controls the current source40. In the simplest case, error value53is simply a difference between the desired d-q vector50and the measured d-q vector48; however, alternatively, this difference may be further processed, for example, under proportional/integral/derivative type control strategies in which the error value53is a weighted combination of the difference value, a time running integration of this difference value, and a derivative of this difference value. It will also be appreciated that other control strategies may be used by comparison circuit54including feedback and/or feedforward of other measured variables derived from the motor12.

Referring still toFIG. 2, the error value53is then provided to a dq-ABC transformation circuit56operating in the reverse direction as the ABC-dq transformation circuit42(as inverse transforms) to change the error value53, being a vector in d-q space, to phases36in a nonrotating frame.

This feedback control process, traversing the loop of ABC-dq transformation circuit42and dq-ABC transformation circuit56, continues during operation of the motor12.

When the command signal34is a different value, for example, a desired rotational speed (e.g., RPM), an additional, optional feedback loop may be incorporated, for example, using the position signal44to deduce speed and using a difference between the desired RPM of the command signal34and the deduced RPM, at optional comparison block58, to create a torque value that may then be treated as discussed above with respect to the torque signal. Other input signals can also be handled in this manner, and in this regard the invention contemplates that programmable command signals34may be used, for example, for soft start and stop of the motor12as well as different regimes at different motor RPMs or operating conditions.

The ABC-dq transformation circuit42, input conversion circuit52, comparison circuit54, and dq-ABC transformation circuit56may be implemented by discrete circuitry or preferably by a high-speed computer processor executing a program stored in non-transient computer memory, for example, as firmware and employing analog-to-digital converters to operate in a digital domain.

Referring now toFIG. 3, a practical implication of sophisticated field control of an electrostatic motor is enabled by the ability to generate “stiff” current output signals at the power levels needed to drive electrostatic motor12, that is, outputs that can provide open-loop current control in the face of rapidly fluctuating voltages at the multiple phases36caused by changes in capacitive coupling with rotation of the motor12. The invention contemplates that the electrostatic motors12will operate at powers in excess of 10 watts, typically in excess of 100 watts, and desirably in excess of 1000 watts.

The necessary “current-source” outputs may be produced through the use of one or more series inductive elements78exploiting a feature of inductance that resists changes in the current flowing through the inductor, a feature of the buildup of self-induced energy within the magnetic field of the inductor. The present invention recognizes that this property can be enlisted to provide sufficient output current stiffness to be able to regulate output voltages without preventing dynamic control of the necessary current for “charge oriented” control of the motor or variable speed capabilities. In this regard the inductance must be of a size to provide current regulation (and hence energy storage) at the expected motor power levels providing, for example, for the control of current output to the motor to within 25 percent of the command value controlling the semiconductor switches, and typically within 10 percent, and desirably within five percent. Construction of such a current-source drive is described in U.S. Pat. No. 9,960,719 assigned to the assignee of the present invention and hereby incorporated by reference.

In one implementation, a source of DC power is provided to set of solid-state switches72, for example, transistors such as MOSFET transistors, receiving ABC current values from the switching logic circuit73. The solid-state switches72, for example, are configured in an H-bridge where each of the phases36connects to a junction between a pair of series-connected switches72, the pair in turn spanning a positive power rail74and a negative power rail76providing a direct current stabilized by inductor70. Rudimentary use of this circuit can produce square wave outputs; however, the present invention contemplates that the phases36produced are continuous waveforms of arbitrary shape and frequency dictated by the control algorithm. Accordingly, the switches72will receive control signals determining their switch state that are pulse-width modulated (or modulated by a similar modulation technique including pulse-density modulation etc.). In pulse width modulation, an on-time of the switch72is varied to determine the average current value output through the phase36. In such modulation, the switches72are operated in switched mode (either on or off) for energy efficiency, but switch at high rates to produce continuous waveforms (e.g., sine waves of different frequencies) smoothed by the capacitance of the electrostatic motor12. In pulse width modulation, the switching speed of the semiconductors is at many times the fundamental frequency of the waveform of phases36and typically more than 10-20 times that frequency.

