JP2010136586A - Magnetic pole position estimator for electric motor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a magnetic pole position estimator for an electric motor, capable of preventing an increase in estimation error in estimating a magnetic pole position while scaling down the electric motor and enhancing output. <P>SOLUTION: The magnetic pole position estimator 10 for an electric motor includes: a magnetic pole position error estimating section 46 for estimating a phase difference Δθe of a γδ coordinate system for a dq coordinate system by utilizing the fact that an induction voltage generated by the motor 11 changes depending on a rotation speed; a rotation speed-magnetic pole position operating section 47 for operating a magnetic pole position estimation value θe from the phase difference Δθe; and a command current generating section 42 for changing a current command value into a value not less than a predetermined value when the current command value is less than the predetermined value in a result of determination for determining whether or not the current command value for the actual value of the motor 11 is less than the predetermined value, and maintaining the torque of the motor 11 at non-changing before and after the change of the current command value. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a magnetic pole position estimation device for an electric motor.

Conventionally, for example, it has a stator core that is formed by laminating a thin plate-like core composed of a cylindrical yoke part and a tooth part, and an armature winding attached to the tooth part. There is known an AC servo motor that is changed in multiple stages so as to narrow toward the tip (see, for example, Patent Document 1).
JP 2002-354716 A

By the way, in the AC servomotor according to the above prior art, in order to prevent the motor control from becoming complicated or difficult, it is desired to have linearity of the output torque with respect to the input current. However, there is a problem that the linearity of the output torque is deteriorated due to torque saturation caused by magnetic saturation in the tooth portion of the armature.
In order to solve such a problem, conventionally, for example, a method of reducing magnetic saturation by increasing a tooth width or shortening a tooth is known.
However, for example, when the tooth width is widened, the area of the armature winding is reduced, and the gap between the tooth tip portions is narrowed, so that the leakage magnetic flux is increased and the output characteristics are deteriorated. Arise. Further, for example, when the teeth are shortened, the area of the armature winding is reduced, and the outer diameter of the rotor is increased to increase the inertia of the rotor.
In addition, since the tip of the tooth is included in the magnetic path of the magnetic flux generated by the winding current supplied to the armature winding, there arises a problem that the inductance changes due to magnetic saturation in the tooth. And the problem that the estimation error at the time of estimating the magnetic pole position of a motor will increase by such a change of an inductance will arise.
The present invention has been made in view of the above circumstances, and provides a magnetic pole position estimating device for an electric motor capable of preventing an increase in estimation error when estimating the magnetic pole position while reducing the size and increasing the output of the electric motor. The purpose is to provide.

  In order to solve the above-described problems and achieve the object, the motor magnetic pole position estimation device according to the first aspect of the present invention is an inverter that sequentially commutates energization to a three-phase AC motor by a pulse width modulation signal. For example, with respect to the inverter 13) in the embodiment, pulse width modulation signal generation means (for example, the PWM signal generation unit 23 in the embodiment) that generates the pulse width modulation signal by a carrier wave signal, and the dq coordinate system Γδ coordinate system having a phase difference is set, and the phase difference is calculated based on a current deviation between an actual current according to a current supplied to the motor and a model current according to a voltage equation of a predetermined model of the motor. A magnetic pole for calculating the magnetic pole position of the motor based on the phase difference calculated by the phase difference calculating means (for example, the magnetic pole position error estimating unit 46 in the embodiment) and the phase difference calculating means. Position calculation means (for example, rotational speed-magnetic pole position calculation unit 47 in the embodiment) and determination means for determining whether or not the current command value for the actual current is less than a predetermined value (for example, in the embodiment) If the current command value is less than a predetermined value in the determination result by the command current generation unit 42) and the determination means, the current command value is set to be equal to or greater than the predetermined value while maintaining the torque of the motor unchanged. Command current setting means for changing (for example, the command current generation unit 42 in the embodiment also serves as).

  Furthermore, the magnetic pole position estimation device for an electric motor according to the second aspect of the present invention is a harmonic voltage applying means for applying a harmonic voltage for detecting the magnetic pole position to the electric motor (for example, a detection voltage applying unit in the embodiment). 49), and the command current setting means maintains the torque of the motor unchanged based on a current change amount of the actual current according to the harmonic voltage applied to the motor by the harmonic voltage application means. However, the current command value is changed so that the actual current becomes equal to or greater than the predetermined value.

