Patent ID: 12212254

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following is a further explanation of the invention in combination with drawings and embodiments.

It should be noted that the following details are illustrative and are intended to provide further explanation for this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as those commonly understood by ordinary technicians in the technical field to which this application relates.

It should be noted that the terminology used here only describes the specific embodiment, not intended to limit the embodiment according to the exemplary embodiment of the invention. As used here, the singular form is also intended to include the plural form unless explicitly stated in the context. In addition, it should be understood that when the terms include and/or comprise are used in this specification, they indicate the presence of features, steps, operations, devices, amounts, and/or combinations of them.

In this invention, terms such as up, down, left, right, front, back, vertical, horizontal, side, and bottom indicate the position or position relationship based on the position or position relationship shown in the attached figures, which is only a relation word determined to facilitate the description of the structural relationship of each amount or amounts of the invention. It does not refer to any amount or amount in the invention and cannot be understood as a restriction on the invention.

In this invention, terms such as ‘fixed connection’, ‘connected’, ‘connecting’, etc. should be understood in a broad sense, indicating that it can be a fixed connection, an integrated connection, or a detachable connection; it can be directly connected or indirectly connected through an intermediate medium. For the relevant scientific research or technical personnel in this field, the specific meaning of the above terms in the actual invention can be determined according to the specific situation, which cannot be understood as a restriction on the invention.

Without conflicts, the embodiments and the characteristics of the embodiments in the invention can be combined.

Embodiment 1

The embodiment of the invention introduces a flux-weakening control method for the salient pole offset permanent magnet synchronous motor.

A flux-weakening control method for the salient pole offset permanent magnet synchronous motor is shown inFIG.1, which includes:

According to the actual speed of the salient pole offset permanent magnet synchronous motor and the given target speed, the given value of the electromagnetic torque is determined.

According to the electromagnetic torque equation and the given value of the electromagnetic torque of the salient pole offset permanent magnet synchronous motor, the current trajectory and the given value of the motor current when the maximum torque per ampere control is operating in the dq coordinate system are calculated.

According to the stator voltage equation of the salient pole offset permanent magnet synchronous motor, the current trajectory when the maximum torque per voltage control is operating in the dq coordinate system is calculated.

Through the rotation transformation of the coordinate system, the current dq coordinate system of the salient pole offset permanent magnet synchronous motor is rotated by a certain angle to obtain a new d′q′ coordinate system, and the current trajectory and the given value of the motor current in the d′q′ coordinate system are calculated.

According to the current trajectory of the maximum torque per voltage control operation in the d′q′ coordinate system, the characteristic current and the quadrature axis current at the characteristic current are obtained.

According to the difference between the limit voltage of the inverter and the given value of the stator voltage, it is judged whether the flux-weakening control needs to be turned on. When it is turned on, the direct axis current compensation is output by the PI controller, the sum of the given value of the direct axis current and the compensation amount of the direct axis current when the maximum torque per ampere control is operating is the given value of the direct axis current in the first flux-weakening region, and the upper limit of the amplitude is not greater than the amplitude of the characteristic current.

According to the difference between the amplitude of the sum of the given value of the direct axis current and the compensation amount of the direct axis current and the amplitude of the characteristic current when the maximum torque per ampere control is operating, the flux-weakening area of the motor is judged, and the output of the compensation amount of the quadrature axis current through the PI controller is determined when the motor works in the second flux-weakening region.

When the first flux-weakening region is operating, the quadrature axis current of the motor is given by the motor current limit circle.

When the second flux-weakening region is operating, the given value of the direct axis current of the motor is the characteristic current, and the given value of the quadrature axis current of the motor is the sum of the quadrature axis current at the characteristic current and the compensation amount of the quadrature axis current.

Through the rotation transformation of the coordinate system, the current d′q′ coordinate system of the salient pole offset permanent magnet synchronous motor is rotated to the corresponding angle to obtain the original dq coordinate system, and the given value of the motor current in the dq coordinate system is obtained at the same time.

According to the given value of the motor current and the obtained actual value of the current, the space vector pulse width modulation signal is generated to drive the operation of the salient pole offset permanent magnet synchronous motor, and the flux-weakening speed regulation of the salient pole offset permanent magnet synchronous motor in full speed range is realized.