An inductor70may be placed in series with the switches72of the H-bridge to stabilize the DC bus which feeds the switches72. Other placements of the inductor (for example with one inductor on each of the phases36) or the use of a transformer having leakage inductance may be provided to similar effect.

Position Sensing

Referring again toFIG. 2, the position signal44and velocity signal45may be obtained from a resolver; however, in the present invention, these signals may be provided by position detection system30receiving voltage signals90from each of the phases36of the current-source drive40. The position detection system30may include two distinct components: a back-current or “back-MMF” (magnetomotive force) detector system93, including MMF detector92and conditioning circuit120, and an injection current system131, including current injection circuit130and conditioning circuit144. Both of these systems receive voltage measurements of the phases36provided to the electrode16of the stator14to produce position signals and velocity signals.

The back-MMF detector93detects a back MMF that is a function of rotor speed and which can also be used to provide a position signal based on variations in the MMF with rotation.

Referring now toFIGS. 8 and 9, the MMF detector92may measure the voltage at each phase36with respect to a common voltage reference94(for example, ground) to provide a raw phase voltage96associated with each phase (e.g., VAGbeing the voltage between phase A and ground, VBGbeing the voltage between phase B and ground, and VCGbeing the voltage between phase C and ground in an example 3 phase motor). These raw phase voltages96will include a common mode voltage which is highly variable and can obscure the desired back-current measurement.

Accordingly, and referring toFIG. 10, each raw phase voltage96may be combined to extract an isolated phase voltage for each electrode16. This extraction process can be understood diagrammatically by envisioning the isolated phase voltages as being phasors98extending at equal angles from and rotating about a common voltage center100which varies as the common mode voltage. It will be appreciated that with the constraint that the phasors98must be at equal angles from each other, the length of each phasor98(the isolated phase voltage) may be uniquely calculated from knowledge of the length and relative angles of the phasors96using geometric analysis, thus eliminating the effect of the common mode voltage.

Referring now toFIG. 8, each of the stator electrodes16may be modeled by a fixed capacitance102, a fixed resistance104, and a current source106representing the back-MMF being a function of rotor speed. The capacitance102will typically vary as a function of rotor position but may be modeled as an average value determined empirically, and the positional variations attributed to the current-source106. The capacitance102and fixed resistance104may be determined empirically or may be deduced during operation of the electrostatic drive system10.

The model may be used to determine the back-MMF of the current-source106by applying the isolated phase voltage (e.g., VA) to this model to determine a received current108(the combined current through capacitor102and resistor104) that would occur if the measured voltage (e.g., VA) were applied across the model. This received current108may then be compared to the commanded current110from the current-source drive40. The difference between currents110and108will be the effective current from current source106being the back-MMF.

Referring now toFIG. 6, this calculated back-MMF current will vary over time because of actual variation of the capacitance102as the rotor18rotates to produce a back-MMF signal115. Nevertheless, the amplitude112of the calculated back-MMF signal115will be proportional to the rotational speed of the rotor18and thus may be used to determine rotor speed. The variations over one cycle114of the MMF signal115provide an indication of position of the rotor18, and the rotational distance of each cycle114will be equal to 360° of rotational travel divided by the number of poles (in this simplified case three) of the motor12. It will be apparent that an angular positions of less than one cycle114may also be resolved according to the regular voltage variations during a cycle114.

Generally, the position signals from each of the phases can be transformed into d and q components with the d component shown in solid line and the q component shown in dotted line inFIG. 6and simply represented as the length of a corresponding quadrature phasor.

Referring now toFIG. 4, the back-MMF signal115may be generally processed by a conditioning circuit120, for example, providing for bandpass filtration122to extract a reduced noise MMF signal115which may be provided to a mapper124, for example, mapping the voltage values within one cycle114to particular angle values as position signals44and a peak follower126extracting the amplitude112for use as a velocity signal45. Other well-known techniques of signal conditioning may be used including, for example, constructing an observer fitting this data to a model or the like.

