JP2007104777A - Electric vehicle drive controller - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a reliable electric vehicle drive controller which avoids nonconformity such as torque deficiency, step out, etc. by computing an accurate velocity estimate, corresponding to various conditions in operation. <P>SOLUTION: This controller has a control unit 28 for inverter which drives a motor 7 for driving an electric vehicle, a velocity estimator 14 which estimates the revolution of the motor 7, based on the applied voltage or current of the motor 7, and a velocity predictor 15 which predicts the revolution of the motor 7, based on a torque command. The velocity predictor 15 predicts the velocity, based on at least one of the seat-load rate, the gradient, and the revolution of the drive motor, and the control unit 28 performs the vector control, using a velocity predicted value in the vicinity of the zero revolution of the motor 7, and performs the vector control, using the velocity estimate in other regions. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an electric vehicle drive control device that performs speed sensorless vector control without detecting the rotation speed or speed of an electric motor.

  The speed sensorless vector control of the induction motor (IM) estimates the speed (number of rotations) based on the applied voltage and current information of the induction motor driven by the inverter and performs torque control. Such a speed sensorless vector The control device includes a speed estimation unit that estimates the speed (number of rotations) of the electric motor, and performs torque control according to the output of the speed estimation unit. Such a speed sensorless vector control device has been widely applied to industrial applications because of the advantage of not using a speed sensor. However, in recent years, application to electric vehicles such as trains and electric cars has been advanced.

  In this case, it is difficult to maintain performance at extremely low speeds where the induced voltage is very small, and in applications to electric vehicles such as trains and electric cars, the vehicle starts to move backwards starting from a gradient section or slope (starting while the vehicle is lowered) ), The inverter frequency crosses zero speed, and such a problem becomes apparent.

As a method for dealing with these problems, there is one that has a speed prediction unit that predicts speed without using feedback information based on a torque command, instead of estimating speed using feedback information such as current (for example, a patent) Reference 1). That is, in the normal speed range, vector control is performed using the speed estimation value, and vector control is performed using the speed prediction value only near the zero speed.
Japanese Patent No. 3316118

  However, when an electric vehicle such as a train or an electric vehicle is operated, the boarding rate, the gradient, the number of motors driven, and the like change. For example, when the motor fails, the number of drive motors changes when the failed motor is cut out and operated. Therefore, depending on the conditions, the predicted speed values may not match, and if the predicted speed values do not match, torque will be insufficient or step out. As a result, the reliability of the system, such as acceleration failure and startup failure, decreases.

  An object of the present invention is to provide a highly reliable electric vehicle drive control device.

  The electric vehicle drive control device of the present invention includes, in addition to a speed estimation unit that estimates a rotation speed of the motor based on an applied voltage and current of a motor driven by an inverter and obtains a speed estimation value, and a torque command of the motor, A speed prediction unit that predicts the speed of the motor based on one of the occupancy rate, the gradient, and the number of drive motors and obtains a speed estimation value, and the speed prediction value is used when the rotation speed of the motor is near zero speed. A control unit that performs vector control and performs vector control using the speed estimation value in other regions.

  ADVANTAGE OF THE INVENTION According to this invention, a reliable electric vehicle drive control apparatus can be provided.

(First embodiment)
FIG. 1 is a block diagram of an electric vehicle drive control apparatus according to the first embodiment of the present invention. FIG. 1 shows a case where a train is assumed as an electric vehicle. The panda graph 1 and the wheel 2 are connected to a DC overhead line. Direct current is fed to the inverter 5 through the filter reactor 3 and the filter capacitor 4. The induction motor 7 is driven by the inverter 5. As a control method for controlling the inverter 5, it is constituted by a speed sensorless vector control system that detects the phase currents Iu and Iw of the motor by the current detector 6 and does not detect the rotation speed of the induction motor 7.

  In FIG. 1, the control part 28 is comprised by the vector control method on a DQ rotation coordinate system which is a well-known technique. As inputs, a magnetic flux command and a torque command are given. The current command calculation unit 8 calculates and outputs the excitation current command Id * and the torque current command Iq *. Further, the phase detectors Iu and Iw of the motor are detected by the current detector 6, and the DQ axis currents Id and Iq on the DQ axis coordinate system are converted by the coordinate conversion unit 12.