This embodiment is illustrated by a salient pole offset permanent magnet synchronous motor, as shown inFIG.2, including a salient pole offset permanent magnet synchronous motor1, a DC power supply2, an inverter bridge3, an ABC-dq converter4, a quadrature axis current PI controller5, a direct axis current PI controller6, a dq-αβ converter7, an SVPWM module8, a photoelectric encoder9, an angular velocity processing module10, a speed PI controller11, an MTPA module12, a dq coordinate system-d′q′ coordinate system converter13, a direct axis current compensation module14, a direct axis current compensation PI controller15, a limit current limiting module16, a quadrature axis current compensation module17, a quadrature axis current compensation amount PI controller18, a characteristic current limiting module19, and a d′q′ coordinate system-dq coordinate system converter20.

In this embodiment, by setting the photoelectric encoder9on the rotor shaft of the salient pole offset permanent magnet synchronous motor1, the rotor mechanical position angle θmof the salient pole offset permanent magnet synchronous motor1is measured and sent to the angular velocity processing module10; the angular velocity processing module10, according to the rotor position angle θmmeasured by the photoelectric encoder9, the speed ωris calculated by differential calculation; according to the speed ωrcalculated by the angular velocity processing module and the given target speed ωr*, the given value of electromagnetic torque Te* is calculated by the speed PI controller11; the MTPA module12, according to the given value of the electromagnetic torque, relying on the auxiliary function, the given values id* and iq* of the d axis current and q axis current of the motor under MTPA condition are obtained; the dq coordinate system-d′q′ coordinate system converter13, the rotation transformation of the coordinate system is used to convert the given values of the d axis current and q axis current of the motor in the dq coordinate system that meet the MTPA conditions into the given values id′* and iq′* of the d axis current and q axis current of the motor in the d′q′ coordinate system that meet the MTPA conditions; the direct axis current compensation module14, according to the difference ΔU between the limit voltage of the inverter Usmaxand the given value of the stator voltage Usto determine whether it is necessary to turn on the flux-weakening control; the direct axis current compensation PI controller15, according to the ΔU obtained by the direct axis current compensation module14, a calculation is performed to obtain the compensation amount of the direct axis current id′fw*; the limit current limiting module16, the amplitude of iq′* is limited in the current limit circle to obtain iq′**; the quadrature axis current compensation module17, according to the difference Δid′between the amplitude of the sum id′** of id′fw* and id′* and the amplitude of the characteristic current icto determine whether the quadrature axis current needs to be compensated; the quadrature axis current compensation amount PI controller18, according to the Δid′obtained by the quadrature axis current compensation module17, a calculation is performed to obtain the compensation amount of the quadrature axis current iq′fw*; the characteristic current limiting module19, the amplitude of id′** is limited within the amplitude range of the characteristic current to obtain id′***; the d′q′ coordinate system-dq coordinate system converter20, the rotation transformation of the coordinate system is used to convert the sum iq′*** of iq′** and iq′fw* and id′*** into the given values of quadrature axis current and direct axis current iq** and id** in dq coordinate system; the ABC-dq converter4, it is used to transform the three-phase current value of the motor input obtained by the current transformer into the dq coordinate system by using the electric angle θc, and the actual current values idand iqof the d axis and q axis are obtained; the direct axis current PI controller6, according to the given value id** of the direct axis current of the motor and the actual value idof the direct axis current, the given value of the d axis voltage ud* is calculated; the quadrature axis current PI controller5, according to the given value iq** of the quadrature axis current of the motor and the actual value iqof the quadrature axis current, the given value of the q axis voltage uq* is calculated; the dq-αβ converter7, the voltage given values ud* and uq* are transformed from d-q coordinate system to α-β coordinate system by using the electric angle θc, and uαand uβare obtained. The SVPWM module8, based on the voltage given uαand uβ, the three-phase PWM signal is obtained and sent to the inverter bridge module; the inverter bridge module3, it is connected to the DC power supply2and the salient pole offset permanent magnet synchronous motor1, and the three-phase voltage value is generated according to the aforementioned three-phase PWM signal to drive the motor.

The rotor topology of the salient pole offset permanent magnet synchronous motor is shown inFIG.3A, the salient pole of the motor is connected with the permanent magnet, and the dq axis orientation position on each pole is shown inFIG.3B. The direction and position of the rotor permanent magnet flux linkage are located at the angle bisector of the dq axis (that is, the direct axis position will be about 45° from the permanent magnet flux linkage position).

