阅读说明：本技术 一种模糊误差反馈的永磁同步电机转速控制方法 (Fuzzy error feedback permanent magnet synchronous motor rotating speed control method ) 是由 孙卫明 王新宇 雷军委 于 2021-01-12 设计创作，主要内容包括：本发明公开一种模糊误差反馈的永磁同步电机转速控制方法。本发明通过铰链耦合对永磁电机转速进行双轴不解耦的同时控制,通过测量永磁同步电机的转速与期望值的比较得到误差信号,然后采用模糊系统的方法设置模糊概念制定模糊规则,得到模糊控制量与确定控制量同时对电机的两轴施加控制作为,因此双轴的收敛同时进行,从而收敛过程中的误差动态特性能够作为驱动电机转速提供控制力,从而比用单轴电流方式效果更佳。同时该方法的优点在于采用模糊语言与模糊控制的方式,也能更好地描述解决电机控制中的模型不确定与精确建模困难问题。(The invention discloses a method for controlling the rotating speed of a permanent magnet synchronous motor by fuzzy error feedback. According to the invention, the rotating speed of the permanent magnet motor is subjected to double-shaft non-decoupling simultaneous control through hinge coupling, an error signal is obtained through comparison between the rotating speed of the permanent magnet synchronous motor and an expected value, then a fuzzy rule is formulated by setting a fuzzy concept by adopting a fuzzy system method, and the obtained fuzzy control quantity and the determined control quantity simultaneously apply control to two shafts of the motor, so that the double shafts are converged simultaneously, and the error dynamic characteristic in the convergence process can be used as the rotating speed of the driving motor to provide control force, so that the effect is better than that of a single-shaft current mode. Meanwhile, the method has the advantages that the problems of model uncertainty and difficult accurate modeling in motor control can be better described and solved by adopting a fuzzy language and fuzzy control mode.)

1. A fuzzy error feedback permanent magnet synchronous motor rotating speed control method is characterized by comprising the following steps:

step S10, measuring the position and the rotating speed of a rotor of the permanent magnet synchronous motor and two-phase current in three-phase current, and performing Clarke coordinate transformation on the two-phase current;

step S20, setting an expected rotating speed signal according to the motor task requirement, measuring the rotating speed signal, comparing the rotating speed signal with the expected rotating speed signal to obtain a rotating speed error, integrating the rotating speed error to obtain an integral signal, and calculating a definite expected value signal of the stator current;

step S30, designing a first fuzzy system according to the rotating speed error to calculate a fuzzy expected value of the stator current, and then superposing the fuzzy expected value of the stator current and the stator current determination expected value to obtain a final stator current expected value;

step S40, comparing the expected signal of the d-axis stator current with the current signal after Park conversion to obtain a stator current error signal, and carrying out nonlinear integration on the stator current error signal to obtain a stator current error integral signal;

step S50, establishing a second fuzzy system according to the error signal and the error nonlinear integral signal of the d-axis stator current, and resolving to obtain a q-axis stator voltage signal to realize the control of the d-axis stator current;

step S60, designing an expected value of the q-axis stator current according to the rotating speed error and the rotating speed error nonlinear integral signal, comparing the expected value with the q-axis stator current obtained after Park conversion to obtain a q-axis stator current error signal, and then carrying out nonlinear conversion and integration on the q-axis stator current error signal to obtain an error nonlinear integral signal;

step S70, carrying out linear combination according to the q-axis current error signal and the error nonlinear integral signal to obtain d-axis control voltage, carrying out Park inverse transformation on the control voltage of the designed two-axis motor to obtain control voltage under a static coordinate system, and outputting the control voltage to the permanent magnet synchronous motor to realize the rotation speed control of the permanent magnet synchronous motor;

wherein, step S10 is as follows:

1.1) measuring the position and the rotating speed of a rotor of the permanent magnet synchronous motor and two-phase current in three-phase current,

wherein i_a、i_bFor measuring two-phase current signals, theta, in three-phase currents of a PMSM_mFor measuring position signals, omega, of the rotor of a permanent-magnet synchronous machine_mMeasuring a rotating speed signal of a permanent magnet synchronous motor rotor;

1.2) performing Clarke coordinate transformation on the two-phase current:

wherein i_α、i_βFor i in three-phase current_a、i_bPerforming Clarke transformation to obtain stator current in a two-phase stationary coordinate system,

i_dand i_qIs i_α、i_βPrak conversion is carried out to obtain stator currents of d and q axes of a two-phase rotating coordinate system,

θ_e＝p_nθ_m，θ_efrom measurements of rotor position theta_mIs transformed to obtain p_nThe number of pole pairs of the motor is;

wherein, step S20 is as follows:

2.1) setting the desired speed signal, i.e. ω, according to the mission requirements of the PMSM_mcThe expected rotating speed of the permanent magnet synchronous motor;

2.2) then measuring the rotational speed signal omega of the permanent magnet synchronous machine_mWith the desired speed signal omega_mcThe rotation speed error e is obtained through comparison_ωAnd integrating to obtain an integral signal s₁，

e_ω＝ω_m-ω_mc；

Wherein, ω is_mcIs the desired speed of the motor, e_ωIs a motor rotating speed error signal and is used as a motor rotating speed error signal,

s₁for the non-linear integral signal of the speed error, dt represents the integral over time, ε₁The parameter is controlled for a constant value,

2.3) then calculating the determined desired value signal i for the d-axis stator current_dc1，

i_dc1＝k_a1e_ω+k_a2s₁

i_dc1Is a determined desired value, k, of the d-axis stator current_a1And k is_a2Constant control parameters;

wherein, step S30 is as follows:

3.1) designing the first fuzzy system

3.11) error of the rotational speed e_ωFive fuzzy concepts NB set as inputs of the first fuzzy system and defining input signals of the first fuzzy system₁、NM₁、ZO₁、PM₁、PB₁As follows below, the following description will be given,

when e is_ω≤-0.6ω_mcWhen the input signal is defined as negative, set to NB₁；

When-0.6 omega_mc≤e_ω＜-0.3ω_mcWhen the input signal is defined as negative, the input signal is set to be of a medium size NM₁；

