CN115833686B - A method, apparatus, and electronic device for determining the initial phase angle of a linear motor. - Google Patents
A method, apparatus, and electronic device for determining the initial phase angle of a linear motor.Info
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- CN115833686B CN115833686B CN202211540593.1A CN202211540593A CN115833686B CN 115833686 B CN115833686 B CN 115833686B CN 202211540593 A CN202211540593 A CN 202211540593A CN 115833686 B CN115833686 B CN 115833686B
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Abstract
本发明公开了一种直线电机的初始相位角确定方法、装置和电子设备。所述初始相位角确定方法包括：向动子的两相线圈分别通入第一电流和第二电流，其中，所述第一电流和所述第二电流均为直流。待所述动子相对于定子不再运动后，获取所述动子的实时位移数据。根据直线电机的磁极距离和所述实时位移数据确定所述直线电机的初始相位角的分析值。本发明方案能够避免确定过程中动子撞击限位，提高了初始相位角确定方法的可靠性。
This invention discloses a method, apparatus, and electronic device for determining the initial phase angle of a linear motor. The initial phase angle determination method includes: passing a first current and a second current, respectively, through the two phase coils of the mover, wherein both the first current and the second current are direct current (DC). After the mover stops moving relative to the stator, real-time displacement data of the mover is acquired. An analytical value of the initial phase angle of the linear motor is determined based on the magnetic pole distance of the linear motor and the real-time displacement data. This invention avoids the mover hitting the limiting position during the determination process, thus improving the reliability of the initial phase angle determination method.
Description
Technical Field
The embodiment of the invention relates to a motor control technology, in particular to a method and a device for determining an initial phase angle of a linear motor and electronic equipment.
Background
With the deep and popular industrial automation and intellectualization, the demand for high-speed and high-precision motion tables is increasing. The driving motor of the motion platform generally adopts a three-phase linear motor. When the controller drives the motion stage for the first time, it is necessary to acquire an initial phase angle of the magnetic field to determine an electrical angle of the three-phase current of the drive motor. If the phase angle is inaccurate, the actual output of the motor is affected, thereby affecting the control accuracy of the motion stage.
In the existing method for determining the initial phase angle, the initial phase value of the motor is determined and calculated according to the acceleration of the rotor under each current.
However, this method of determining the initial phase angle has a limited risk of impact and is less reliable.
Disclosure of Invention
The invention provides a method and a device for determining an initial phase angle of a linear motor and electronic equipment, which are used for avoiding the occurrence of rotor impact limit in the determining process and improving the reliability of the initial phase angle determining method.
In a first aspect, an embodiment of the present invention provides a method for determining an initial phase angle of a linear motor, where the method includes:
Respectively introducing a first current and a second current into two-phase coils of the mover, wherein the first current and the second current are both direct currents;
acquiring real-time displacement data of the rotor after the rotor does not move relative to the stator;
And determining an analysis value of the initial phase angle of the linear motor according to the magnetic pole distance of the linear motor and the real-time displacement data.
Optionally, the first current and the second current are equal to each other and equal to a preset current.
Optionally, the values of the first current and the second current are set according to the friction coefficient and the mass of the mover.
Optionally, determining an analysis value of an initial phase angle of the linear motor according to the magnetic pole distance of the linear motor and the real-time displacement data includes:
substituting the magnetic pole distance of the linear motor and the real-time displacement data into a first calculation formula to determine an analysis value of an initial phase angle of the linear motor, wherein the first calculation formula is that Wherein P is an analysis value of the initial phase angle of the linear motor, tau is the magnetic pole distance, and x is the real-time displacement data.
Optionally, after determining the analysis value of the initial phase angle of the linear motor according to the magnetic pole distance of the linear motor and the displacement data, the method further includes:
establishing a simulation model of the linear motor;
setting an initial phase angle of the simulation model as the analysis value;
respectively introducing the first current and the second current into two-phase coils of the simulation model;
after the model rotor does not move relative to the model stator, obtaining simulation displacement data of the model rotor;
and determining the accuracy of the analysis value according to the simulated displacement data.