The unique topology of the salient pole offset permanent magnet synchronous motor makes the maximum permanent magnet torque Tpmand the maximum reluctance torque Tresuperimposed at the same current phase angle to obtain the total torque Tem, as shown inFIG.4A. Compared with the traditional salient pole permanent magnet motor (as shown inFIG.4B), the maximum total torque is improved, so that the motor has a larger torque density.

According to the distribution of magnetic field lines, the motor space vector diagram shown inFIG.5is obtained, where isis a stator current space vector, idand iqare the quadrature and direct axis amounts of isrespectively, and id2+iq2≤ismax2, ismaxis the motor limit current (the motor current limit circle is shown inFIG.6), ψpmis the permanent magnet flux linkage generated by the permanent magnet, the permanent magnet flux linkage offset angle is 45°, ψ0is the flux linkage generated by is, and ψsis the combined flux linkage of ψ0and ψpm.

The electromagnetic torque equation of the salient pole offset permanent magnet synchronous motor is:

Te=32⁢p⁡(ψp⁢m(22⁢iq-22⁢id)+id⁢iq(Ld-Lq))(1)
where p is a pole pair of the motor, Ldis the inductance of the d axis, Lqis the inductance of the q axis, and Teis the electromagnetic torque.

Ignoring the stator resistance, since the permanent magnet flux linkage ψpmof the salient pole offset permanent magnet synchronous motor is 45° ahead of the d axis, the d axis voltage udand the q axis voltage uqof the motor under a stable state can be expressed as:

{ud≈-ωr⁢Lq⁢iq-22⁢ωr⁢ψpmuq≈ωr⁢Ld⁢id+22⁢ωr⁢ψpm(2)
therefore,

U=ωr2(Lq⁢iq+22⁢ψp⁢m)2+ωr2(Ld⁢id+22⁢ψp⁢m)2(3)
U is the stator voltage of the salient pole offset permanent magnet synchronous motor.

A flux-weakening control method for the salient pole offset permanent magnet synchronous motor provided in this embodiment includes:According to the measured rotor position angle of the salient pole offset permanent magnet synchronous motor and the given target speed, the given value of electromagnetic torque is determined;according to the electromagnetic torque equation of the salient pole offset permanent magnet synchronous motor, the auxiliary function is constructed, under the condition of MTPA, the Lagrange multiplier is used to introduce the auxiliary function to obtain the objective function, and the extreme point of the objective function is solved; by giving the given value of the electromagnetic torque, the MTPA control current trajectory in the dq coordinate system (as shown inFIG.6) and the given values of the quadrature axis current and direct axis current that meet the MTPA conditions are obtained;in the MTPA module of this embodiment, in order to obtain the relationship between current and torque, that is, to obtain the minimum value of iq2+id2under a certain Te, and to obtain the relationship between iqand idunder this condition, the Lagrange extremum theorem is used, the Lagrange multiplier λ is used and introduced into the auxiliary function, and the following results are obtained:

F=id2+iq2+λ⁡(32⁢p⁡(ψp⁢m(22⁢iq-22⁢id)+id⁢iq(Ld-Lq))-Te)(4)according to the Lagrange extreme value theorem, the required relationship between iqand idis the extreme point of the above function F, that is:

{∂F∂id=0∂F∂iq=0Te=32⁢p⁡(ψpm(22⁢iq-22⁢id)+id⁢iq(Ld-Lq))(5)the extraneous root is rounded down to obtain:

id=2⁢ψp⁢m4⁢(Lq-Ld)-ψp⁢m28⁢(Lq-Ld)2+2⁢ψp⁢m2⁢(Lq-Ld)⁢iq+iq2(6)due to the limitation of the limit voltage of the inverter Usmax, according to the stator voltage equation (3) of the salient pole offset permanent magnet synchronous motor, the voltage limit equation of the motor can be obtained:

(ωr⁢Lq⁢iq+22⁢ωr⁢ψp⁢m)2+(ωr⁢Ld⁢id+22⁢ωr⁢ψp⁢m)2≤Us⁢max2(7)that is:

(id+22⁢ψp⁢mLd1Ld⁢Us⁢maxωr)2+(iq+22⁢ψp⁢mLq1Lq⁢Us⁢maxωr)2≤1(8)where Usmaxis the limit voltage of the inverter.