When-0.3 omega_mc≤e_ω＜0.3ω_mcWhen the input signal is defined to be almost zero, the input signal is set to ZO₁；

When 0.3 omega_mc≤e_ω＜0.6ω_mcWhen the input signal is defined to be positive, the input signal is set to be PM with a medium magnitude₁；

When 0.6 omega_mc≤e_ωWhen the input signal is defined to be positive, it is set to PB₁；

3.12) defining the output quantity of the first fuzzy system as fuzzy desired value of stator current, denoted as i_dc2And defining the output of the first fuzzy systemFive fuzzy concepts NB of the outgoing signal₂、NM₂、ZO₂、PM₂、PB₂The following were used:

when i is_dcWhen the output signal is less than or equal to-0.8, defining that the output signal is negative and large, setting the output signal as NB₂；

When-0.6 is less than or equal to i_dc2When < -0.3, the output signal is defined as negative and medium, and set as NM₂；

When-0.3 is less than or equal to i_dc2When < 0.3, the output signal is defined to be almost zero and set to ZO₂；

When i is more than or equal to 0.3_dc2When < 0.6, the output signal is defined to be positive and medium, and PM is set₂；

When i is more than or equal to 0.6_dc2When the output signal is defined to be positive, it is set to PB₂；

3.13) then define the fuzzy rule as follows:

when inputting signal e_ωIs NB₁Time, output signal i_dc2Is NB₂；

When inputting signal e_ωIs NM₁Time, output signal i_dc2Is NM₂；

When inputting signal e_ωIs ZO₁Time, output signal i_dc2Is ZO₂；

When inputting signal e_ωIs PM₁Time, output signal i_dc2Is PM₂；

When inputting signal e_ωIs PB₁Time, output signal i_dc2Is PB₂；

3.14) establishing a fuzzy rule base according to the fuzzy rule of 3.13), and outputting the input signal according to the fuzzy rule of 3.13), namely obtaining a fuzzy expected value i of the stator current_dc2；

3.2) the determined desired value of the d-axis stator current is superimposed on the fuzzy desired value of the stator current, the desired value of the d-axis stator current is obtained and is denoted as i_dcThe calculation method is as follows:

i_dc＝i_dc1+i_dc2；

wherein, step S40 is as follows:

4.1) desired Signal i of d-axis stator Current_dcCurrent signal i converted with Park_dComparing to obtain stator current error signal e_id，

e_id＝i_d-i_dc；

Wherein e is_idIs a d-axis current error signal that is,

4.2) carrying out nonlinear integration on the d-axis current error signal to obtain a stator current error integral signal s_eid，

e_id＝i_d-i_dc；

Wherein s is_eidFor d-axis current error non-linear integral signal, dt represents the integral over time signal, ε₂Constant control parameters;

wherein, step S50 is as follows:

according to the error signal e of the d-axis stator current_idAnd error non-linear integral signal s_eidEstablishing a second fuzzy system and a fuzzy rule, and resolving to obtain a stator voltage signal of a q axis, wherein the steps are as follows:

5.1) setting e_idFive fuzzy concepts NB being inputs of the first input signal of the second fuzzy system and defining the first input signal of the second fuzzy system₃、NM₃、ZO₃、PM₃、PB₃The following were used:

when e is_idWhen the value is less than or equal to-4/3, the input signal is defined as negative and is set as NB₃；

When-2/3 is not more than e_idWhen < -4/3, the input signal is defined as negative and medium, and set as NM₃；

When-2/3 is not more than e_id< 2/3, the input signal is defined to be almost zero and set to ZO₃；

When 2/3 is less than or equal to e_idIf < 4/3, the input signal is defined to be positive and medium, and set to PM₃；

When e is_idAt least 4/3, the input signal is defined as positive and set to PB₃；

5.2) setting s_eidFive fuzzy concepts NB being second inputs of the second fuzzy system and defining second input signals of the second fuzzy system₄、NM₄、ZO₄、PM₄、PB₄The following were used:

when s is_eidWhen the input signal is less than or equal to-4, defining that the input signal is negative, setting the input signal as NB₄；

When-2 is less than or equal to s_eidWhen < -4 >, the input signal is defined as negative and medium, and set as NM₄；

When-2 is less than or equal to s_eidWhen < 2, the input signal is defined to be almost zero and set to ZO₄；

When s is more than or equal to 2_eidIf < 4, the input signal is defined to be positive and medium, and set to PM₄；

When s is_eidWhen the input signal is greater than or equal to 4, defining the input signal as positive and setting the input signal as PB₄；

5.3) setting u_qFive fuzzy concepts NB for the output of the second fuzzy system and defining the output signal of the second fuzzy system₅、NM₅、ZO₅、PM₅、PB₅The following were used:

when u is_qWhen the output signal is less than or equal to-20, defining that the output signal is negative, setting the output signal as NB₅；

When u is more than or equal to-20_q-10, defining the output signal as negative medium, and setting NM₅；

When u is more than or equal to-10_qWhen < 10, defining the output signal to be almost zero, and setting to ZO₅；

When u is more than or equal to 10_qWhen < 20, the output signal is defined as positive and medium, and PM is set₅；

When u is more than or equal to 20_qWhen the output signal is defined to be positive, it is set to PB₅；

5.4) establishing the following 13 fuzzy rules:

when inputting informationNumber e_idIs NB₃Time, output signal u_qIs NB₅；

When inputting signal e_idIs NM₃Time, output signal u_qIs NM₅；

When inputting signal e_idIs ZO₃Time, output signal u_qIs ZO₅；

When inputting signal e_idIs PM₃Time, output signal u_qIs PM₅；

When inputting signal e_idIs PB₃Time, output signal u_qIs PB₅；

When inputting signal e_idIs NB₃And input a signal s_eidIs NB₄Time, output signal u_qIs NB₅；

When inputting signal e_idIs NB₃And input a signal s_eidIs PB₄Time, output signal u_qIs NB₅；

When inputting signal e_idIs PB₃And input a signal s_eidIs NB₄Time, output signal u_qIs PB₅；

When inputting signal e_idIs PB₃And input a signal s_eidIs PB₄Time, output signal u_qIs PB₅；

When inputting signal e_idIs ZO₃And input a signal s_eidIs NB₄Time, output signal u_qIs ZO₅；

