Embodiments of the subject matter described herein relate generally to vehicle drive systems, and more particularly, embodiments of the subject matter relate to absolute position sensing for field-oriented control of induction motors.
In recent years, advances in technology, as well as ever evolving tastes in style, have led to substantial changes in the design of automobiles. One of the changes involves the power usage and complexity of the various electrical systems within automobiles, particularly alternative fuel vehicles, such as hybrid, electric, and fuel cell vehicles. Many of these vehicles use electric motors to provide traction power to the vehicle.
For induction motors, the speed of the rotor and the speed of the rotating magnetic field in the stator must be different, a concept known as slip, in order to induce current. In order to operate the induction motor at its highest efficiency, the slip is controlled using feedback control loops. In conventional control systems, as the rotor speed increases, the rotor approaches a base speed (or rated speed), where the voltage across the motor terminals reaches a value at which no more current can be provided to the motor. In order to operate the motor at higher speeds than the base speed, a technique known as flux weakening, controlled by non-torque generating current is employed.
Accordingly, field-oriented control methods have been developed to control the torque generating current supplied to the induction motor separately from the non-torque generating current. These methods use the relative position and speed of the rotor to maintain a desired relationship between the stator flux and rotor flux. The non-torque generating current is adjusted based on the speed of the rotor and the flux characteristics of the induction motor. By compensating for the undesired flux, field-oriented control can be used to improve efficiency, the motor transient response, and tracking of the torque command at speeds higher than the base speed. As a result of the improved performance, induction motors and drive systems may be appropriately sized for an application, thereby lowering cost and improving overall efficiency.
Most field-oriented control methods for induction motors utilize incremental encoders to measure the relative position and speed of the rotor. Typically, these encoders are either magnetic or optical. For automotive environments, packaging space is often at a premium and the encoders are often exposed to demanding environmental conditions. For example, the operating temperature may range from −40° C. to 150° C., which exceeds the operating temperature ratings for most optical encoders. While magnetic encoders may be able to tolerate automotive temperatures, they often cannot sustain operation when exposed to vibration forces and frequencies encountered in automotive applications. Furthermore, in order to achieve high-levels of accuracy, magnetic encoders must be implemented in a large physical size, which is undesirable from a packaging and automotive design perspective.
An apparatus is provided for an automotive drive system. The automotive drive system comprises an induction motor having a rotor, and a position sensor coupled to the induction motor. The position sensor is configured to sense the absolute angular position of the rotor. A processor may be coupled to the position sensor and configured to determine the relative angular position of the rotor based on a difference between the absolute angular position and an initial angular position obtained when the induction motor is started. A controller may be coupled to the induction motor and the processor and configured to provide field-oriented control of the induction motor based on the relative angular position of the rotor.
An apparatus is provided for a drive system for use in a vehicle. The drive system comprises an induction motor having a rotor, and a position sensor integrated with the induction motor. The position sensor is configured to sense the absolute angular position of the rotor. The position sensor may further comprise a resolver having a resolver rotor coupled to a shaft of the induction motor, and a resolver stator coupled to the induction motor.
A method is provided for controlling an induction motor. The method comprises obtaining an initial angular position of the rotor using an absolute position sensor, wherein the initial angular position of the rotor is obtained when the induction motor is started. The method further comprises obtaining a subsequent angular position of the rotor using the absolute position sensor. The method comprises determining a relative angular position of the rotor based on the initial angular position and the subsequent angular position, and determining a magnetizing current command based on the relative angular position.
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.
A more complete understanding of the subject matter may be derived by referring to the detailed description and claims when considered in conjunction with the following figures, wherein like reference numbers refer to similar elements throughout the figures.
The following detailed description is merely illustrative in nature and is not intended to limit the embodiments of the subject matter or the application and uses of such embodiments. As used herein, the word “exemplary” means “serving as an example, instance, or illustration.” Any implementation described herein as exemplary is not necessarily to be construed as preferred or advantageous over other implementations. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary or the following detailed description.