  According to the magnetic pole position estimation device of the electric motor according to the first aspect of the present invention, an area where the nonlinearity of the inductance is generated by maintaining the current command value at a predetermined value or more while maintaining the torque of the electric motor unchanged, that is, It is possible to avoid a region where the inductance varies depending on the magnitude of the actual current. As a result, when the motor is downsized and increased in output, even if it is not possible to increase the spacing between the teeth tip portions of the stator, the actual current becomes less than the predetermined value and the contribution of leakage flux increases. Thus, it is possible to prevent a state in which the inductance changes depending on the magnitude of the actual current, and it is possible to prevent the output characteristics of the motor from being deteriorated. Even if the magnetic pole position is estimated by using the saliency of the inductance in an IPM (Interior Permanent Magnet) motor, for example, by avoiding the region where the inductance non-linearity occurs when the motor is energized. Therefore, it is possible to prevent the estimation accuracy from being lowered.

  Furthermore, according to the magnetic pole position estimation device for an electric motor according to the second aspect of the present invention, even when the magnetic pole position is estimated using the fact that the inductance of the electric motor changes depending on the magnetic pole position, the application of the harmonic voltage Based on the current change amount of the actual current according to the current, the current command value is changed so that the actual current fluctuates accurately while maintaining the motor torque unchanged. Therefore, it is possible to accurately avoid the region where the characteristic occurs and to perform appropriate estimation, and to prevent the estimation accuracy from deteriorating.

Embodiments of a magnetic pole position estimating apparatus for an electric motor according to the present invention will be described below with reference to the accompanying drawings.
The magnetic pole position estimation device 10 (hereinafter simply referred to as the magnetic pole position estimation device 10) of the electric motor according to this embodiment is, for example, a magnetic pole position (that is, simply referred to as the motor 11) of a three-phase AC brushless DC motor 11 (hereinafter simply referred to as the motor 11). The rotation angle of the magnetic pole of the rotor from a predetermined reference rotation position is estimated, and the motor 11 generates a rotor (not shown) having a permanent magnet used for a field and a rotating magnetic field for rotating the rotor. And a stator (not shown).
As shown in FIG. 1, for example, the magnetic pole position estimation device 10 includes an inverter 13 that uses a battery 12 as a DC power source and a motor control device 14.

The three-phase (for example, U-phase, V-phase, and W-phase) AC motor 11 is driven by the inverter 13 in response to a control command output from the motor control device 14.
The inverter 13 includes a bridge circuit 13a formed by bridge connection using a plurality of switching elements (for example, MOSFETs: Metal Oxide Semi-conductor Field Effect Transistors) and a smoothing capacitor C, and the bridge circuit 13a performs pulse width modulation ( It is driven by the PWM signal.

  In this bridge circuit 13a, for example, a high-side and low-side U-phase transistor UH, UL paired for each phase, a high-side and low-side V-phase transistor VH, VL, a high-side and low-side W-phase transistor WH, WL is bridge-connected. Each transistor UH, VH, WH has a drain connected to the positive terminal of the battery 12 to form a high side arm, and each transistor UL, VL, WL has a source connected to the grounded negative terminal of the battery 12. It constitutes the low side arm. For each phase, the sources of the high-side arm transistors UH, VH, WH are connected to the drains of the low-side arm transistors UL, VL, WL, and the transistors UH, UL, VH, VL, WH, WL. Each of the diodes DUH, DUL, DVH, DVL, DWH, DWL is connected between the drain and the source so as to be in the forward direction from the source to the drain.

  The inverter 13 is, for example, a gate signal (that is, a PWM signal) that is a switching command that is output from the motor control device 14 when driving the motor 11 and is input to the gates of the transistors UH, VH, WH, UL, VL, WL. ), The DC power supplied from the battery 12 is converted into the three-phase AC power by switching the on / off (cut-off) state of each pair of transistors for each phase. By sequentially commutating energization to the windings, AC U-phase current Iu, V-phase current Iv and W-phase current Iw are passed through the stator windings of each phase.