Optionally, determining the accuracy of the analysis value according to the simulated displacement data includes:
Judging whether the simulation displacement data are equal to the real-time displacement data or not;
and if the simulated displacement data are equal to the real-time displacement data, the analysis value is an accurate value.
Optionally, determining the accuracy of the analysis value according to the simulated displacement data includes:
According to substituting the simulation displacement data and the magnetic pole distance into a second calculation formula, determining an inspection value of an initial phase angle of the simulation model, wherein the second calculation formula is that Wherein P ′ is the check value of the initial phase angle of the simulation model, τ is the magnetic pole distance, x ′ is the simulated displacement data;
judging whether the check value is equal to the analysis value or not;
and if the check value is equal to the analysis value, the analysis value is an accurate value.
The embodiment of the invention also provides an initial phase angle determining device of the linear motor, which comprises a current flowing module, a position determining module and a determining module, wherein the current flowing module is used for respectively flowing a first current and a second current into two-phase coils of the mover, the first current and the second current are both direct currents, the position determining module is used for acquiring real-time displacement data of the mover after the mover does not move relative to the stator, and the determining module is used for determining an analysis value of the initial phase angle of the linear motor according to the magnetic pole distance of the linear motor and the real-time displacement data.
Optionally, the initial phase angle determining device of the linear motor further comprises a simulation verification module, wherein the simulation verification module is used for establishing a simulation model of the linear motor, then the initial phase angle of the simulation model is set to be the analysis value, the first current and the second current are respectively led into two-phase coils of the simulation model, after the model rotor does not move relative to the model stator, simulation displacement data of the model rotor are obtained, and finally the accuracy of the analysis value is determined according to the simulation displacement data.
In a third aspect, an embodiment of the present invention further provides an electronic device, where the electronic device includes at least one processor, and a memory communicatively coupled to the at least one processor,
The memory stores a computer program executable by the at least one processor to enable the at least one processor to perform the initial phase angle determination method of the linear motor of any of the first aspects.
According to the method, the device and the electronic equipment for determining the initial phase angle of the linear motor, when the initial phase angle is determined, the first current and the second current are respectively fed into the two-phase coils of the rotor, wherein the first current and the second current are both direct currents. And after the mover does not move relative to the stator, acquiring real-time displacement data of the mover. According to the method, the analysis value of the initial phase angle of the linear motor is determined according to the magnetic pole distance and the real-time displacement data of the linear motor, and the determination of the initial phase angle of the linear motor is realized.
Drawings
Fig. 1 is a schematic flow chart of a method for determining an initial phase angle of a linear motor according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a linear motor according to an embodiment of the present invention;
Fig. 3 is a flowchart of another method for determining an initial phase angle of a linear motor according to an embodiment of the present invention;
fig. 4 is a flowchart of another method for determining an initial phase angle of a linear motor according to an embodiment of the present invention;
Fig. 5 is a schematic diagram of a displacement change of a mover after a direct current is passed through a two-phase coil according to an embodiment of the present invention;
Fig. 6 is a schematic diagram of an initial phase angle determining device of a linear motor according to an embodiment of the present invention;
fig. 7 is a schematic diagram illustrating an initial phase angle determining apparatus of another linear motor according to an embodiment of the present invention;
fig. 8 is a schematic diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting thereof. It should be further noted that, for convenience of description, only some, but not all of the structures related to the present invention are shown in the drawings.
In order to solve the problems in the background art, the embodiment of the invention provides a method for determining an initial phase angle of a linear motor, which can be used for determining the initial phase angle of a magnetic field of a three-phase linear motor. Fig. 1 is a schematic flow chart of a method for determining an initial phase angle of a linear motor according to an embodiment of the present invention, and referring to fig. 1, the method for determining an initial phase angle includes:
s101, respectively introducing a first current and a second current into two-phase coils of the rotor.