The following description refers to elements or nodes or features being “connected” or “coupled” together. As used herein, unless expressly stated otherwise, “connected” means that one element/node/feature is directly joined to (or directly communicates with) another element/node/feature, and not necessarily mechanically. Likewise, unless expressly stated otherwise, “coupled” means that one element/node/feature is directly or indirectly joined to (or directly or indirectly communicates with) another element/node/feature, and not necessarily mechanically. Thus, although the schematics shown herein depict exemplary arrangements of elements, additional intervening elements, devices, features, or components may be present in an embodiment of the depicted subject matter. Furthermore, 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.
For the sake of brevity, conventional techniques related to signaling, sensors, and other functional aspects of the systems (and the individual operating components of the systems) may not be described in detail herein. Furthermore, the connecting lines shown in the various figures contained herein are intended to represent exemplary functional relationships and/or physical couplings between the various elements. It should be noted that many alternative or additional functional relationships or physical connections may be present in an embodiment of the subject matter.
Technologies and concepts discussed herein relate to systems and methods for implementing field-oriented control of induction motors using absolute position sensors. Field-oriented control involves separate current control loops for the torque generating current and the non-torque generating current supplied to the induction motor. The relative position and speed of the rotor is used to maintain a desired relationship between the stator flux and rotor flux to improve motor efficiency, as described in greater detail below. As used herein, subscripts d and q are quantities in the Cartesian frame of reference synchronous with the rotation of a rotor within an induction motor, where the q axis (or quadrature axis) is orthogonal to the rotor pole axis (i.e., torque generating) and the d axis (or direct axis) is parallel to the rotor pole axis (i.e., non-torque generating).
Depending on the embodiment, the automobile 100 may be any one of a number of different types of automobiles, such as, for example, a sedan, a wagon, a truck, or a sport utility vehicle (SUV), and may be two-wheel drive (2WD) (i.e., rear-wheel drive or front-wheel drive), four-wheel drive (4WD), or all-wheel drive (AWD). The automobile 100 may also incorporate any one of, or combination of, a number of different types of engines, such as, for example, a gasoline or diesel fueled combustion engine, a “flex fuel vehicle” (FFV) engine (i.e., using a mixture of gasoline and alcohol), a fuel cell vehicle engine, a gaseous compound (e.g., hydrogen and natural gas) fueled engine, a combustion/electric motor hybrid engine, or an electric motor.
In the exemplary embodiment illustrated in
Depending on the embodiment, the energy source 104 may comprise a battery, a fuel cell, or another suitable voltage source. It should be understood that although
In an exemplary embodiment, the inverter assembly 106 includes one or more inverters, each including switches (e.g., semiconductor devices, such as transistors and/or switches) with antiparallel diodes (i.e., antiparallel to each switch), with windings of the induction motor 102 electrically connected between the switches to provide voltage and create torque in the induction motor 102, as will be understood in the art. The electronic control system 108 is in operable communication and/or electrically connected to the inverter assembly 106. Although not shown in detail, the electronic control system 108 includes various sensors and automotive control modules, or electronic control units (ECUs), such as an inverter control module for controlling the inverter assembly 106, and may further include a processor and/or a memory which includes instructions stored thereon (or in another computer-readable medium) for carrying out the processes and methods as described below.
In accordance with one embodiment, the electronic control system 108 is responsive to commands received from the driver of the automobile 100 (i.e. via an accelerator pedal) and provides commands to the inverter assembly 106 to utilize high frequency pulse width modulation (PWM) to manage the voltage provided to the induction motor 102 by the inverter assembly 106, as will be understood. In an exemplary embodiment, the electronic control system 108 implements a field-oriented control loop to operate the inverter assembly 106 and improve the efficiency and performance of the induction motor 102, as described in greater detail below.
Referring now to
Referring again to
In an exemplary embodiment, the absolute position sensor 206 provides information or signals representative of the absolute angular position of the rotor. The absolute position sensor 206 may be configured to sense or measure the absolute angular position of the rotor of the induction motor 102 relative to the stator or some other fixed reference point based on the positioning of the absolute position sensor 206. In an exemplary embodiment, the absolute position sensor 206 is a resolver, although other suitable means for sensing absolute angular position may be used in alternative embodiments. In an exemplary embodiment, a resolver having two pole pairs (e.g., two-pole resolver) is used. In alternative embodiments, multipole resolvers may be used, however, multipole resolvers are generally more costly and require additional mathematical computations to be implemented, which are known in the art and beyond the scope of this disclosure. The resolver is capable of producing accurate position information even while being packaged and designed for compact size. Additionally, resolvers are highly durable and can sustain reliable and accurate operation in the presence of demanding environmental conditions (e.g., automotive temperature and vibration levels).