  The voltage command calculation unit 9 calculates and outputs the D-axis voltage command Vd * and the Q-axis voltage command Vq * so that the current command values Id * and Iq * coincide with the actual current values Id and Iq. The DQ axis voltage commands Vd * and Vq * are converted into three-phase voltage commands Vu * and Vv * .Vw * by the coordinate conversion unit 10 and input to the PWM circuit 11. The PWM circuit 11 controls the gate of the inverter 5 by, for example, a triangular wave comparison PWM control that is a well-known technique so that a voltage that matches the three-phase voltage command is output.

  The speed estimator 14 receives the DQ axis voltage commands Vd * and Vq * and the actual DQ axis currents Id and Iq as inputs, and estimates and outputs the speed of the induction motor 7, that is, the rotational speed of the motor. The speed prediction unit 15 predicts the speed, that is, the rotation speed of the electric motor, using the torque command and the variable load representing the vehicle weight as inputs. Detailed implementation of the speed prediction unit 15 will be described later.

  The output of the speed estimation unit 14 that is the first speed calculation unit and the output of the speed prediction unit 15 that is the output of the second speed calculation unit are input to the switch 17. When the output Flg_ZeroSpeed of the speed region determination unit 20 is 1, the switch 17 outputs the speed prediction value that is the output of the speed prediction unit 15 as the final speed estimation value ωrh. Further, when the output Flg_ZeroSpeed is 0, the speed estimation value output from the speed estimation unit 14 is output as the final speed estimation value ωrh.

  The slip frequency reference calculation unit 16 calculates and outputs the slip frequency reference ωs * based on the DQ axis current command values Id * and Iq *, for example, as in the following equation (1).

ωs * = R2 / L2 × Iq * / Id * (1)
Here, R2: secondary resistance, L2: secondary inductance. The adder 19 adds the final estimated speed value ωrh and the slip frequency reference ωs * and outputs the result as an inverter frequency ω1. The inverter frequency ω1 is input to the integrator 13. The integrator 13 integrates the input and calculates the phase angle θ of the rotating coordinate system D axis from the stationary coordinate system A axis, and is used in the coordinate converters 10 and 12.

  Based on the final estimated speed value ωrh, the speed region determination unit 20 determines whether or not it is near zero speed and outputs a zero speed flag Flg_ZeroSpeed. For example, the determination can be realized as the following equation (2).

if ((ωrh> = α) and (ωrh <β))
Flg_ZeroSpeed = 1
else
Flg_ZeroSpeed = 0 (2)
Here, α is the lower limit value of the zero speed region and is normally set to a negative value. Β is an upper limit value of the zero speed region, and is usually set to a positive value. That is, Flg_ZeroSpeed = 1 near zero speed, and Flg_ZeroSpeed = 0 in other areas. In the above description, the determination of the zero speed is performed based on the final estimated speed value ωrh, but it may be configured similarly based on the inverter frequency ω1 instead of the estimated speed value.

  FIG. 2 is a configuration diagram of the speed prediction unit 15 in the first embodiment. The subtractor 21 subtracts the running resistance of the vehicle from the torque command, calculates acceleration torque, and outputs it to the acceleration prediction calculation unit 22. Here, as the running resistance, for example, a gradient force, a resistance force caused by a running wind, a mechanical friction force such as a gear ratio, or the like may be simulated. It is assumed that the running resistance has been converted into the dimension of the rotational torque of the electric motor using the wheel diameter and gear ratio. On the other hand, the variable load inertia conversion unit 24 converts the variable load signal, that is, the total weight of the vehicle into an equivalent inertia J around the rotation axis of the electric motor, and outputs it to the acceleration prediction calculation unit 22.

  In the acceleration prediction calculation unit 22, the predicted value of the acceleration torque is input and divided by the equivalent inertia J of the rotor of the electric motor 7 to output the predicted acceleration value. The predicted acceleration value is input to the integrator 23, and the predicted speed value is calculated by integrating the acceleration value. Here, the equivalent inertia J is considered to be a combination of the inertia of the motor itself, the inertia of the gear and the wheel, and the weight of the vehicle converted into the rotary inertia of the motor shaft through the gear and the wheel diameter.

  According to the electric vehicle drive control device configured as described above, a predicted speed value that matches the actual speed can be calculated even if the running resistance such as the gradient or the boarding rate and the equivalent inertia change. . Further, the running resistance is a gradient force or a dominant factor, and the gradient force may be 30% or more of the torque generated by the electric motor of the electric vehicle. By incorporating this into the prediction calculation unit model according to the operation conditions, the accuracy of the speed prediction value can be significantly improved.