  As will be described later, the motor control device 14 performs feedback control (vector control) of current on the γ-δ coordinates forming the rotation orthogonal coordinates, and calculates the command γ-axis current Iγc and the command δ-axis current Iδc. The phase voltage commands Vu, Vv, and Vw are calculated based on the command γ-axis current Iγc and the command δ-axis current Iδc, and a PWM signal that is a gate signal for the inverter 13 is calculated according to the phase voltage commands Vu, Vv, and Vw. Output. Then, the γ-axis current Iγ and the δ-axis current Iδ obtained by converting the phase currents Iu, Iv, Iw actually supplied from the inverter 13 to the motor 11 on the γ-δ coordinates, the command γ-axis current Iγc, and Control is performed so that each deviation from the command δ-axis current Iδc becomes zero.

The motor control device 14 includes, for example, a phase current sensor I / F (interface) 21, a control device 22, and a PWM signal generation unit 23.
A phase current sensor I / F (interface) 21 is provided between the bridge circuit 13a of the inverter 13 and the motor 11, and each phase current of at least any two of the three phase currents (for example, the U phase current and the V-phase current) is detected, and a detection signal output from each phase current sensor 32 is output to the control device 22.

For example, as shown in FIG. 2, the control device 22 has a phase difference Δθe that is a difference between the actual rotation angle and the estimated or designated rotation angle with respect to the dq axes of the rotation orthogonal coordinates of the actual motor 11. Then, a γ-δ axis of rotation orthogonal coordinates having a rotation speed ωe is set, and current feedback control (vector control) is performed on the γ-δ coordinates.
The control device 22 generates a command γ-axis current Iγc and a command δ-axis current Iδc, calculates each phase voltage command Vu, Vv, Vw based on the command γ-axis current Iγc and the command δ-axis current Iδc, and generates a PWM signal. To the unit 23.
In addition, the control device 22 includes a γ-axis current Iγ and a δ-axis current Iδ obtained by converting the phase currents Iu, Iv, and Iw corresponding to the detection signals output from the phase current sensors 32 into γδ coordinates, Current feedback control (vector control) is performed so that each deviation between the command γ-axis current Iγc and the command δ-axis current Iδc becomes zero.
Details of the operation of the control device 22 will be described later.

  The PWM signal generation unit 23 compares each phase voltage command Vu, Vv, Vw with a carrier signal such as a triangular wave in order to pass a sinusoidal current to the three-phase stator winding, and A gate signal (that is, a PWM signal) for driving the transistors UH, VH, WH, UL, VL, WL on / off is generated. Then, the inverter 13 converts the DC power supplied from the battery 12 into three-phase AC power by switching the on (conductive) / off (cut-off) state of each transistor that forms a pair for each of the three phases. By sequentially commutating energization to each stator winding of the three-phase motor 11, AC U-phase current Iu, V-phase current Iv, and W-phase current Iw are energized to each stator winding.

  For example, as illustrated in FIG. 3, the control device 22 includes a speed control unit 41, a command current generation unit 42, a current control unit 43, a γδ-3 phase conversion unit 44, a three phase-γδ conversion unit 45, A magnetic pole position error estimation unit 46, a rotation speed-magnetic pole position calculation unit 47, and an electrical angle-mechanical angle conversion unit 48 are provided.

The speed control unit 41 is based on the rotational speed command value ωrc input from the outside, for example, by the closed loop control corresponding to the rotational speed ωr (mechanical angle) output from the electrical angle-mechanical angle conversion unit 48, and the torque command Tc. Is calculated. Then, a torque command Tc is output.
The control device 22 may include a torque control unit instead of the speed control unit 41 and execute torque control.

The command current generation unit 42 outputs a command δ-axis current Iδc and a command γ-axis current Iγc based on the torque command Tc output from the speed control unit 41.
For example, as shown in FIG. 2, the command current generator 42 calculates two points G1 and G2 on the γ-axis at which the command γ-axis current Iγc becomes the predetermined values Iγn and (−Iγn) on the γ-δ coordinates. A region surrounded by a circle G centered on the origin O is an inductance non-linear region in which the inductance changes depending on the actual current of the motor 11, and the command δ-axis current is avoided so as to avoid this inductance non-linear region. Iδc and command γ-axis current Iγc are set.