In an exemplary embodiment, the processor 208 is coupled to the absolute position sensor 206 and is configured to convert the signals (analog signals in the case of a resolver) or measurements from the absolute position sensor 206 to a digital representation (e.g., digital word). The processor 208 may be a resolver-to-digital converter or another suitable means for processing signals from the absolute position sensor 206. The processor 208 may be configured to perform additional tasks and functions, as described in greater detail below.
In an exemplary embodiment, the induction motor control system 200 may further include a current calculator 210. In an exemplary embodiment, the output of the current calculator 210 is coupled to an input of the controller 202, and the current calculator 210 is configured to provide a torque producing current command (iq*) to the controller 202. The current calculator 210 may determine the torque producing current command in response to a torque command (Te*) (e.g., provided by the electronic control system 108), an estimated rotor flux (Φr), and a commanded rotor flux (Φr*), as described in greater detail below.
In an exemplary embodiment, the controller 202 is configured to control the voltage provided by the energy source 104 to the induction motor 102 by utilizing PWM techniques to regulate the output of the inverter 204, as will be understood. The controller 202 is configured to utilize information regarding the relative position of the rotor of the induction motor 102 to implement field-oriented control. In an exemplary embodiment, the controller 202 may further include, without limitation, a speed observer 212, a flux reference table 214, a magnetizing current estimator 216, a synchronous frame current regulator 218, a stationary coordinate transformer 220, a space vector modulator 222, a synchronous coordinate transformer 224, a flux estimator and slip angle calculator 226, and an adder 228. These and other elements may be coupled together to implement field-oriented control of the induction motor 102 based on the relative rotor position, as described in greater detail below.
Referring now to
Referring again to
In an exemplary embodiment, the induction motor control process 300 is configured to determine the relative angular position (θr) of the rotor based on the absolute angular position (task 308). The induction motor control process 300 may determine a relative angular position of the rotor based on a difference between the subsequent angular position and the initial angular position. For example, the processor 208 may be configured to store the initial angular position of the rotor as an offset, and subtract the initial angular position from each subsequent angular position measurement to produce a relative angular position (e.g., relative to the initial angular position or angular position at startup). In alternative embodiments, the controller 202 may be configured to receive the absolute angular position and determine the relative angular position. In an exemplary embodiment, the induction motor control process 300 is configured to provide the relative angular position to a field-oriented control system (e.g., controller 202). For example, the output of the processor 208 may be coupled to an input of the controller 202.
In an exemplary embodiment, the induction motor control process 300 is configured to determine the speed of the rotor (ωr) based on the relative position (task 310). For example, the processor 208 may coupled to and/or provide the relative rotor position information to the speed observer 212. The speed observer 212 may be configured to determine the rotor speed by differentiating the relative rotor position with respect to time. In an exemplary embodiment, the induction motor control process 300 utilizes the rotor speed to determine a magnetizing current command (id*) to compensate for transient changes in rotor flux based on the rotor speed (task 312). For example, the speed observer 212 may provide the rotor speed to the input of the flux reference table 214, which obtains a rotor flux command (Φr*) In accordance with one embodiment, the flux reference table 214 is a lookup table containing predetermined rotor flux commands (Φr*) based on the rotor speed (ωr), the voltage of the energy source 104 (VDC), and the flux characteristics of the induction motor 102. The output of the flux reference table 214 may be provided to the magnetizing current estimator 216, which is configured to determine the magnetizing current command (id*) to produce the desired rotor flux based on the rotor flux command (Φr*).