Referring toFIGS. 2 and 5, an alternative source of position information may be obtained through a current injection provided by a current injection circuit130. Generally, the current injection circuit130may create a high-frequency injection signal through injection signal generator132, for example, having a frequency at least 10 times that of a cycle114. The injection signal generator132may provide for injection output134which may be summed to the output of transformation circuit56to superimpose an additional current signal onto one electrode16of the stator14through the current-source drive40.

This injection signal may be used in two ways. A first approach uses the injection signal to measure capacitive coupling between the stator16and the rotor20such as changes with rotation of the rotor20. in this case, a voltage signal136may be received by the rotor118induced by the injection output134on the stator14but modified by changing mutual capacitance between the rotor18and stator14as the rotor18rotates. This signal136may be received by a high-pass filter139to reduce noise content and then demodulated, for example, using an extraction circuit such as a demodulator138, depicted schematically as a rectifier141and low-pass filter143, to extract the envelope of the signal136having a modulation frequency. The modulation frequency will have a period representing a frequency corresponding with a rotational speed of the rotor20and hence may be used to determine rotor speed45, for example, using a frequency detector145, for example, measuring this period and inverting the same. The phase of the envelope can be used to provide a position signal44measurement in a manner analogous to that described above with respect toFIG. 6. These output signals44and45may again be processed by a conditioning circuit144, for example, providing for filtration or more sophisticated signal conditioning using observer technology or the like.

Referring momentarily toFIG. 11, it will be appreciated that the injection process may be reversed with the injection circuit130injecting directly into the rotor20and then monitoring the resultant changes in the signals90. In this case signal134shown inFIG. 2is not needed.

As an alternative to measuring changes in capacitive coupling described above, the injection signal may be used to detect changes in saliency of the electrostatic motor12. Referring also toFIG. 7, in this case the voltage signals90may be monitored by a saliency detection circuit131to detect the changes in loading of the injection signal from the current source drive40caused by changes in saliency of the stator16. Voltage signals90may be received by the saliency circuit131providing the same functional components as the current injection circuit130including a high-pass filter to reduce noise content and a demodulator and low-pass filter143to extract the envelope150of the signal136having a modulation frequency. The modulation frequency will have a period152representing a frequency generally twice as fast as cycle114and thus may be used to determine rotor speed45, for example, using a frequency detector145, for example, measuring period152and inverting the same. The phase of the envelope150can be used to provide a position signal44measurement in a manner analogous to that described above with respect toFIG. 6. Output signals from either the saliency circuit131or the current injection circuit130may be selected by switch161to be used as output signals44and45.

Referring again toFIG. 2, each of the MMF detector92and the current injection circuit130or saliency circuit131can provide both position and rate signals; however, the MMF detector92has poor signal-to-noise ratio at low rotor speeds, and accordingly at low rotor speeds the current injection circuit130or the saliency detection circuit131may be used to provide position and velocity measurements. On the other hand, when the motor12is moving at high speed, the superior measurements provided by the MMF detector92may be used.

In this regard, a switching circuit160may automatically select between outputs from the conditioning circuit120and from the conditioner140according to a speed signal obtained from the comparison circuit54. In this regard, comparison circuit54switches between these different detection systems' position detection systems according to the rate of speed of the rotor18.

It will be appreciated that the present invention provides the ability to properly control a voltage vector applied to the electrostatic motor by a closed loop voltage regulation, thereby also providing the ability to control torque and in this way to provide torque control.

Certain terminology is used herein for purposes of reference only, and thus is not intended to be limiting. For example, terms such as “upper,” “lower,” “above,” and “below,” refer to directions in the drawings to which reference is made. Terms such as “front,” “back,” “rear,” “bottom,” and “side,” describe the orientation of portions of the component within a consistent but arbitrary frame of reference which is made clear by reference to the text and the associated drawings describing the component under discussion. Such terminology may include the words specifically mentioned above, derivatives thereof, and words of similar import. Similarly, the terms “first,” “second,” and other such numerical terms referring to structures do not imply a sequence or order unless clearly indicated by the context. Although the stator and rotors are shown as disks in the disclosed embodiments, there is no requirement that the stator or rotor be in a disk form.