When inputting signal e_idIs ZO₃And input a signal s_eidIs PB₄Time, output signal u_qIs ZO₅；

When inputting signal e_idIs ZO₃And input a signal s_eidIs NB₄Time, output signal u_qIs ZO₅；

When inputting signal e_idIs ZO₃And input a signal s_eidIs PB₄Time, output signal u_qIs ZO₅；

5.5) establishing a fuzzy rule base according to the fuzzy rule of 5.4), and outputting the input signal according to the fuzzy rule of 5.4), namely obtaining the controlled quantity u of the stator current_q。

Wherein, step S60 is as follows:

6.1) design expected value of q-axis stator current as i_qc，

i_qc＝k_a3e_ω+k_a4s₁，

Wherein i_qcFor desired value of q-axis stator current, k_a3、k_a4Constant control parameters;

6.2) desired value of q-axis stator Current i_qcComparing the q-axis stator current obtained after Park conversion to obtain a q-axis stator current error signal, and then performing nonlinear conversion and integration on the error signal to obtain an error nonlinear integral signal, wherein the error nonlinear integral signal comprises:

e_iq＝i_q-i_qc；

s₂＝∫e_iqdt/(|∫e_iqdt|+ε₃)；

wherein e is_iqIs a q-axis current error signal, s₂For the current error non-linearly integrating signal, epsilon₃Constant control parameters;

wherein, step S70 is as follows:

7.1) designing d-axis control voltage u according to the linear combination of the q-axis current error signal and the error nonlinear integral signal_d，

u_d＝k_a5e_iq+k_a6s₂；

Wherein u is_dFor d-axis control of voltage, k_a5、k_a6Constant control parameters;

7.2) control Voltage u for two-shaft Motor_d、u_qCarrying out Park inverse transformation, and calculating to obtain the control voltage u under the static coordinate system_α、u_β，

Wherein u is_α、u_βThe stator voltages of the alpha axis and the beta axis in the two-phase static coordinate system,

7.3) mixing u_α、u_βThe output is transmitted to space vector pulse width modulation and a three-phase inverter and finally transmitted to a permanent magnet synchronous motor, so that the rotating speed of the permanent magnet synchronous motor is enabled to be in accordance with an expected rotating speed signal omega_mcAnd (6) outputting.

Technical Field

The invention relates to the field of permanent magnet synchronous motors, in particular to a method for realizing stable control of the rotating speed of a permanent magnet synchronous motor by adopting a fuzzy language and fuzzy method and double-axis error simultaneous feedback.

Background

The motor is used as an important tool for converting electric energy and mechanical energy, and is widely applied to various fields of national economy. Dc motors dominate transmission applications in the early stages. At present, most of high-performance servo systems adopt permanent magnet synchronous alternating current servo motors, and the permanent magnet synchronous motor alternating current servo systems are mature in technology and have excellent performance. The permanent magnet synchronous servo motor adopts the permanent magnet to generate a magnetic field required by electromechanical energy conversion, and has the advantages of simple structure, reliable operation, light weight, small volume, energy conservation, high efficiency and the like. However, one problem faced in the control of the permanent magnet synchronous motor at present is that accurate modeling of the motor is not easy, accurate measurement of partial states is not easy, and the load of the motor is difficult to accurately predict, thereby causing the problem of uncertainty of the system and further improving the control performance.

It is to be noted that the information invented in the above background section is only for enhancing the understanding of the background of the present invention, and therefore, may include information that does not constitute prior art known to those of ordinary skill in the art.

Disclosure of Invention

In order to solve the technical problem caused by uncertainty in the control process of the permanent magnet synchronous motor in the prior art, the invention aims to provide a method for controlling the rotating speed of the permanent magnet synchronous motor by fuzzy error feedback, and further solve the problem that the effect is poor due to the fact that the fuzzy uncertainty of a permanent magnet motor system cannot be processed by a determined method in the prior art.

In order to realize the purpose, the technical scheme is as follows:

a fuzzy error feedback permanent magnet synchronous motor rotating speed control method comprises the following steps:

step S10, measuring the position and the rotating speed of a rotor of the permanent magnet synchronous motor and two-phase current in three-phase current, and performing Clarke coordinate transformation on the two-phase current;

step S20, setting an expected rotating speed signal according to the requirement of the motor task, measuring the rotating speed signal, comparing the rotating speed signal with the expected rotating speed signal to obtain a rotating speed error, integrating the rotating speed error to obtain an integral signal, and calculating a definite expected value signal of the stator current;

step S30, designing a first fuzzy system according to the rotating speed error to calculate a fuzzy expected value of the stator current, and combining the fuzzy expected value with the stator current determined expected value to obtain a final stator current expected value;

step S40, comparing the expected signal of the d-axis stator current with the current signal after Park conversion to obtain a stator current error signal, and performing nonlinear integration to obtain a stator current error integral signal;

step S50, establishing a second fuzzy system according to the error signal and the error nonlinear integral signal of the d-axis stator current, and resolving to obtain a q-axis stator voltage signal to realize the control of the d-axis stator current;

step S60, designing the expected value of the q-axis stator current as i according to the rotation speed error and the rotation speed error nonlinear integral signal_qcComparing the q-axis stator current with q-axis stator current obtained after Park conversion to obtain a q-axis stator current error signal, and then carrying out nonlinear conversion and integration on the q-axis stator current error signal to obtain an error nonlinear integral signal;

step S70, the q-axis current error signal and the error nonlinear integral signal are linearly combined to obtain d-axis control voltage, the obtained control voltage of the two-axis motor is subjected to Park inverse transformation calculation to obtain control voltage under a static coordinate system, and the control voltage is output to the permanent magnet synchronous motor to enable the rotating speed of the permanent magnet synchronous motor to be in accordance with the expected rotating speed signal omega_mcAnd outputting to realize the rotation speed control of the synchronous motor.