For example, when the command γ-axis current Iγc calculated based on the torque command Tc is in a range greater than or equal to a predetermined value (−Iγn) and less than or equal to zero, the command current generation unit 42 sets the command γ-axis current Iγc to a predetermined value ( −Iγn), and when the command γ-axis current Iγc calculated based on the torque command Tc is in the range of zero to a predetermined value Iγn, the command γ-axis current Iγc is set to the predetermined value Iγn.
For example, as shown in the following formula (1), the torque command Tc output from the speed control unit 41, the newly set command γ-axis current Iγc, the number of pole pairs q of the motor 11, and the magnetic flux component of the permanent magnet Based on φ, d-axis inductance Ld, and q-axis inductance Lq, command δ-axis current Iδc is calculated.

  The predetermined values Iγn, (−Iγn) are set in advance based on tests to be performed. For example, in the test results shown in FIGS. 4A and 4B, the correspondence between the d-axis inductance Ld and the command d-axis current Idc when the command q-axis current Iqc is each predetermined value a, 0, (−a). From the relationship and the correspondence between the q-axis inductance Lq and the command d-axis current Idc when the command q-axis current Iqc is each predetermined value a, (−a), the absolute value of the command d-axis current Idc is a predetermined value. It can be seen that there is a nonlinearity in which the inductance changes abruptly when it is smaller than a. In this case, by setting the predetermined value Iγn = a and the predetermined value (−Iγn) = (− a), the inductance nonlinear region can be avoided.

  The current control unit 43 calculates a deviation ΔIγ between the command γ-axis current Iγc output from the command current generation unit 42 and the γ-axis current Iγ output from the three-phase-γδ conversion unit 45, and the command current generation unit 42 A deviation ΔIδ between the output command δ-axis current Iδc and the δ-axis current Iδ output from the three-phase-γδ converter 45 is calculated. Then, for example, by PI (proportional / integral) operation, the deviation ΔIγ is controlled and amplified to calculate the γ-axis voltage command value Vγ, and the deviation ΔIδ is controlled and amplified to calculate the δ-axis voltage command value Vδ. Then, the γ-axis voltage command value Vγ and the δ-axis voltage command value Vδ are output.

The γδ-3 phase conversion unit 44 uses the estimated magnetic pole position value θe of the motor 11 output from the rotation speed-magnetic pole position calculation unit 47 to generate a γ-axis voltage command value Vγ and a δ-axis voltage command value on the γ-δ coordinates. Vδ is converted into a U-phase voltage command Vu, a V-phase voltage command Vv, and a W-phase voltage command Vw, which are voltage command values on a three-phase AC coordinate that is a stationary coordinate.
The three-phase-γδ converter 45 is based on the detection signals of the phase currents Iu and Iv output from the phase current sensor I / F (interface) 21 and the sum of the current values of the phase currents at the same timing is zero. Using this, the current value of the other one-phase phase current (for example, W-phase current Iw) is calculated from the current value of the two-phase phase current (for example, each phase current Iu, Iv). Then, the phase currents Iu, Iv, Iw are converted into the γ-axis current Iγ and δ-axis current Iδ on the γ-δ coordinates based on the estimated magnetic pole position θe of the motor 11 output from the rotation speed-magnetic pole position calculation unit 47. Convert to

  The magnetic pole position error estimation unit 46, for example, the γ-axis voltage command value Vγ and the δ-axis voltage command value Vδ output from the current control unit 43 and the γ-axis currents Iγ and δ output from the three-phase-γδ conversion unit 45. Based on the shaft current Iδ, the phase difference Δθe is estimated using the fact that the induced voltage generated by the motor 11 when the motor 11 rotates changes with the rotational speed. For example, the magnetic pole position error estimation unit 46 calculates the actual current (that is, the γ-axis current Iγ and the δ-axis current Iδ) corresponding to the current supplied to the motor 11 and the model current corresponding to the voltage equation of a predetermined model of the motor 11. A phase difference Δθe is calculated based on the current deviation.

  Based on the phase difference Δθe output from the magnetic pole position error estimator 46, the rotation speed-magnetic pole position calculator 47 performs phase synchronization processing using a PLL (Phase-locked loop) or tracking calculation processing using the same-dimensional observer, and the like. The speed estimated value ωe and the magnetic pole position estimated value θe are calculated.