The voltage limit equation is an ellipse whose center is

(-22⁢ψp⁢mLd,-22⁢ψp⁢mLq),
the vertex of its long axis is

(±1Ld⁢Us⁢maxωr,-22⁢ψp⁢mLq),
and the vertex of its short axis is

(-22⁢ψp⁢mLd,±1Lq⁢Us⁢maxωr).

The connection between the voltage limit ellipse and the motor torque hyperbolic tangent point is the MTPV trajectory, the MTPV equation of the motor can be expressed by the following formula:

∂Te∂id⁢∂U∂iq-∂Te∂iq⁢∂U∂id=0(9)
according to (1), (3), (9), the following is obtained:

[-22⁢ψp⁢m+iq(Ld-Lq)]⁢(Lq2⁢iq+22⁢Lq⁢ψp⁢m)-[22⁢ψp⁢m+id(Ld-Lq)]⁢(Ld2⁢id+22⁢Ld⁢ψp⁢m)=0(10)
that is:

-22⁢ψp⁢m⁢Lq2⁢iq-12⁢ψp⁢m2⁢Lq+(Ld-Lq)⁢Lq2⁢iq2-22⁢ψp⁢m⁢Ld2⁢id-12⁢ψp⁢m2⁢Ld-(Ld-Lq)⁢Ld2⁢id2+22⁢(Ld-Lq)⁢ψp⁢m⁢Lq⁢iq-22⁢(Ld-Lq)⁢ψp⁢m⁢Ld⁢id=0(11)

The obtained MTPV trajectory is shown inFIG.6, this trajectory can be approximated as a straight line y=kx+C (C is a constant) with a slope of k, and θ=−90°+arctan (k);through the rotation transformation of the coordinate system (as shown inFIG.7), the current dq coordinate system of the salient pole offset permanent magnet synchronous motor is rotated by a certain angle θ to obtain a new d′q′ coordinate system, so that the MTPV control current trajectory in the d′q′ coordinate system of the salient pole offset permanent magnet synchronous motor is perpendicular to the abscissa axis (that is, the d′ coordinate axis);then the given value of the current (id*, iq*) in the dq coordinate system during MTPA operation can be expressed as (id′*, iq′*) in the d′q′ coordinate system after the rotation transformation of the coordinate system, including:

{id′*=id*⁢cos⁢θ+iq*⁢sin⁢θiq′*=-id*⁢sin⁢θ+iq*⁢cos⁢θ(12)

The direct axis current at the intersection of the MTPV control current trajectory in the d′q′ coordinate system after the rotation transformation of the coordinate system and the abscissa axis (that is, the d′ coordinate axis) is the characteristic current ic, and the cross-axis current at the intersection of the MTPV control current trajectory in the d′q′ coordinate system after the rotation transformation of the coordinate system and the current limit circle in the d′q′ coordinate system is icq;as shown inFIG.7, the current limit circle and the voltage limit ellipse in the dq coordinate system of the motor can be obtained by the rotation transformation of the coordinate system to obtain the current limit circle and the voltage limit ellipse in the d′q′ coordinate system;as shown inFIG.7, the MTPA control current trajectory in the dq coordinate system of the motor and the given values of the quadrature axis current and direct axis current that meet the MTPA conditions, and the MTPV control current trajectory and the given values of the quadrature and direct axis currents that meet the MTPV conditions can be obtained by the rotation transformation of the coordinate system. The MTPA control current trajectory in the d′q′ coordinate system and the given values of the quadrature axis current and direct axis current that meet the MTPA conditions, and the MTPV control current trajectory and the given values of the quadrature axis current and direct axis current that meet the MTPV conditions;according to the difference ΔU between the limit voltage Usmaxof the inverter and the given value Usof the stator voltage, it is judged whether the flux-weakening control needs to be turned on, including:

{Us⁢max=Ud⁢c3Us=ud*2+uq⋆2(13)where Udcis the DC bus voltage, ud* is the given value of d axis voltage, and uq* is the given value of q axis voltage.
Then ΔU is:
ΔU=Us max−Us(14)