In an exemplary embodiment of the present invention, step S10, measuring the position and the rotation speed of the rotor of the permanent magnet synchronous motor and the two-phase current of the three-phase current, and performing Clarke coordinate transformation on the two-phase current includes the following steps:

wherein i_a、i_bThe signal is a two-phase current signal in the three-phase current of the permanent magnet synchronous motor detected by a Hall current sensor.

i_α、i_βFor i in three-phase current_a、i_bObtaining stator current i in a two-phase static coordinate system after Clarke transformation_dAnd i_qIs i_α、i_βCarrying out Prak transformationAnd obtaining stator currents of d and q axes of the two-phase rotating coordinate system after conversion.

θ_eFrom measurements of rotor position theta_mIs converted to obtain_e＝p_nθ_mWherein p is_nThe number of pole pairs of the motor is shown.

θ_mMeasuring a position signal of a rotor of the permanent magnet synchronous motor for a position detection sensing unit;

ω_mand measuring a rotating speed signal of the rotor of the permanent magnet synchronous motor for the speed detection sensing unit.

In an exemplary embodiment of the present invention, step S20, setting a desired rotation speed signal, comparing the measured rotation speed signal with the desired rotation speed signal to obtain a rotation speed error, and integrating the rotation speed error to obtain an integral signal, so as to obtain a determined desired value signal of the stator current, includes the following steps:

e_ω＝ω_m-ω_mc；

i_dc1＝k_a1e_ω+k_a2s₁；

wherein, ω is_mcIs the desired speed of rotation, ω, of the motor_mAs a measure of the rotational speed of the motor, e_ωIs the motor rotating speed error signal.

s₁For the non-linear integral signal of the speed error, dt represents the integral over time, ε₁The parameter is controlled for a constant value,

i_dc1is a determined desired value, k, of the d-axis stator current_a1And k is_a2The parameter is controlled to be constant.

In an exemplary embodiment of the present invention, step S30, designing a first fuzzy system according to the rotation speed error and calculating a fuzzy desired value of the stator current, and then combining the fuzzy desired value of the stator current with the determined desired value of the stator current to obtain a final desired value of the stator current, includes the following steps:

error of rotation speed e_ωFive fuzzy concepts NB set as inputs of the first fuzzy system and defining input signals of the first fuzzy system₁、NM₁、ZO₁、PM₁、PB₁As follows below, the following description will be given,

when e is_ω≤-0.6ω_mcWhen the input signal is defined as negative, set to NB₁；

When-0.6 omega_mc≤e_ω＜-0.3ω_mcWhen the input signal is defined as negative, the input signal is set to be of a medium size NM₁；

When-0.3 omega_mc≤e_ω＜0.3ω_mcWhen the input signal is defined to be almost zero, the input signal is set to ZO₁；

When 0.3 omega_mc≤e_ω＜0.6ω_mcWhen the input signal is defined to be positive, the input signal is set to be PM with a medium magnitude₁；

When 0.6 omega_mc≤e_ωWhen the input signal is defined to be positive, it is set to PB₁；

Defining the output quantity of the first fuzzy system as the fuzzy desired value of the stator current is denoted as i_dc2And defining five fuzzy concepts NB of the output signal of the first fuzzy system₂、NM₂、ZO₂、PM₂、PB₂The following were used:

when i is_dcWhen the output signal is less than or equal to-0.8, defining that the output signal is negative and large, setting the output signal as NB₂；

When-0.6 is less than or equal to i_dc2When < -0.3, the output signal is defined as negative and medium, and set as NM₂；

When-0.3 is less than or equal to i_dc2When < 0.3, the output signal is defined to be almost zero and set to ZO₂；

When i is more than or equal to 0.3_dc2When < 0.6, the output signal is defined to be positive and medium, and PM is set₂；

When i is more than or equal to 0.6_dc2When the output signal is defined to be positive, it is set to PB₂；

The fuzzy rule is then defined as follows:

when the input signal is negative and large, the output signal is also negative and large;

when the input signal is of negative medium magnitude, the output signal is also of negative medium magnitude;

when the input signal is almost zero, the output signal is also almost zero;

when the input signal is positive medium, the output signal is also positive medium;

when the input signal is positive and large, the output signal is also positive and large.

And then, establishing a fuzzy rule base according to the fuzzy rule, and performing fuzzy operation and defuzzification according to the magnitude of the input signal to obtain a fuzzy expected value of the stator current.

Finally, the expected value of the d-axis stator current obtained by superposing the determined expected value of the d-axis stator current and the fuzzy expected value of the stator current is recorded as i_dcThe calculation method is as follows:

i_dc＝i_dc1+i_dc2。

in an exemplary embodiment of the present invention, in step S40, comparing the expected signal of the d-axis stator current with the Park converted current signal to obtain a stator current error signal, and performing a non-linear integration to obtain a stator current error integrated signal, includes the following steps:

e_id＝i_d-i_dc；

wherein i_dcIs a desired value of d-axis stator current, i_dIs a d-axis current signal obtained after Park conversion, e_idIs a d-axis current error signal, s_eidFor d-axis current error non-linear integral signal, dt represents the integral over time signal, ε₂The parameter is controlled to be constant.

In an exemplary embodiment of the present invention, in step S50, a second fuzzy system and a fuzzy rule are established according to the error signal and the error non-linear integral signal of the d-axis stator current, and the stator voltage signal of the q-axis is obtained through calculation, including the following steps:

first, set e_idFive fuzzy concepts NB being inputs of the first input signal of the second fuzzy system and defining the first input signal of the second fuzzy system₃、NM₃、ZO₃、PM₃、PB₃The following were used:

when e is_idWhen the value is less than or equal to-4/3, the input signal is defined as negative and is set as NB₃；

When-2/3 is not more than e_idWhen < -4/3, the input signal is defined as negative and medium, and set as NM₃；

When-2/3 is not more than e_id< 2/3, the input signal is defined to be almost zero and set to ZO₃；

When 2/3 is less than or equal to e_idIf < 4/3, the input signal is defined to be positive and medium, and set to PM₃；

When e is_idAt least 4/3, the input signal is defined as positive and set to PB₃；

Next, set s_eidFive fuzzy concepts NB being second inputs of the second fuzzy system and defining second input signals of the second fuzzy system₄、NM₄、ZO₄、PM₄、PB₄The following were used:

when s is_eidWhen the input signal is less than or equal to-4, defining that the input signal is negative, setting the input signal as NB₄；