Wherein, the first current and the second current are both direct currents.
Specifically, fig. 2 is a schematic structural diagram of a linear motor according to an embodiment of the present invention, and in combination with fig. 1 and 2, the linear motor includes a stator 202 and a mover 201, the stator 202 includes a plurality of permanent magnets 204 (S and N denote two poles of the permanent magnets), and the mover 201 includes a, b, and c three-phase coils 203 and a position sensor 205. During normal operation, three-phase coils 203 are respectively energized with three-phase alternating currents. a. The current expressions of the b, c three-phase coils 203 are respectively: And Wherein I a、Ib and I c correspond to the currents in coil a, coil b and coil c respectively,Is the effective value of the current in the coil, x is the displacement of the mover relative to the origin of the motor,For the initial electrical angle, τ is the pole distance,A. the expressions of the magnetic field strengths of the b, c three-phase coils 203 in the magnetic field provided by the stator permanent magnet 204 are respectively: And Wherein, B a、Bb and B c are respectively corresponding to the magnetic field intensity of the coil a, the coil B and the coil c,For the effective value of the coil field strength, P is the initial phase angle of the linear motor field,The alternating current flowing through the three-phase coil enables the mover to receive Lorentz force in the magnetic field provided by the permanent magnet. The sum expression of Lorentz forces applied to the three-phase coil in the magnetic field isIn the lorentz force sum expression, P represents the initial phase angle of the magnetic field,The initial electrical angle is indicated, and the linear motor can be utilized to maximize the output only when the initial electrical angle is the same as the initial phase angle.
The two-phase coils 203 of the mover are respectively supplied with a first current and a second current, both of which are direct currents, and the values of the first current and the second current may be set according to the friction coefficient and the mass of the mover, for example. The first current and the second current are respectively supplied to two phases of the three-phase coil of the linear motor, and the first current I 1 and the second current I 2 are respectively supplied to the a-phase coil and the b-phase coil, so that the current in the c-phase coil is I 3＝-(I1+I2. At this time, the sum expression of lorentz forces received by the linear motor mover is: If I 1＝M*I,I2 =n×i, N is a positive number, the sum expression of lorentz forces applied to the linear motor mover can be simplified as The value of k is related to M and N.
S102, acquiring real-time displacement data of the rotor after the rotor does not move relative to the stator.
Specifically, acquiring real-time displacement data of the mover may be implemented by a position sensor provided on the mover. Displacement data may refer to the vector distance, both distance and direction, of any point on the mover relative to the origin of the motor. Illustratively, the position sensor may be a grating scale, and the displacement sensing accuracy of the nanometer scale may be obtained.
S103, determining an analysis value of an initial phase angle of the linear motor according to the magnetic pole distance and the real-time displacement data of the linear motor.
Specifically, after the first current and the second current are respectively supplied to the two-phase coils of the mover, the sum of lorentz forces applied to the linear motor mover is represented as a sinusoidal curve related to displacement. Because damping and friction force generally exist between the rotor and the stator, finally, the rotor with direct current applied to the two-phase coil can oscillate and converge and be static at a position, and the sum of Lorentz forces applied to the rotor at the position is close to 0. Thus, in the rest position, can be obtainedDue toThenThereby can be determinedAccording to the magnetic pole distance tau of the linear motor and the real-time displacement data x, an analysis value of the initial phase angle of the linear motor can be determined.
According to the initial phase angle determining method of the linear motor, a first current and a second current are respectively fed into two-phase coils of a rotor, wherein the first current and the second current are both direct currents. And after the mover does not move relative to the stator, acquiring real-time displacement data of the mover. According to the method, the analysis value of the initial phase angle of the linear motor is determined according to the magnetic pole distance and the real-time displacement data of the linear motor, and the determination of the initial phase angle of the linear motor is realized.