In an exemplary embodiment, the induction motor control process 300 is configured to determine a duty cycle for inverter 204 based on the relative position of the rotor and the synchronous frame current commands (id*,iq*) (task 314). The synchronous frame current regulator 218 may be coupled to the current calculator 210 and the magnetizing current estimator 216, such that it receives the synchronous frame current commands (id*,iq*). The synchronous frame current regulator 218 may be coupled to the output of the synchronous coordinate transformer 224. The synchronous coordinate transformer 224 is coupled to the output of the inverter 204 and configured to measure (or sense) the current in the induction motor 102. The synchronous coordinate transformer 224 performs a coordinate transformation to obtain the value of the measured currents in the synchronous reference frame (id,iq) and provides the measured currents to the synchronous frame current regulator 218. The synchronous frame current regulator 218 is configured to determine synchronous frame duty cycles (dd*,dq*) such that the measured currents (id,iq) track the current commands (id*,iq*).
In an exemplary embodiment, the stationary coordinate transformer 220 is coupled to the output of the synchronous frame current regulator 218 and the output of the adder 228. The adder 228 is coupled to the flux estimator and slip angle calculator 226, which is configured to receive as inputs the measured current (id,iq) commanded current (id*,iq*), and the rotor flux command (Φr*) and from those inputs determine an estimated rotor flux (Φr) and an optimized slip angle (θslip), as will be appreciated in the art. The adder 228 is also configured to receive the relative rotor position (θr) and add the relative rotor position and the slip angle (θslip) to produce a transformation angle (θt). In an exemplary embodiment, the stationary coordinate transformer 220 is configured to convert the synchronous frame duty cycle commands (dd*,dq*) to the stationary frame (dα,dβ) based on the transformation angle (θt). In an exemplary embodiment, the output of the stationary coordinate transformer 220 is coupled to the input of the space vector modulator 222. The space vector modulator 222 is configured to determine operative duty cycle commands for the switches of the inverter 204 based on the stationary frame duty cycle commands, such that the inverter 204 utilizes PWM modulation to provide voltage from the energy source 104 to operate the induction motor 102 as desired. In an exemplary embodiment, the loop defined by task 306, task 308, task 310, task 312, and task 314 repeats indefinitely during operation of the induction motor 102.
Referring now to
In an exemplary embodiment, the shaft 402 is mechanically coupled to the rotor 404, such that the shaft 402 rotates synchronously with the rotor 404. In an exemplary embodiment, the shaft 402 has length such that a portion of the shaft 402 extends beyond the rotor 404 and through a gap in the housing 406. The resolver rotor 408 is mechanically coupled to the shaft 402 (e.g., by bolting the resolver rotor 408 to the shaft 402). In an exemplary embodiment, the shaft 402 is concentric with the resolver rotor 408. The resolver stator 410 may be mechanically coupled to the housing 406 and concentric with the resolver rotor 408. The resolver stator 410 is configured to sense the absolute angular position of the rotor 404 based on the angular position of the resolver rotor 408, which tracks the angular position of the rotor 404 via the mechanical coupling to the shaft 402, as will be understood in the art.
The systems and/or methods described above provide a field-oriented control system for induction motors using absolute position sensors. Because field-oriented control systems for induction motors are designed for incremental or relative position measurements, implementing an absolute position sensor (such as a resolver) is more complex than using an incremental encoder. However, the space savings exceed the additional implementation costs. Additionally, resolvers are durable can be reliably used in demanding environments where incremental encoders are less reliable. As described above, the performance of the motor is not impaired and the field-oriented control of the induction motor may be achieved without modifying existing control systems, even though a relative position sensor is not used.
Other embodiments may utilize system and method described above in different types of automobiles, different vehicles (e.g., watercraft and aircraft), or in different electrical systems altogether, as it may be implemented in any situation where an induction motor is operated using field-oriented control. Further, the motor and the inverters may have different numbers of phases, and the systems described herein should not be construed as limited to a three-phase design. The basic principles discussed herein may be extended to higher-order phase systems as will be understood in the art.
While at least one exemplary embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or embodiments described herein are not intended to limit the scope, applicability, or configuration of the claimed subject matter in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the described embodiment or embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope defined by the claims, which includes known equivalents and foreseeable equivalents at the time of filing this patent application.