When ΔU<0, the flux-weakening control is turned on, and the direct axis current compensation id′fw* is output through the PI controller with ΔU as the input;

the amplitude of the sum id′** of the given value of the direct axis current id′* and the compensation amount of the direct axis current id′fw** and the compensation amount of the direct axis current that conform to the MTPA condition in the d′q′ coordinate system are limited to the amplitude of the characteristic current ic, so as to obtain the given value of the direct axis current id′*** in the d′q′ coordinate system.

id′***={id′**=id′*+id′⁢fw*,❘"\[LeftBracketingBar]"id′**❘"\[RightBracketingBar]"≤❘"\[LeftBracketingBar]"ic❘"\[RightBracketingBar]"ic,❘"\[LeftBracketingBar]"id′**❘"\[RightBracketingBar]">❘"\[LeftBracketingBar]"ic❘"\[RightBracketingBar]"(15)

The flux-weakening control of this embodiment is divided into the first flux-weakening region and the second flux-weakening region, when the amplitude of the sum id′** of the compensation amount of the direct axis current id′fw* and the given value of the direct axis current id′* in the d′q′ coordinate system that meets the MTPA condition is less than or equal to the amplitude of the characteristic current ic, it is the first flux-weakening region, at this time, the given value of the quadrature axis current in the d′q′ coordinate system of the flux-weakening control (the first flux-weakening region) is given by the current limit circle in the d′q′ coordinate system of the motor, that is, iq′* is limited to the current limit circle, and iq′* is obtained.

iq′**={iq′*,iq′*2+id′***2≤is⁢max2is⁢max2-id′***2,iq′*2+id′***2>is⁢max2(16)

When the amplitude of id′** is greater than the amplitude of the characteristic current ic, it is the second flux-weakening region, at this time, the amplitude of id′** exceeds the amplitude of the characteristic current ic, and the part Δid′of the amplitude of id′* exceeds the amplitude of the characteristic current ic, the compensation amount of the quadrature axis current iq′fw* obtained by the PI controller, the sum of the quadrature axis current icqat the intersection of the compensation amount of the quadrature axis current iq′fw* and the MTPV control current trajectory in the d′q′ coordinate system and the current limit circle in the d′q′ coordinate system are the given values of the quadrature axis current in the d′q′ coordinate system under flux-weakening control (the second flux-weakening region).

iq′***={iq′**,the⁢first⁢flux⁢‐⁢weaking⁢regioniq′⁢fw*+icq,the⁢second⁢flux⁢‐⁢weaking⁢region(17)

In the full speed range, the d′q′ coordinate system of the motor's d axis and quadrature axis given values of the current iq′**** and id′*** can be expressed as:

{id′*,MTPA⁢regionid′***=id′*+id′⁢fw*,first⁢flux⁢‐⁢weakening⁢regionic,second⁢flux⁢‐⁢weakening⁢regioniq′*,MTPA⁢regioniq′***=is⁢max2-id′***⁢2,first⁢flux⁢‐⁢weakening⁢regioniq′⁢fw+ic⁢q,second⁢flux⁢‐⁢weakening⁢region(18)
where iq′* is the given value of the quadrature axis current in the d′q′ coordinate system, which satisfies the MTPA condition.

Then iq′*** and id′*** can be transformed into the given values of quadrature axis current and direct axis current iq** and id** in dq coordinate system by rotation transformation of the coordinate system, namely:

{id**=id′***⁢cos⁡(-θ)+iq′***⁢sin⁡(-θ)iq**=-id′***⁢sin⁡(-θ)+iq′***⁢cos⁡(-θ)(19)

The d axis and q axis current simulation scatters of the motor in this embodiment are shown inFIG.8, andFIG.9andFIG.10show the speed and torque simulation waveforms of the given motor with a speed of 5000 rpm in this embodiment.FIG.11andFIG.12show the speed and torque simulation waveforms when the motor speed reaches the limit when the traditional method is used for flux-weakening control, In this embodiment, Udcis 60V.