  The electrical angle-mechanical angle conversion unit 48 converts the rotational speed estimated value ωe output from the rotational speed-magnetic pole position calculation unit 47 into a rotational speed ωr (mechanical angle) according to the number of pole pairs q of the motor 11 and rotates. The speed ωr (mechanical angle) is output.

  As described above, according to the magnetic pole position estimation device 10 of the motor according to the present embodiment, the absolute value of the command γ-axis current Iγc is maintained at a predetermined value a or more while the torque command Tc of the motor 11 is maintained unchanged. From the above, the magnitude of the current vector corresponding to the command γ-axis current Iγc and the command δ-axis current Iδc is a value within a region where inductance nonlinearity occurs, that is, a region where the inductance varies depending on the magnitude of the current supplied to the motor 11. Can be avoided. Thereby, when the motor 11 is reduced in size and increased in output, even if the interval between the teeth tip portions of the stator cannot be increased, the magnitude of the current supplied to the motor 11 is less than a predetermined value. Thus, it can be prevented that the contribution of the leakage magnetic flux increases and the state in which the inductance changes depending on the magnitude of the current, and the output characteristics of the motor 11 can be prevented from deteriorating. Even when the magnetic pole position is estimated by using the saliency of the inductance in an IPM (Interior Permanent Magnet) motor, for example, by avoiding a region where inductance nonlinearity occurs when the motor 11 is energized, Appropriate estimation can be performed, and a reduction in estimation accuracy can be prevented.

In the above-described embodiment, the magnetic pole position error estimation unit 46 estimates the phase difference Δθe by utilizing the fact that the induced voltage generated by the motor 11 changes according to the rotation speed when the motor 11 rotates. As a modification of the embodiment described above, for example, a harmonic voltage is applied to the γ-axis voltage command value Vγ and the δ-axis voltage command value Vδ output from the current control unit 43, and the inductance depends on the magnetic pole position. The phase difference Δθe may be estimated using the change.
As shown in FIG. 5, for example, the control device 22 of the magnetic pole position estimation device 10 according to this modification includes a speed control unit 41, a command current generation unit 42, a current control unit 43, and a γδ-3 phase conversion unit 44. And a three-phase-γδ conversion unit 45, a magnetic pole position error estimation unit 46, a rotation speed-magnetic pole position calculation unit 47, an electrical angle-mechanical angle conversion unit 48, and a detection voltage application unit 49. Has been.
That is, the magnetic pole position estimation apparatus 10 according to the modification differs from the magnetic pole position estimation apparatus 10 according to the above-described embodiment in the configuration of the apparatus in the magnetic pole position estimation apparatus 10 according to the modification. The detection voltage application unit 49 is added.

  In this modification, the current control unit 43 calculates a deviation ΔIγ between the command γ-axis current Iγc output from the command current generation unit 42 and the γ-axis current Iγ output from the three-phase-γδ conversion unit 45, A deviation ΔIδ between the command δ-axis current Iδc output from the current generator 42 and the δ-axis current Iδ output from the three-phase-γδ converter 45 is calculated. Then, for example, by PI (proportional / integral) operation, the deviation ΔIγ is controlled and amplified to calculate the γ-axis voltage command value Vγc, and the deviation ΔIδ is controlled and amplified to calculate the δ-axis voltage command value Vδc. Then, the γ-axis voltage command value Vγc and the δ-axis voltage command value Vδc are output.

The detection voltage applying unit 49 detects the γ-axis detected from, for example, a pulse voltage having a predetermined frequency as a harmonic voltage superimposed on the γ-axis voltage command value Vγc and the δ-axis voltage command value Vδc output from the current control unit 43. Output voltage Vhγ and δ-axis detection voltage Vhδ.
Then, each γ-axis voltage command value Vγc and δ-axis voltage command value Vδc output from the current control unit 43, and each γ-axis detection voltage Vhγ and δ-axis detection voltage Vhδ output from the detection voltage application unit 49. Are added to the γδ-3 phase converter 44 and the magnetic pole position error estimator 46 as γ-axis voltage command values Vγ (= Vγc + Vhγ) and δ-axis voltage command values Vδ (= Vδc + Vhδ).