This application claims the benefit of U.S. provisional patent application Ser. No. 60/954,096, filed Aug. 6, 2007, and incorporated by reference herein.
Number | Name | Date | Kind |
---|---|---|---|
3710223 | Cottrell | Jan 1973 | A |
4962976 | Takahashi et al. | Oct 1990 | A |
4972332 | Luebbering et al. | Nov 1990 | A |
5077507 | Mitani et al. | Dec 1991 | A |
5298847 | Kerkman et al. | Mar 1994 | A |
5329217 | Kerkman et al. | Jul 1994 | A |
5925953 | Shibata | Jul 1999 | A |
5965995 | Seibel et al. | Oct 1999 | A |
6087829 | Jager | Jul 2000 | A |
6222335 | Hiti et al. | Apr 2001 | B1 |
6255794 | Staebler | Jul 2001 | B1 |
6278195 | Yamaguchi et al. | Aug 2001 | B1 |
6329781 | Matsui et al. | Dec 2001 | B1 |
6373219 | Obara et al. | Apr 2002 | B1 |
6483270 | Miyazaki | Nov 2002 | B1 |
6674261 | Takahashi | Jan 2004 | B2 |
6674262 | Kitajima et al. | Jan 2004 | B2 |
6832148 | Bennett | Dec 2004 | B1 |
6834244 | Kim | Dec 2004 | B2 |
6850033 | Gallegos-Lopez et al. | Feb 2005 | B1 |
6868318 | Cawthorne | Mar 2005 | B1 |
6894454 | Patel | May 2005 | B2 |
6927551 | Yoshimoto | Aug 2005 | B2 |
6946808 | Kandori | Sep 2005 | B2 |
6984954 | Leonardi | Jan 2006 | B2 |
7002318 | Schulz et al. | Feb 2006 | B1 |
7064504 | Imai | Jun 2006 | B2 |
7154236 | Heap | Dec 2006 | B1 |
7263452 | Kawamura | Aug 2007 | B2 |
7307415 | Seger et al. | Dec 2007 | B2 |
7881567 | Bosselmann et al. | Feb 2011 | B2 |
7999496 | Gleason et al. | Aug 2011 | B2 |
8179127 | West et al. | May 2012 | B2 |
20020030488 | Ito | Mar 2002 | A1 |
20020172509 | Kameya et al. | Nov 2002 | A1 |
20030218458 | Seger et al. | Nov 2003 | A1 |
20040150359 | Yaguchi et al. | Aug 2004 | A1 |
20050007044 | Qiu | Jan 2005 | A1 |
20050076958 | Foster | Apr 2005 | A1 |
20050077867 | Cawthorne | Apr 2005 | A1 |
20050077877 | Cawthorne | Apr 2005 | A1 |
20050080523 | Bennett | Apr 2005 | A1 |
20050080527 | Tao | Apr 2005 | A1 |
20050080535 | Steinmetz | Apr 2005 | A1 |
20050080537 | Cawthorne | Apr 2005 | A1 |
20050080538 | Hubbard | Apr 2005 | A1 |
20050080539 | Hubbard | Apr 2005 | A1 |
20050080540 | Steinmetz | Apr 2005 | A1 |
20050080541 | Sah | Apr 2005 | A1 |
20050182526 | Hubbard | Aug 2005 | A1 |
20050182543 | Sah | Aug 2005 | A1 |
20050182546 | Hsieh | Aug 2005 | A1 |
20050182547 | Sah | Aug 2005 | A1 |
20050189918 | Weisgerber | Sep 2005 | A1 |
20050206253 | Hertz | Sep 2005 | A1 |
20050216225 | Anghel | Sep 2005 | A1 |
20050248307 | Okado | Nov 2005 | A1 |
20050252283 | Heap | Nov 2005 | A1 |
20050252305 | Hubbard | Nov 2005 | A1 |
20050252474 | Sah | Nov 2005 | A1 |
20050255963 | Hsieh | Nov 2005 | A1 |
20050255964 | Heap | Nov 2005 | A1 |
20050255965 | Tao | Nov 2005 | A1 |
20050255966 | Tao | Nov 2005 | A1 |
20050255967 | Foster | Nov 2005 | A1 |
20050255968 | Sah | Nov 2005 | A1 |