Fig. 3 is a flowchart of another method for determining an initial phase angle of a linear motor according to an embodiment of the present invention, and referring to fig. 3, the method for determining an initial phase angle includes:
S301, respectively supplying preset currents to the two-phase coils of the mover.
Specifically, the direct current introduced into the two-phase coils is equal to the preset current. The direct currents introduced by the two phase lines are equal, so that the calculation of the analysis value of the initial phase angle can be simplified. For example, a predetermined current is applied to the a-phase coil and the b-phase coil, respectively, because the sum expression of lorentz forces applied to the linear motor mover is given by I 1＝I2 =tiCan be simplified intoThe simplifying step is simpler. The motor force appears as a sinusoidal curve with respect to position, as the motor typically has damping and friction forces, and eventually the motor will oscillate to converge to rest to a position where the actual force of the motor is close to 0. The simplified Lorentz force sum expression can be directly obtainedThe value of P ′ can directly obtain an accurate value, is not related to the relative relation between the currents passing through the two-phase coils, and has great simplification in the calculation and simplification processes.
The preset current can be positively correlated with the friction coefficient and the mass of the mover respectively, wherein the mass refers to the total mass of the mover and can be the sum of the self mass of the mover and the load mass of the stator. The preset current is positively correlated with the friction coefficient and the mass of the rotor respectively, so that the moving speed of the rotor is proper, the safety problem caused by collision on limit is avoided, and the safety and the reliability of the initial phase angle determining method are improved.
S302, acquiring real-time displacement data of the rotor after the rotor does not move relative to the stator.
The content of step S302 is the same as that of step S102, and will not be described here again.
S303, substituting the magnetic pole distance and the real-time displacement data of the linear motor into a first calculation formula to determine an analysis value of an initial phase angle of the linear motor.
The first calculation formula is a calculation formula for calculating an initial phase angle according to the magnetic pole distance and real-time displacement data, and can be determined according to the relative relation between the current values introduced by the two-phase coils.
Illustratively, the two-phase coils in step S301 are respectively supplied with a preset current, which can be obtained by calculating and simplifying the lorentz force sum expressionDue toThen it can be obtainedAnd then the first calculation formula can be determinedIn this step, the magnetic pole distance τ of the linear motor and the real-time displacement data x obtained in step S302 are substituted into the first calculation formula, so that the analysis value of the initial phase angle P of the linear motor can be determined. For example, if the real-time displacement data x= -6mm, the magnetic pole distance τ=24 mm, the analysis value of the initial phase angle is equal to
In the initial phase angle determining method of the linear motor provided by the embodiment, the current values of the two-phase coils are equal to each other and equal to the preset current, and the calculation and simplification processes when the first calculation formula is obtained by simplifying the lorentz force sum expression are greatly simplified, so that the calculation workload in the early-stage preparation work is reduced. The value of the preset current is positively correlated with the friction coefficient and the quality of the rotor respectively, so that the moving speed of the rotor is proper, the safety problem caused by collision on limit is avoided, and the safety and the reliability of the initial phase angle determining method are improved.
Fig. 4 is a flowchart of another method for determining an initial phase angle of a linear motor according to an embodiment of the present invention, and referring to fig. 4, the method for determining an initial phase angle of a linear motor includes:
s401, respectively introducing a first current and a second current into two-phase coils of the mover.
S402, acquiring real-time displacement data of the rotor after the rotor does not move relative to the stator.
S403, determining an analysis value of the initial phase angle of the linear motor according to the magnetic pole distance and the real-time displacement data of the linear motor.
The content of the step S401, the step S402, and the step S403 are the same as that of the step S101, the step S102, and the step S103, respectively, and are not described herein.
S404, establishing a simulation model of the linear motor.