  FIG. 3 is a characteristic diagram of the start-up characteristics when traveling resistance such as gradient is not considered. The inverter starts at time t1, and becomes predictive control (time t2 to t3) through estimation control (time t1 to t2). Since the running resistance such as the gradient is not taken into consideration, the acceleration of the speed predicted value calculated by the speed predicting unit 15 is higher than the acceleration to be given at the time t2 to t3. For this reason, the slip frequency of the induction motor 7 is low, and the output torque decreases, that is, close to a step-out state. In FIG. 3, after that (after time t3), the drawing shows the state of successful pulling and stable acceleration, but if the accelerations do not match, a system trouble such as a start failure occurs.

  FIG. 4 is a characteristic diagram of the starting characteristics when traveling resistance such as a gradient is taken into consideration. The inverter starts at time t1 and goes through estimation control (time t1 to t2) to become predictive control (time t2 to t3). Considering running resistance such as gradient, it should be given originally at time t2 to t3. As a result of the predicted acceleration, it is possible to accelerate at a stable and predetermined acceleration.

  The gradient force that has a critical effect on the predicted speed varies depending on the driving conditions. That is, there is a possibility that the electric vehicle is started from a section having various slopes. Therefore, if the gradient force is regarded as a constant value or zero, the optimum acceleration cannot be obtained and there is a possibility of starting failure as described above. Therefore, as in the first embodiment, a highly accurate speed prediction is performed based on these pieces of information to avoid a startup failure and improve the reliability of the system.

  For information on the slope, in the case of a train, if the train has a device having data of the route to travel, such as an automatic train control device (ATO), an automatic train stop device (TASC), a navigation device, Gradient information can be acquired and set from the same device. Even in the case of an automobile, it is feasible to acquire the gradient of the travel section by using the navigation system.

  In the case of a train, the weight varies up to about two times depending on the passenger rate. In addition, the weight of several tens of percent varies even in an electric vehicle. According to the speed prediction unit 15 illustrated in FIG. 2, the total weight of the vehicle may be calculated by using a variable load signal (weight sensor) that can detect a change in weight due to the number of passengers. The variable load inertia conversion unit 24 converts the variable load signal, that is, the total weight of the vehicle, into an equivalent inertia J around the rotating shaft of the motor. In this conversion, the force acting on the linear system is simply converted into torque of the rotational diameter using the wheel diameter and gear ratio.

  According to the first embodiment, accurate speed prediction is possible even when the boarding rate fluctuates. Therefore, under various operating conditions assumed in operating an electric vehicle, it is possible to accurately predict the speed by taking in these driving conditions and taking them into consideration. As a result, the slip frequency is properly maintained, and it is possible to suppress the occurrence of torque shortage and step-out, thereby improving the reliability of the system.

  Various methods have been proposed for speed sensorless vector control, and the method is not limited to the method shown in the first embodiment. Moreover, although the induction motor was shown as an electric motor, even if it is a permanent magnet synchronous motor, the same effect can be obtained.

(Second Embodiment)
FIG. 5 is a configuration diagram of a speed prediction unit in the electric vehicle drive control apparatus according to the second embodiment of the present invention. This second embodiment omits external input such as running resistance such as gradient and response load representing the boarding rate, and is the maximum possible running as compared to the first embodiment shown in FIG. The equivalent inertia Jmax corresponding to the resistance and the maximum occupancy is set.

  In FIG. 5, the subtractor 21 calculates the difference between the torque command and the maximum running resistance and inputs the difference to the acceleration prediction calculation unit 22. In the acceleration prediction calculation unit 22, an equivalent inertia corresponding to the maximum boarding rate is set, and the acceleration prediction value obtained by the acceleration prediction calculation unit 22 is input to the integrator 23 and integrated by the integrator 23 to be speed prediction. Output as a value.

  As described above, the speed prediction unit 15 in the second embodiment has no input from the outside such as a running resistance such as a gradient and a response load representing the boarding rate, and the subtractor 21 can assume the maximum running resistance. Then, the acceleration prediction calculation unit 22 sets an equivalent inertia corresponding to the maximum boarding rate. By comprising in this way, speed prediction based on the smallest acceleration in the driving | running conditions which can be assumed will be performed.