20050256617 | Cawthorne | Nov 2005 | A1 |
20050256618 | Hsieh | Nov 2005 | A1 |
20050256623 | Hubbard | Nov 2005 | A1 |
20050256625 | Sah | Nov 2005 | A1 |
20050256626 | Hsieh | Nov 2005 | A1 |
20050256627 | Sah | Nov 2005 | A1 |
20050256629 | Tao | Nov 2005 | A1 |
20050256631 | Cawthorne | Nov 2005 | A1 |
20050256633 | Heap | Nov 2005 | A1 |
20050256919 | Cawthorne | Nov 2005 | A1 |
20050280320 | Utsumi | Dec 2005 | A1 |
20060125439 | Ajima et al. | Jun 2006 | A1 |
20060194670 | Heap | Aug 2006 | A1 |
20060250124 | Ether et al. | Nov 2006 | A1 |
20070078580 | Cawthorne | Apr 2007 | A1 |
20070093953 | Heap | Apr 2007 | A1 |
20070149348 | Holmes | Jun 2007 | A1 |
20070191181 | Burns | Aug 2007 | A1 |
20070225886 | Morris | Sep 2007 | A1 |
20070225887 | Morris | Sep 2007 | A1 |
20070225888 | Morris | Sep 2007 | A1 |
20070225889 | Morris | Sep 2007 | A1 |
20070260381 | Sah | Nov 2007 | A1 |
20070276569 | Sah | Nov 2007 | A1 |
20070284162 | Zettel | Dec 2007 | A1 |
20070284163 | Heap | Dec 2007 | A1 |
20070284176 | Sah | Dec 2007 | A1 |
20070285059 | Zettel | Dec 2007 | A1 |
20070285060 | Zettel | Dec 2007 | A1 |
20070285061 | Zettel | Dec 2007 | A1 |
20070285063 | Zettel | Dec 2007 | A1 |
20070285097 | Zettel | Dec 2007 | A1 |
20080004779 | Sah | Jan 2008 | A1 |
20080028879 | Robinette | Feb 2008 | A1 |
20080032855 | Sah | Feb 2008 | A1 |
20080064559 | Cawthorne | Mar 2008 | A1 |
20080064562 | Aettel et al. | Mar 2008 | A1 |
20080103003 | Sah | May 2008 | A1 |
20080119320 | Wu | May 2008 | A1 |
20080119321 | Heap | May 2008 | A1 |
20080120000 | Heap | May 2008 | A1 |
20080120001 | Heap | May 2008 | A1 |
20080120002 | Heap | May 2008 | A1 |
20080176706 | Wu | Jul 2008 | A1 |
20080176709 | Wu | Jul 2008 | A1 |
20080181280 | Wang | Jul 2008 | A1 |
20080182696 | Sah | Jul 2008 | A1 |
20080183372 | Snyder | Jul 2008 | A1 |
20080234097 | Sah | Sep 2008 | A1 |
20080236921 | Huseman | Oct 2008 | A1 |
20080243346 | Huseman | Oct 2008 | A1 |
20080249745 | Heap | Oct 2008 | A1 |
20080262694 | Heap | Oct 2008 | A1 |
20080262698 | Lahti | Oct 2008 | A1 |
20080272717 | Gleason | Nov 2008 | A1 |
20080275611 | Snyder | Nov 2008 | A1 |
20080275624 | Snyder | Nov 2008 | A1 |
20080275625 | Snyder | Nov 2008 | A1 |
20080287255 | Snyder | Nov 2008 | A1 |
20090069148 | Heap | Mar 2009 | A1 |
20090069989 | Heap | Mar 2009 | A1 |
20090070019 | Heap | Mar 2009 | A1 |
20090082170 | Heap | Mar 2009 | A1 |
20090088294 | West | Apr 2009 | A1 |
20090105039 | Sah | Apr 2009 | A1 |
20090105896 | Tamai | Apr 2009 | A1 |
20090105898 | Wu | Apr 2009 | A1 |
20090105914 | Buur | Apr 2009 | A1 |
20090107745 | Buur | Apr 2009 | A1 |
20090107755 | Kothari | Apr 2009 | A1 |
20090108673 | Wang | Apr 2009 | A1 |
20090111637 | Day | Apr 2009 | A1 |
20090111640 | Buur | Apr 2009 | A1 |
20090111642 | Sah | Apr 2009 | A1 |