Specifically, a simulation model with the same basic parameters is built on simulation software according to the basic parameters of the linear motor, wherein the basic parameters can include all basic parameters related to the design of the linear motor body, such as construction data, dimension data, material data, and the like, and the basic data can include motor basic parameters, such as magnetic pole materials, magnetic pole distances, coil materials, coil turns, dimensions of each component element of the stator, dimensions of each component element of the rotor, friction coefficient, load weight, and the like, for example. The simulation software can be any one of ANSYS finite element analysis software, COMSOL multiple physical field simulation software, motor-CAD software and the like which can perform simulation analysis on the electric field and the magnetic field of the Motor.
S405, setting the initial phase angle of the simulation model as an analysis value.
Specifically, the initial phase angle in the simulation model of the linear motor is set to be equal to the analysis value of the initial phase angle determined in step S403.
S406, respectively introducing a first current and a second current into the two-phase coils of the simulation model.
Specifically, the first current and the second current are respectively supplied to two-phase coils of the simulation model of the linear motor, and the two-phase coils correspond to the two-phase coils in step S401. Illustratively, corresponding to step S401, a first current is applied to the a-phase coil of the mover in the simulation model, and a second current is applied to the b-phase coil of the mover in the simulation model.
S407, after the model rotor does not move relative to the model stator, obtaining simulation displacement data of the model rotor.
Specifically, fig. 5 is a schematic diagram of a displacement change of a mover after a direct current is passed through a two-phase coil, and in combination with fig. 4 and fig. 5, after a first current and a second current are respectively passed through the two-phase coil of a simulation model, the mover of the simulation model will perform an oscillating movement, and the sum of lorentz forces applied to the mover is represented as a sinusoidal curve related to the displacement. Because damping and friction force are arranged between the rotor and the stator in the simulation model, the rotor of which the direct current is introduced into the two-phase coil in the final simulation model can oscillate, converge and be static at one position. The simulation displacement data of the simulation model during standing can be obtained by measuring or directly reading on simulation software.
S408, determining the accuracy of the analysis value according to the simulated displacement data.
Specifically, the simulated displacement data refers to displacement data after the initial phase angle of the simulation model is set to be an analysis value, and then a first current and a second current are respectively introduced into two-phase coils of the simulation model, wherein the simulation model mover is stationary. The simulated displacement data may represent a relative relationship between the analyzed value and the actual value of the initial phase angle. Accuracy includes both accuracy and inaccuracy.
In an exemplary embodiment, according to one manner of determining accuracy of the analysis value according to the simulated displacement data, it is determined whether the simulated displacement data is equal to the real-time displacement data, and if the simulated displacement data is equal to the real-time displacement data, the analysis value is the accurate value. For example, if the simulated displacement data is equal to-6 mm, which is equal to the real-time displacement data acquired by the displacement sensor in step S402, the analysis value is an accurate value.
According to another mode of determining the accuracy of the analysis value by the simulated displacement data, the checking value of the initial phase angle of the simulation model is determined by substituting the simulated displacement data and the magnetic pole distance into a second calculation formula, wherein the second calculation formula is thatWherein P ′ is an experimental value of an initial phase angle of the simulation model, τ is a magnetic pole distance, and x ′ is simulation displacement data. And judging whether the check value is equal to the analysis value. If the check value is equal to the analysis value, the analysis value is an accurate value. For example, if the simulated displacement data is equal to-6 mm and the magnetic pole distance is 24mm, the value of the initial phase angle of the simulation model is checkedIf the check value is equal to the analysis value determined in step S403, the analysis value is an accurate value.
According to the initial phase angle determining method for the linear motor, after the analysis value of the initial phase angle is determined, the simulation displacement data under the condition that the initial phase angle is the analysis value is obtained in a simulation analysis mode, whether the analysis value is accurate or not is determined according to the simulation displacement data, the analysis value of the initial phase angle is checked, and the reliability of the initial phase angle determining method is further improved.