When-2 is less than or equal to s_eidWhen < -4 >, the input signal is defined as negative and medium, and set as NM₄；

When-2 is less than or equal to s_eidWhen < 2, the input signal is defined to be almost zero and set to ZO₄；

When s is more than or equal to 2_eidIf < 4, the input signal is defined to be positive and medium, and set to PM₄；

When s is_eidWhen the input signal is greater than or equal to 4, defining the input signal as positive and setting the input signal as PB₄；

Then, u is set_qAs output of the second fuzzy systemAnd defining five fuzzy concepts NB for the output signal of the second fuzzy system₅、NM₅、ZO₅、PM₅、PB₅The following were used:

when u is_qWhen the output signal is less than or equal to-20, defining that the output signal is negative, setting the output signal as NB₅；

When u is more than or equal to-20_q-10, defining the output signal as negative medium, and setting NM₅；

When u is more than or equal to-10_qWhen < 10, defining the output signal to be almost zero, and setting to ZO₅；

When u is more than or equal to 10_qWhen < 20, the output signal is defined as positive and medium, and PM is set₅；

When u is more than or equal to 20_qWhen the output signal is defined to be positive, it is set to PB₅；

On the basis of the above, the following 13 fuzzy rules are established:

when inputting signal e_idWhen it is negative and large, the output signal u_qIs also very negative;

when inputting signal e_idAt a negative medium magnitude, the output signal u_qMedium size, also negative;

when inputting signal e_idWhen almost zero, output signal u_qIs also almost zero;

when inputting signal e_idAt positive medium magnitude, the output signal u_qMedium size, also positive;

when inputting signal e_idWhen it is positive, the output signal u is large_qAlso positive and very large.

When inputting signal e_idIs very negative and the input signal s_eidWhen it is negative and large, the output signal u_qIs also very negative;

when inputting signal e_idIs very negative and the input signal s_eidWhen it is positive, the output signal u is large_qIs also very negative;

when inputting signal e_idIs positive and large and the input signal s_eidIs very negativeTime, output signal u_qIs also positive and very large;

when inputting signal e_idIs positive and large and the input signal s_eidWhen it is positive, the output signal u is large_qIs also positive and very large;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is negative and large, the output signal u_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is positive, the output signal u is large_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is negative and large, the output signal u_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is positive, the output signal u is large_qAnd is also almost zero.

And finally, establishing a fuzzy rule base according to the fuzzy rule, and performing fuzzy operation and defuzzification by adopting a computer according to the magnitude of the input signal to obtain a controlled quantity u of the stator current_q。

In an exemplary embodiment of the present invention, step S60, the desired value of the q-axis stator current is designed to be i_qcAnd comparing the q-axis stator current with q-axis stator current obtained after Park conversion to obtain a q-axis stator current error signal, and then performing nonlinear conversion and integration on the error signal to obtain an error nonlinear integral signal, wherein the method comprises the following steps:

i_qc＝k_a3e_ω+k_a4s₁；

e_iq＝i_q-i_qc；

s₂＝∫e_iqdt/(|∫e_iqdt|+ε₃)；

wherein e_ωAs a rotational speed error signal, s₁For the non-linear integral signal of the speed error, i_qcIs the desired value of the q-axis stator current, where k_a3And k is_a4The parameter is controlled to be constant.

e_iqFor q-axis current error signal, i_qFor the Park-transformed q-axis current signal, s₂For the current error non-linearly integrating signal, epsilon₃The parameter is controlled to be constant.

In an exemplary embodiment of the present invention, in step S70, the q-axis current error signal and the error non-linear integral signal are linearly combined to obtain a d-axis control voltage, and the Park inverse transformation calculation is performed on the control voltage of the two-axis motor to obtain a control voltage under a stationary coordinate system, including the following steps:

u_d＝k_a5e_iq+k_a6s₂；

wherein e_iqIs a q-axis current error signal, s₂For non-linearly integrating the signal u_dFor d-axis control of voltage, k_a5And k_a6The parameter is controlled to be constant.

u_α、u_βIs the stator voltage of alpha and beta axes in a two-phase stationary coordinate system_eIs a measure of rotor position θ_mAnd (5) carrying out transformation to obtain the product.

Finally, u is added_α、u_βThe output is sent to a space vector pulse width modulation and three-phase inverter and finally sent to a permanent magnet synchronous motor, and the rotating speed of the motor is controlled to reach a given speed omega_mc。

The space vector pulse width modulation and the three-phase inverter are well-known technologies in the art and are not protected by the present invention, and therefore, they will not be described in detail herein.

In the traditional method, one-axis current of a permanent magnet motor is always completely stabilized, the other-axis current is used for implementing the control action of the rotating speed, the coupling between two axes is eliminated, and then the rotating speed tracking of the synchronous motor is realized through decoupled single-axis control. Compared with the traditional method, the key point of the method is that the rotating speed of the permanent magnet motor is controlled in a double-shaft non-decoupling mode through hinge coupling, specifically, an error signal is obtained through comparison between the rotating speed of the permanent magnet synchronous motor and an expected value, then a fuzzy rule is formulated by adopting a fuzzy system method to set a fuzzy concept, a fuzzy control quantity is obtained and a control quantity is determined, and the two shafts of the motor are controlled at the same time, so that the double shafts are converged at the same time, the error dynamic characteristic in the convergence process can be used as the rotating speed of the driving motor to provide control force, and the effect is better compared with the traditional method using single-shaft current. Meanwhile, the invention has the advantages that the problems of model uncertainty and difficult accurate modeling in motor control can be better described and solved by adopting a fuzzy language and fuzzy control mode.

Advantageous effects

The invention discloses a fuzzy error feedback permanent magnet synchronous motor rotating speed control method which has the following main advantages.

The invention adopts fuzzy language, fuzzy concept and fuzzy system to form fuzzy output method, to describe the uncertainty of permanent magnet synchronous motor system, and to describe and implement the fuzzy physical mechanism that the permanent magnet synchronous motor system should follow, so it has better completeness than using definite control rule to control the fuzzy uncertain object logically, and it can obtain richer dynamic character and better control effect.