As shown inFIG.11andFIG.12, the limit of the motor speed is about 1500 rpm when the traditional method (only the d axis flux-weakening current is introduced) is used for flux-weakening control. When the given speed exceeds the limit, the motor is out of control; as shown inFIG.9andFIG.10, the flux-weakening control method provided in this embodiment can make the motor reach a given speed of 5000 rpm smoothly. At the same time, as shown inFIG.8, the motor realizes the operation of MTPA, the first flux-weakening region, and the second flux-weakening region (MTPV operation), so as to maximize the torque output of the motor when the flux-weakening control system is operating. It should be noted that the given speed of the motor in this embodiment is 5000 rpm does not mean that the maximum speed range of the motor in the flux-weakening control method provided in this embodiment is 5000 rpm, in order to illustrate the specific working mode of the flux-weakening control in this embodiment, in fact, if the influence of factors such as wind friction loss of the motor is ignored, the speed range of the motor in this embodiment can reach infinity in theory, and the full speed range of the flux-weakening speed regulation of the salient pole offset permanent magnet synchronous motor can be realized.

The control method introduced in this embodiment is not only applicable to three-phase motors, but also can be extended to the flux-weakening control of the salient pole offset permanent magnet synchronous motors with any number of phases.

Embodiment 2

The second embodiment of the invention introduces a flux-weakening control system of the salient pole offset permanent magnet synchronous motor.

The flux-weakening control system of the salient pole offset permanent magnet synchronous motor, shown inFIG.13, includes:

An electromagnetic torque given module, the electromagnetic torque given module is configured to obtain the real-time speed of the salient pole offset permanent magnet synchronous motor, combined with the given speed of the motor, the given value of the electromagnetic torque of the motor is obtained;a maximum torque per ampere control module, the maximum torque per ampere control module is configured to calculate the given values of the quadrature axis current and direct axis current of the motor when the maximum torque per ampere control is operating according to the electromagnetic torque equation and the given value of the electromagnetic torque;a dq coordinate system-d′q′ coordinate system transformation module, the dq coordinate system-d′q′ coordinate system transformation module is configured to transform the given value of the current in the dq coordinate system into the given value of the current in the d′q′ coordinate system;a maximum torque per voltage control module, the maximum torque per voltage control module is configured to calculate the current trajectory of the motor when the maximum torque per voltage control is operating according to the stator voltage equation, according to the calculation result of the dq coordinate system-d′q′ coordinate system transformation module and the current trajectory when the maximum torque per voltage control is operating, the characteristic current and the quadrature axis current at the characteristic current are obtained;a direct axis current compensation module, the direct axis current compensation module is configured to determine whether the flux-weakening control needs to be turned on according to the difference between the limit voltage of the inverter and the given value of the stator voltage, and output the compensation amount of the direct axis current when it is turned on, according to the calculation result of the dq coordinate system-d′q′ coordinate system transformation module and the compensation amount of the direct axis current, the given value of the current of the salient pole offset permanent magnet synchronous motor operating in the first flux-weakening region is calculated;a quadrature axis current compensation module, the quadrature axis current compensation module is configured to determine whether it is necessary to turn on the second flux-weakening region according to the difference between the amplitude of the sum of the given value of the direct axis current and the compensation amount of the direct axis current and the amplitude of the characteristic current when the maximum torque per ampere control is operating, and output the compensation amount of the quadrature axis current when turning on, according to the calculation result of the direct axis current compensation module, the quadrature axis current at the characteristic current and the compensation amount of the quadrature axis current, the given value of the current of the salient pole offset permanent magnet synchronous motor operating in the second flux-weakening region is calculated;a d′q′ coordinate system-dq coordinate system transformation module, the d′q′ coordinate system-dq coordinate system transformation module is configured to transform the given value of the current in the d′q′ coordinate system into the given value of the current in the dq coordinate system;a space vector pulse width modulation module, the space vector pulse width modulation module is configured to generate a space vector pulse width modulation signal according to the given value of the motor current and an obtained actual value of the current, the space vector pulse width modulation module is used to drive the operation of the salient pole offset permanent magnet synchronous motor, complete the flux-weakening control of the salient pole offset permanent magnet synchronous motor, and realize the flux-weakening speed regulation of the salient pole offset permanent magnet synchronous motor in the full speed range.

The detailed steps are the same as the flux-weakening control method for the salient pole offset permanent magnet synchronous motor provided in Embodiment 1, which will not be repeated here.

The above content shows only the preferred embodiments of the embodiments, and is not used to limit this embodiment, for technicians in this field, this embodiment can have various amendments and changes. Any modification, equivalent replacement, improvement, etc., within the spirit and principles of this embodiment, shall be included in the scope of protection of the embodiments.