20090111643 | Sah | Apr 2009 | A1 |
20090111644 | Kaminsky | Apr 2009 | A1 |
20090111645 | Heap | Apr 2009 | A1 |
20090112385 | Heap | Apr 2009 | A1 |
20090112392 | Buur | Apr 2009 | A1 |
20090112399 | Buur | Apr 2009 | A1 |
20090112412 | Cawthorne | Apr 2009 | A1 |
20090112416 | Heap | Apr 2009 | A1 |
20090112417 | Kaminsky | Apr 2009 | A1 |
20090112418 | Buur | Apr 2009 | A1 |
20090112419 | Heap | Apr 2009 | A1 |
20090112420 | Buur | Apr 2009 | A1 |
20090112421 | Sah | Apr 2009 | A1 |
20090112422 | Sah | Apr 2009 | A1 |
20090112423 | Foster | Apr 2009 | A1 |
20090112427 | Heap | Apr 2009 | A1 |
20090112428 | Sah | Apr 2009 | A1 |
20090112429 | Sah | Apr 2009 | A1 |
20090112495 | Center | Apr 2009 | A1 |
20090115349 | Heap | May 2009 | A1 |
20090115350 | Heap | May 2009 | A1 |
20090115351 | Heap | May 2009 | A1 |
20090115352 | Heap | May 2009 | A1 |
20090115353 | Heap | May 2009 | A1 |
20090115354 | Heap | May 2009 | A1 |
20090115365 | Heap | May 2009 | A1 |
20090115373 | Kokotovich | May 2009 | A1 |
20090115377 | Schwenke | May 2009 | A1 |
20090115491 | Anwar | May 2009 | A1 |
20090118074 | Zettel | May 2009 | A1 |
20090118075 | Heap | May 2009 | A1 |
20090118076 | Heap | May 2009 | A1 |
20090118077 | Hsieh | May 2009 | A1 |
20090118078 | Wilmanowicz | May 2009 | A1 |
20090118079 | Heap | May 2009 | A1 |
20090118080 | Heap | May 2009 | A1 |
20090118081 | Heap | May 2009 | A1 |
20090118082 | Heap | May 2009 | A1 |
20090118083 | Kaminsky | May 2009 | A1 |
20090118084 | Heap | May 2009 | A1 |
20090118085 | Heap | May 2009 | A1 |
20090118086 | Heap | May 2009 | A1 |
20090118087 | Hsieh | May 2009 | A1 |
20090118089 | Heap | May 2009 | A1 |
20090118090 | Heap | May 2009 | A1 |
20090118091 | Lahti | May 2009 | A1 |
20090118093 | Heap | May 2009 | A1 |
20090118094 | Hsieh | May 2009 | A1 |
20090118877 | Center | May 2009 | A1 |
20090118879 | Heap | May 2009 | A1 |
20090118880 | Heap | May 2009 | A1 |
20090118882 | Heap | May 2009 | A1 |
20090118883 | Heap | May 2009 | A1 |
20090118884 | Heap | May 2009 | A1 |
20090118885 | Heap | May 2009 | A1 |
20090118886 | Tamai | May 2009 | A1 |
20090118887 | Minarcin | May 2009 | A1 |
20090118888 | Minarcin | May 2009 | A1 |
20090118901 | Cawthorne | May 2009 | A1 |
20090118914 | Schwenke | May 2009 | A1 |
20090118915 | Heap | May 2009 | A1 |
20090118916 | Kothari | May 2009 | A1 |
20090118917 | Sah | May 2009 | A1 |
20090118918 | Heap | May 2009 | A1 |
20090118919 | Heap | May 2009 | A1 |
20090118920 | Heap | May 2009 | A1 |
20090118921 | Heap | May 2009 | A1 |
20090118922 | Heap | May 2009 | A1 |
20090118923 | Heap | May 2009 | A1 |
20090118924 | Hsieh | May 2009 | A1 |
20090118925 | Hsieh | May 2009 | A1 |
20090118926 | Heap | May 2009 | A1 |
20090118927 | Heap | May 2009 | A1 |
20090118928 | Heap | May 2009 | A1 |