The second method is that the double-shaft error of double-shaft decoupling is simultaneously fed back to drive the generated control quantity to eliminate the rotating speed error, compared with the method for driving the other shaft error to eliminate the rotating speed error while stabilizing one shaft adopted in the prior art, the method can fully utilize the coupling energy between the double shafts, thereby having more direct and better control effect than the existing decoupling control method.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.

FIG. 1 is a flow chart of a method for controlling the rotating speed of a permanent magnet synchronous motor with fuzzy error feedback provided by the invention.

FIG. 2 is a plot of measured motor speed for a method provided by an embodiment of the present invention;

FIG. 3 is a plot of a motor speed error signal according to a method provided by an embodiment of the present invention;

FIG. 4 is a graph of expected value signals for d-axis stator current in accordance with a method provided by an embodiment of the present invention;

FIG. 5 is a d-axis stator current error signal plot for a method provided by an embodiment of the present invention;

FIG. 6 is a graph of a control voltage signal for the q-axis of a method provided by an embodiment of the invention;

FIG. 7 is a plot of expected value signals for q-axis stator current in accordance with a method provided by an embodiment of the present invention;

FIG. 8 is a q-axis stator current error signal plot for a method provided by an embodiment of the present invention;

FIG. 9 is a graph of a d-axis control voltage signal according to a method provided by an embodiment of the invention.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, devices, steps, and so forth. In other instances, well-known technical solutions have not been shown or described in detail to avoid obscuring aspects of the invention.

The invention provides a method for forming an error signal by measuring the rotation speed of a permanent magnet synchronous motor and comparing the rotation speed with an expected rotation speed, then forming a fuzzy control quantity by simultaneously acting two shafts of the permanent magnet synchronous motor through the error signal and taking the integral of the error and the error as the input of a fuzzy system, establishing the fuzzy system, and forming the fuzzy control quantity by modeling rich fuzzy rules, thereby realizing the purpose of eliminating the rotation speed error of the motor and realizing the accurate and rapid control of the rotation speed of the motor.

The method for controlling the rotating speed of the permanent magnet synchronous motor with fuzzy error feedback according to the present invention will be further explained and explained with reference to the accompanying drawings.

A fuzzy error feedback permanent magnet synchronous motor rotating speed control method comprises the following steps:

step S10, measuring the position and the rotating speed of the rotor of the permanent magnet synchronous motor and the two-phase current in the three-phase current, and carrying out coordinate transformation on the two-phase current;

specifically, firstly, the position and rotation speed signals of the rotor of the permanent magnet synchronous motor are measured through a position/speed detection sensing unit, wherein the position of the rotor is recorded as theta_mThe rotational speed is recorded as ω_m；

Secondly, three-phase current signals of the permanent magnet synchronous motor are detected through a Hall current sensor and are respectively recorded as i_a、i_b、i_c。

Then, for i in three-phase current_a、i_bPerforming Clarke transformation to obtain stator current i in a two-phase static coordinate system_α、i_β. Wherein the Clarke transformation is as follows:

again, the following Prak transform is performedObtaining stator current i of d and q axes of a two-phase rotating coordinate system_qAnd i_d. Wherein Park is transformed as follows:

wherein theta is_eFrom measurements of rotor position theta_mIs converted to obtain_e＝p_nθ_mWherein p is_nThe number of pole pairs of the motor is shown.

And step S20, setting an expected rotating speed signal according to the requirement of the motor task, measuring the rotating speed signal, comparing the rotating speed signal with the expected rotating speed signal to obtain a rotating speed error, and integrating to obtain an integral signal to obtain a fixed expected value signal of the stator current.

Specifically, first, a desired rotation speed of the motor is set to ω according to the duty of the motor_mcThen with the measured value ω of the motor speed_mComparing to obtain a motor rotation speed error signal, and recording as e_ωThe calculation method is as follows: e.g. of the type_ω＝ω_m-ω_mc。

Secondly, according to the rotating speed error signal e of the motor_ωThe following non-linear integral signal of the rotation speed error is constructed and is marked as s₁The calculation method is as follows:

where dt represents the integral of the time signal, ε₁The parameter is controlled to be constant.

Finally, according to the error signal and the non-linear integral signal, linear combination is carried out, a definite expected value of the d-axis stator current is obtained through calculation and is recorded as i_dc1The calculation method is as follows:

i_dc1＝k_a1e_ω+k_a2s₁；

wherein k is_a1And k is_a2The parameter is controlled to be constant.

And step S30, designing a first fuzzy system according to the rotation speed error, calculating a fuzzy expected value of the stator current, and combining the fuzzy expected value with the stator current determined expected value to obtain a final stator current expected value.

Specifically, the error e of the rotation speed is first determined_ωFive fuzzy concepts NB set as inputs of the first fuzzy system and defining input signals of the first fuzzy system₁、NM₁、ZO₁、PM₁、PB₁The following were used:

wherein NB₁Large, NM, indicating the input signal is negative₁Medium-sized, ZO, indicating that the input signal is negative₁Indicating that the input signal is almost zero, PM₁Medium size, PB, indicating positive input signal₁Indicating that the input signal is positive and large.

Specifically, the following judgment method is established in the design:

when e is_ω≤-0.6ω_mcWhen the input signal is defined as negative, set to NB₁；

When-0.6 omega_mc≤e_ω＜-0.3ω_mcWhen the input signal is defined as negative, the input signal is set to be of a medium size NM₁；

When-0.3 omega_mc≤e_ω＜0.3ω_mcWhen the input signal is defined to be almost zero, the input signal is set to ZO₁；

When 0.3 omega_mc≤e_ω＜0.6ω_mcWhen the input signal is defined to be positive, the input signal is set to be PM with a medium magnitude₁；

When 0.6 omega_mc≤e_ωWhen the input signal is defined to be positive, it is set to PB₁；

Then, the output quantity of the first fuzzy system is defined as the fuzzy expected value of the stator current, which is recorded as i_dc2And defines five fuzzy concepts NB of the output signal of the fuzzy system₂、NM₂、ZO₂、PM₂、PB₂The following were used:

wherein NB₂Large, NM indicating the output signal is negative₂Medium size, ZO, indicating that the output signal is negative₂Indicating that the output signal is almost zero, PM₂Medium size, PB, indicating that the output signal is positive₂Indicating that the output signal is positive and large.