The embodiment of the invention also provides a device for determining the initial phase angle of the linear motor. Fig. 6 is a schematic diagram of the initial phase angle determining device of a linear motor according to an embodiment of the present invention, and referring to fig. 6, the initial phase angle determining device 600 of a linear motor includes a current flowing module 601, a position determining module 602, and a determining module 603, where the current flowing module 601 is configured to respectively supply a first current and a second current to two-phase coils of a mover, and the first current and the second current are both direct currents. The position determining module 602 is configured to obtain real-time displacement data of the mover after the mover is no longer moving relative to the stator. The determining module 603 is configured to determine an analysis value of an initial phase angle of the linear motor according to the magnetic pole distance and the real-time displacement data of the linear motor.
Optionally, fig. 7 is a schematic diagram of the initial phase angle determining device of another linear motor according to the embodiment of the present invention, referring to fig. 7, on the basis of the foregoing embodiment, the initial phase angle determining device 600 of the linear motor further includes a simulation verification module 604, where the simulation verification module 604 is configured to establish a simulation model of the linear motor, then set the initial phase angle of the simulation model as an analysis value, and further respectively introduce a first current and a second current to two-phase coils of the simulation model, obtain simulation displacement data of the model mover after the model mover does not move relative to the model stator, and finally determine accuracy of the analysis value according to the simulation displacement data.
The embodiment of the invention also provides electronic equipment. Fig. 8 is a schematic diagram of an electronic device according to an embodiment of the present invention, and referring to fig. 8, an electronic device 800 includes at least one processor 801 (5 processors are shown in an exemplary manner), and a memory 802 communicatively connected to the at least one processor 801, where the memory 802 stores a computer program executable by the at least one processor 801, and the computer program is executed by the at least one processor 801, so that the at least one processor 801 can perform an initial phase angle determining method of any linear motor according to an embodiment of the present invention.
The embodiment of the invention also provides a computer readable storage medium. The computer readable storage medium stores computer instructions for causing the processor to implement the method for determining the initial phase angle of any linear motor according to the embodiments of the present invention when executed.
According to the method, the device, the equipment and the storage medium for determining the initial phase angle of the linear motor, in the process of determining the initial phase angle, the first current and the second current are respectively fed into the two-phase coils of the rotor, wherein the first current and the second current are both direct currents. And after the mover does not move relative to the stator, acquiring real-time displacement data of the mover. According to the method, the analysis value of the initial phase angle of the linear motor is determined according to the magnetic pole distance and the real-time displacement data of the linear motor, and the determination of the initial phase angle of the linear motor is realized.
Various implementations of the devices and techniques described here above may be implemented in digital electronic circuitry, integrated circuitry, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include being implemented in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be a special or general purpose programmable processor, operable to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.
A computer program for carrying out methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the computer programs, when executed by the processor, cause the functions/acts specified in the flowchart and/or block diagram block or blocks to be implemented. The computer program may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.
In the context of the present invention, a computer-readable storage medium may be a tangible medium that can contain, or store a computer program for use by or in connection with an instruction execution system, apparatus, or device. The computer readable storage medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. Alternatively, the computer readable storage medium may be a machine readable signal medium. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
To provide for interaction with a user, the systems and techniques described here can be implemented on an electronic device having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the electronic device. Other kinds of devices may also be used to provide for interaction with a user, for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback), and input from the user may be received in any form, including acoustic input, speech input, or tactile input.
The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a Local Area Network (LAN), a Wide Area Network (WAN), a blockchain network, and the Internet.
The computing system may include clients and servers. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server can be a cloud server, also called a cloud computing server or a cloud host, and is a host product in a cloud computing service system, so that the defects of high management difficulty and weak service expansibility in the traditional physical hosts and VPS service are overcome.
It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps described in the present invention may be performed in parallel, sequentially, or in a different order, so long as the desired results of the technical solution of the present invention are achieved, and the present invention is not limited herein.
The above embodiments do not limit the scope of the present invention. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
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