20090118929 | Heap | May 2009 | A1 |
20090118930 | Heap | May 2009 | A1 |
20090118931 | Kaminsky | May 2009 | A1 |
20090118932 | Heap | May 2009 | A1 |
20090118933 | Heap | May 2009 | A1 |
20090118934 | Heap | May 2009 | A1 |
20090118935 | Heap | May 2009 | A1 |
20090118936 | Heap | May 2009 | A1 |
20090118937 | Heap | May 2009 | A1 |
20090118938 | Heap | May 2009 | A1 |
20090118939 | Heap | May 2009 | A1 |
20090118940 | Heap | May 2009 | A1 |
20090118941 | Heap | May 2009 | A1 |
20090118942 | Hsieh | May 2009 | A1 |
20090118943 | Heap | May 2009 | A1 |
20090118944 | Heap | May 2009 | A1 |
20090118945 | Heap | May 2009 | A1 |
20090118946 | Heap | May 2009 | A1 |
20090118947 | Heap | May 2009 | A1 |
20090118948 | Heap | May 2009 | A1 |
20090118949 | Heap | May 2009 | A1 |
20090118950 | Heap | May 2009 | A1 |
20090118951 | Heap | May 2009 | A1 |
20090118952 | Heap | May 2009 | A1 |
20090118954 | Wu | May 2009 | A1 |
20090118957 | Heap | May 2009 | A1 |
20090118962 | Heap | May 2009 | A1 |
20090118963 | Heap | May 2009 | A1 |
20090118964 | Snyder | May 2009 | A1 |
20090118969 | Heap | May 2009 | A1 |
20090118971 | Heap | May 2009 | A1 |
20090118999 | Heap | May 2009 | A1 |
20090144002 | Zettel | Jun 2009 | A1 |
20100014072 | Bosselmann et al. | Jan 2010 | A1 |
20110282552 | Gebregergis et al. | Nov 2011 | A1 |
Number | Date | Country |
---|---|---|
1517683 | Aug 2004 | CN |
69709033 | Aug 2002 | DE |
0839683 | May 1998 | EP |
2002323911 | Nov 2002 | JP |
Entry |
---|
Fishbane et al. “Physics for Scientists and Engineers”, second edition, Prentice Hall Publishing, NJ 07458. 1996. ISBN 0-13-231150-X, pp. 28-31, 67, 236 and 237. These pages show how to calculate velocity. |
Chinese Office Action dated Oct. 27, 2010, for Application No. 200810146006.4. |
German Office Action dated Jul. 8, 2011 for German Patent Application No. 10 2008 036 013.9. |
Chinese Office Action, dated Sep. 7, 2011, for Chinese Patent Application No. 200810146006.4. |
AKSYS Corp; Pancake Resolvers Handbook; 2005; Axsys Technologies Inc; San Diego, CA; www.axsys.com |
Restriction Requirement, dated Jan. 26, 2011, issued in U.S. Appl. No. 12/245,790. |
Response to Restriction Requirement, dated Feb. 24, 2011, filed in U.S. Appl. No. 12/245,790. |
Restriction Requirement, dated May 13, 2011, issused in U.S. Appl. No. 12/245,790. |
Response to Restriction Requirement, dated Jun. 13, 2011, filed in U.S. Appl. No. 12/245,790. |
U.S. Office Action, dated Aug. 11, 2011, issued in U.S. Appl. No. 12/245,790. |
Response to Office Action, dated Nov. 7, 2011, filed in U.S. Appl. No. 12/245,790. |
Notice of Allowance, dated Jan. 18, 2012, issued in U.S. Appl. No. 12/245,790. |
Number | Date | Country | |
---|---|---|---|
20090039825 A1 | Feb 2009 | US |
Number | Date | Country | |
---|---|---|---|
60954096 | Aug 2007 | US |