Specifically, the following judgment method is established in the design:

when i is_dcWhen the output signal is less than or equal to-0.8, defining that the output signal is negative and large, setting the output signal as NB₂；

When-0.6 is less than or equal to i_dc2When < -0.3, the output signal is defined as negative and medium, and set as NM₂；

When-0.3 is less than or equal to i_dc2When < 0.3, the output signal is defined to be almost zero and set to ZO₂；

When i is more than or equal to 0.3_dc2When < 0.6, the output signal is defined to be positive and medium, and PM is set₂；

When i is more than or equal to 0.6_dc2When the output signal is defined to be positive, it is set to PB₂；

On this basis, the fuzzy rule is defined as follows:

when the input signal is negative and large, the output signal is also negative and large;

when the input signal is of negative medium magnitude, the output signal is also of negative medium magnitude;

when the input signal is almost zero, the output signal is also almost zero;

when the input signal is positive medium, the output signal is also positive medium;

when the input signal is positive and large, the output signal is also positive and large.

Then, a fuzzy rule base is established according to the fuzzy rule, and a computer is adopted to perform fuzzy operation and defuzzification according to the magnitude of the input signal, so that the fuzzy expected value of the stator current can be obtained.

Finally, the expected value of the d-axis stator current is obtained by superposing the determined expected value of the d-axis stator current and the obtained fuzzy expected value of the stator current and is recorded as i_dcThe calculation method is as follows:

i_dc＝i_dc1+i_dc2；

and step S40, comparing the expected signal of the d-axis stator current with the current signal after Park conversion to obtain a stator current error signal, and performing nonlinear integration to obtain a stator current error integral signal.

Specifically, first, a desired value of the d-axis stator current is set to i_dcAnd i obtained after conversion with Park_dThe values are compared to obtain a d-axis current error signal, which is recorded as e_idThe calculation method is as follows:

e_id＝i_d-i_dc；

next, based on the d-axis current error signal e_idDesigning d-axis current error nonlinear integral signal s_eidIt is calculated as follows:

where dt represents the integral of the time signal, ε₂The parameter is controlled to be constant.

And step S50, establishing a second fuzzy system and a fuzzy rule according to the error signal and the error nonlinear integral signal of the d-axis stator current, resolving to obtain a q-axis stator voltage signal, and realizing the control of the d-axis stator current.

Specifically, a two-input one-output second fuzzy system is established.

And taking the stator current error signal and the error nonlinear integral signal as input signals of a second fuzzy system, and taking output signals of the second fuzzy system as resolved stator voltage signals.

First, set e_idFive fuzzy concepts NB being inputs of the first input signal of the second fuzzy system and defining the first input signal of the second fuzzy system₃、NM₃、ZO₃、PM₃、PB₃The following were used:

wherein NB₃Large, NM, indicating the input signal is negative₃Medium-sized, ZO, indicating that the input signal is negative₃Indicating that the input signal is almost zero, PM₃Medium size, PB, indicating positive input signal₃Indicating that the input signal is positive and large.

Specifically, the following judgment method is established in the design:

when e is_idWhen the value is less than or equal to-4/3, the input signal is defined as negative and is set as NB₃；

When-2/3 is not more than e_idWhen < -4/3, the input signal is defined as negative and medium, and set as NM₃；

When-2/3 is not more than e_id< 2/3, the input signal is defined to be almost zero and set to ZO₃；

When 2/3 is less than or equal to e_idIf < 4/3, the input signal is defined to be positive and medium, and set to PM₃；

When e is_idAt least 4/3, the input signal is defined as positive and set to PB₃；

Next, set s_eidFive fuzzy concepts NB being second inputs of the second fuzzy system and defining second input signals of the second fuzzy system₄、NM₄、ZO₄、PM₄、PB₄。

Specifically, the following judgment method is established in the design:

when s is_eidWhen the input signal is less than or equal to-4, defining that the input signal is negative, setting the input signal as NB₄；

When-2 is less than or equal to s_eidWhen < -4 >, the input signal is defined as negative and medium, and set as NM₄；

When-2 is less than or equal to s_eidWhen < 2, the input signal is defined to be almost zero and set to ZO₄；

When s is more than or equal to 2_eidIf < 4, the input signal is defined to be positive and medium, and set to PM₄；

When s is_eidWhen the input signal is greater than or equal to 4, defining the input signal as positive and setting the input signal as PB₄；

Then, u is set_qFive fuzzy concepts NB for the output of the second fuzzy system and defining the output signal of the second fuzzy system₅、NM₅、ZO₅、PM₅、PB₅。

Specifically, the following judgment method is established in the design:

when u is_qWhen the output signal is less than or equal to-20, defining that the output signal is negative, setting the output signal as NB₅；

When u is more than or equal to-20_q-10, defining the output signal as negative medium, and setting NM₅；

When u is more than or equal to-10_qWhen < 10, defining the output signal to be almost zero, and setting to ZO₅；

When u is more than or equal to 10_qWhen < 20, the output signal is defined as positive and medium, and PM is set₅；

When u is more than or equal to 20_qWhen the output signal is defined to be positive, it is set to PB₅；

On the basis, according to the fact that the larger the error of the stator current error signal is, the larger the nonlinear integral of the stator current error signal is, the larger the control quantity is; the smaller the error of the stator current error signal is, the smaller the nonlinear integral of the stator current error signal is, and the smaller the control quantity is; the idea that the control quantity is smaller when the error of the stator current error signal is smaller and the nonlinear integral of the stator current error signal is larger is established as follows 13 fuzzy rules:

when inputting signal e_idWhen it is negative and large, the output signal u_qIs also very negative;

when inputting signal e_idAt a negative medium magnitude, the output signal u_qMedium size, also negative;

when inputting signal e_idWhen almost zero, output signal u_qIs also almost zero;

when inputting signal e_idAt positive medium magnitude, the output signal u_qMedium size, also positive;

when inputting signal e_idWhen it is positive, the output signal u is large_qAlso positive and very large.