  The magnetic pole position error estimation unit 46, for example, the γ-axis voltage command value Vγ and the δ-axis voltage command value Vδ output from the current control unit 43 and the γ-axis currents Iγ and δ output from the three-phase-γδ conversion unit 45. Based on the shaft current Iδ, the phase difference Δθe is estimated using the fact that the inductance changes depending on the magnetic pole position when the motor 11 rotates.

In this modification, the command current generator 42 takes into account the current change caused by the inductance when the detection voltage application unit 49 applies the γ-axis detection voltage Vhγ and the δ-axis detection voltage Vhδ, and the command δ-axis current Iδc. The command γ-axis current Iγc is set.
For example, the command current generation unit 42, for example, as shown in the following formula (2), one cycle Ts of the carrier signal that is known in advance, the d-axis inductance Ld, the q-axis inductance Lq, the phase difference Δθ, and the γ-axis Based on the detection voltage Vhγ and the γδ-axis harmonic voltage ΔVγδ corresponding to the δ-axis detection voltage Vhδ, the maximum value of the current change ΔIγδ is calculated. Note that the maximum value of the current change ΔIγδ may be set based on a test that is performed in advance. The command δ-axis current Iδc and the command γ-axis current Iγc are determined so as to avoid the inductance nonlinear region even when the magnitude of the current supplied to the motor 11 is changed by the maximum value of the current change ΔIγδ. Set.

  In the above-described embodiment, instead of each phase current sensor 32, the DC side current of the bridge circuit 13a of the inverter 13 is between the bridge circuit 13a of the inverter 13 and the negative terminal or the positive terminal of the battery 12. A DC-side current sensor that detects Idc may be provided. In this case, each phase current is estimated based on the detection signal output from the DC-side current sensor and the gate signal input from the PWM signal generation unit 23 to the inverter 13, and the estimated value of each phase current is set to three phases. What is necessary is just to input into -γdelta conversion part 45.

It is a block diagram of the magnetic pole position estimation apparatus of the electric motor which concerns on embodiment of this invention. It is a figure which shows an example of the (gamma) -delta axis | shaft of a rotation orthogonal coordinate and dq axis which concerns on embodiment of this invention. It is a block diagram of the magnetic pole position estimation apparatus of the electric motor which concerns on embodiment of this invention. FIG. 4A is a graph showing the correspondence between the d-axis inductance Ld and the command d-axis current Idc when the command q-axis current Iqc is each predetermined value a, 0, (−a). (B) is a graph showing the correspondence between the q-axis inductance Lq and the command d-axis current Idc when the command q-axis current Iqc is the predetermined values a and (−a). It is a block diagram of the magnetic pole position estimation apparatus of the electric motor which concerns on the modification of embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Electric pole position estimation apparatus 11 Motor 13 Inverter 22 Control apparatus 23 PWM signal generation part (pulse width modulation signal generation means)
42 Command current generator (determination means, command current setting means)
46 Magnetic pole position error estimation unit (phase difference calculation means)
47 Rotational speed-magnetic pole position calculator (magnetic pole position calculator)

Claims (2)

An inverter that sequentially commutates energization of a three-phase AC motor using a pulse width modulation signal; and a pulse width modulation signal generation unit that generates the pulse width modulation signal using a carrier wave signal;
A γδ coordinate system having a phase difference with respect to the dq coordinate system is set, and based on the current deviation between the actual current according to the current supplied to the motor and the model current according to the voltage equation of the predetermined model of the motor. A phase difference calculating means for calculating a phase difference; a magnetic pole position calculating means for calculating a magnetic pole position of the electric motor based on the phase difference calculated by the phase difference calculating means;
Determination means for determining whether or not a current command value for the actual current is less than a predetermined value;
Command current setting means for changing the current command value to the predetermined value or more while maintaining the torque of the motor unchanged when the current command value is less than a predetermined value in the determination result by the determination means. An apparatus for estimating the magnetic pole position of an electric motor. Harmonic voltage application means for applying a harmonic voltage for magnetic pole position detection to the electric motor,
The command current setting means maintains the torque of the motor unchanged while maintaining the torque of the motor unchanged based on the current change amount of the actual current according to the harmonic voltage applied to the motor by the harmonic voltage application means. The apparatus for estimating a magnetic pole position of an electric motor according to claim 1, wherein the current command value is changed so that a current becomes equal to or greater than the predetermined value.

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