When inputting signal e_idIs very negative and the input signal s_eidWhen it is negative and large, the output signal u_qIs also very negative;

when inputting signal e_idIs very negative and the input signal s_eidWhen it is positive, the output signal u is large_qIs also very negative;

when inputting signal e_idIs positive and large and the input signal s_eidWhen it is negative and large, the output signal u_qIs also positive and very large;

when inputting signal e_idIs positive and large and the input signal s_eidWhen it is positive, the output signal u is large_qIs also positive and very large;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is negative and large, the output signal u_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is positive, the output signal u is large_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is negative and large, the output signal u_qIs also almost zero;

when inputting signal e_idAlmost zero and input signal s_eidWhen it is positive, the output signal u is large_qIs also almost zero;

finally, a fuzzy rule base is established according to the fuzzy rules, particularly, the weight of the last 8 rules is increased, and fuzzy operation and defuzzification are carried out by adopting a computer according to the magnitude of the input signal, so that the control quantity u of the stator current can be obtained_q。

Step S60, the expected value of the q-axis stator current is designed to be i according to the rotation speed error and the rotation speed error nonlinear integral signal_qcAnd comparing the q-axis stator current with q-axis stator current obtained after Park conversion to obtain a q-axis stator current error signal, and then carrying out nonlinear conversion and integration on the error signal to obtain an error nonlinear integral signal.

Specifically, first, the rotation speed error signal e_ωSignal s integrated non-linearly with the speed error₁Linear combination is carried out to obtain the expected value of the stator current of the q axis, which is recorded as i_qcThe design is as follows:

i_qc＝k_a3e_ω+k_a4s₁；

wherein k is_a3And k is_a4The parameter is controlled to be constant.

Secondly, according to i obtained after Park transformation_qThe value of the q-axis stator current and the expected value i of the q-axis stator current_qcComparing to obtain q-axis current error signal, and recording as e_iq，

e_iq＝i_q-i_qc。

Finally, for q-axis current error signal e_iqPerforming nonlinear integration to obtain a q-axis current error nonlinear integration signal, which is recorded as s₂It is calculated as follows:

s₂＝∫e_iqdt/(|∫e_iqdt|+ε₃)；

wherein epsilon₃The parameter is controlled to be constant.

And step S70, the q-axis current error signal and the error nonlinear integral signal are linearly combined to obtain d-axis control voltage, the Park inverse transformation is carried out on the control voltage of the two-axis motor to obtain control voltage under a static coordinate system, and the control voltage is output to the synchronous motor to realize the rotation speed control of the synchronous motor.

Specifically, the q-axis current error signal e is first generated_iqAnd a non-linear integral signal s₂Form d-axis control voltage, denoted as u_dThe calculation method is as follows:

u_d＝k_a5e_iq+k_a6s₂；

wherein k is_a5And k_a6The parameter is controlled to be constant.

Then, for the designed q-axis stator voltage u_qAnd d-axis stator voltage u_dInverse Park transformation is performed as follows

Wherein u is_α、u_βIn a two-phase stationary coordinate systemThe stator voltages of the alpha and beta axes of the motor,

finally u is to_α、u_βThe output is sent to a space vector pulse width modulation and three-phase inverter and finally sent to a permanent magnet synchronous motor, and the rotating speed of the motor is controlled to reach a given speed omega_mc。

The space vector pulse width modulation and the three-phase inverter are well-known technologies in the art and are not protected by the present invention, and therefore, they will not be described in detail herein.

Case implementation and computer simulation result analysis:

in the present case, the load torque T of the permanent magnet synchronous motor is selected_l1 N.m, selecting p as the number of pole pairs of the motor_n＝2。

The measurement process and the coordinate transformation process of step S10 are the same as those described above and will not be repeated here.

In step S20 and step S30, ∈₁＝0.5，k_a1＝-80，k_a2The measured value of the motor speed signal is obtained as shown in fig. 2, the speed error signal is shown in fig. 3, and the expected value of the d-axis stator current is obtained as shown in fig. 4.

In step S40 and step S50, ∈ is set₂The obtained d-axis stator current error signal is shown in fig. 5, and the obtained q-axis control voltage signal is shown in fig. 6, where 1.5 is the same.

In step S60, k is selected_a3＝-120，k_a4＝-20，ε₃The desired value signal for the q-axis stator current is obtained as shown in fig. 7, and the q-axis stator current error signal is obtained as shown in fig. 8.

In step S70, k is selected_a5-15 and k_a6The d-axis control voltage was obtained as shown in fig. 9.

As can be seen from fig. 2 and 3, the method provided by the present invention can quickly and stably track the given rotation speed of the permanent magnet synchronous motor, the response time is about 2s, and finally there is no static error, and the speed control is very accurate. As can be seen from fig. 5 and 8, the current error in both axial directions can converge to zero rapidly, indicating that the time current can track the designed current desired value. The expected values of the two axial currents given in fig. 4 and 7 show that the method of the present invention is reasonably designed, and the expected values of the currents do not appear to be too large. Fig. 6 and 9 show that the control voltage in both axial directions is not more than 20 in a reasonable range. Moreover, the characteristics of the burrs shown in fig. 2 to 9 are caused by the nonlinear characteristics caused by the fuzzy rules, and the advantages brought by the burrs are similar to the switching characteristics of the sliding mode control, which can improve the system anti-interference and resist the adverse effects caused by the motor model and the load uncertainty, and are also the advantages that the conventional PID control and other linear controls do not have, that is, the method provided by the present invention can make the rotation speed control of the permanent magnet synchronous motor have good rapidity and accuracy, especially good anti-interference capability.

Compared with the traditional method that the coupling between the double shafts is eliminated, and then the rotating speed tracking of the synchronous motor is realized through the decoupled single-shaft control, the method adopts the fuzzy feedback of errors and error integrals, particularly the method of the simultaneous feedback of the double shafts to realize the accurate and rapid control of the rotating speed of the synchronous motor, so that the method for eliminating the errors through the simultaneous control of the double shafts can effectively utilize the coupling energy between the double shafts to serve the common target of the rotating speed control. Moreover, the cases show that the fuzzy system and the fuzzy rule designed by the invention are effective, and can reasonably process the uncertainty in the permanent magnet synchronous motor, so that the effect of controlling the rotating speed of the whole permanent magnet synchronous motor is very ideal, and the invention has high engineering application value.

Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.