  FIG. 6 is a characteristic diagram of the start-up characteristic in the absence of running resistance in the second embodiment of the present invention. The inverter starts at time t1, and becomes predictive control (time t2 to t3) through estimation control (time t1 to t2). Since the speed prediction unit 15 performs speed prediction assuming the maximum gradient, the acceleration temporarily decreases when passing through zero speed. However, the activation failure occurs when the acceleration is higher than what should be given. Conversely, when the acceleration is small, the acceleration decreases, but the activation can be performed stably and reliably.

  According to the second embodiment, since the speed prediction assuming the maximum adverse condition is performed, the system can be stably and reliably started under any operating condition, and the system reliability is improved. Of course, a decrease in acceleration as shown in FIG. 6 is also not preferable, but it is not a fatal failure of the system that results in a startup failure, so if the slope, vehicle weight, etc. can be grasped, the first embodiment Needless to say, the configuration is more suitable because it does not reduce acceleration and enables accurate speed prediction. However, in many cases, information cannot be obtained for travel resistance such as a gradient, and the second embodiment is suitable for such a case.

(Third embodiment)
FIG. 7 is a configuration diagram of a speed prediction unit in the electric vehicle drive control apparatus according to the third embodiment of the present invention. In the third embodiment, the process of subtracting the maximum running resistance from the torque command is omitted and the equivalent inertia Jmax2 is set to be the minimum acceleration as compared with the second embodiment shown in FIG. Is.

  In FIG. 7, the torque command is input to the acceleration prediction calculation unit 22, and an equivalent inertia Jmax2 that sets the minimum acceleration is set in the acceleration prediction calculation unit 22. The acceleration prediction value obtained by the acceleration prediction calculation unit 22 is integrated. Is input to the integrator 23, integrated by the integrator 23, and output as a predicted speed value.

  In the third embodiment, unlike the second embodiment shown in FIG. 5, there is no processing for subtracting the maximum running resistance from the torque command, and the equivalent inertia is set to be the minimum acceleration. is there. That is, the equivalent inertia is set to the maximum value Jmax2 so that the acceleration of the speed prediction value becomes the minimum acceleration.

  According to the third embodiment, the same operational effects as those of the second embodiment can be realized by a simpler block, and thus there is an advantage that the calculation load can be reduced.

(Fourth embodiment)
FIG. 8 is a configuration diagram of a speed prediction unit in the electric vehicle drive control apparatus according to the fourth embodiment of the present invention. In the fourth embodiment, an inertia correction unit 25 is provided with respect to the first embodiment shown in FIG. 2, and an equivalent inertia J is set according to the number of drive units of the motor. .

  In FIG. 8, the torque command and the running resistance of the vehicle are input to and subtracted from the subtracter 21, and the acceleration torque is calculated and output to the acceleration prediction calculation unit 22. On the other hand, the variable load inertia conversion unit 24 converts the variable load signal, that is, the total weight of the vehicle into an equivalent inertia around the rotating shaft of the electric motor, and the inertia correction unit 25 sets the equivalent inertia J according to the number of drive units. To do.

  For example, if the overall mass of the knitting is M, the number of drive motors is N, the wheel radius is R, and the gear ratio is G, the equivalent inertia J around the rotation axis of the motor 7 can be calculated by the following equation (3). However, for the sake of simplicity, the motor, gear, wheel inertia, etc. are ignored here.

J = (R / G) 2 × M / N (3)
According to the fourth embodiment, even when some of the motors 7 of the vehicle are disconnected due to a failure or the like, the equivalent inertia corresponding to the load to be borne by the remaining healthy motors 7 is appropriately calculated and predetermined Acceleration is obtained. In addition, when the motor 7 is cut out, the acceleration decreases accordingly. However, if this is not taken into account, torque shortage or step-out may occur. However, taking into account the cut-out of the motor 7 By appropriately calculating the acceleration, it is possible to avoid such problems and provide a highly reliable system.

(Fifth embodiment)
FIG. 9 is a configuration diagram of a speed prediction unit in the electric vehicle drive control apparatus according to the fifth embodiment of the present invention. The speed prediction unit 15 in the fifth embodiment includes an acceleration calculation unit 27, an acceleration storage unit 26, and an integrator 23.

  The output of the switch 17 that selects and outputs the outputs of the speed estimation unit 14 and the speed prediction unit 15, that is, the speed estimation value ωrh is input to the acceleration calculation unit 27. The acceleration calculator 27 calculates acceleration based on the estimated speed value. The acceleration storage unit 26 inputs the same acceleration and stores the input only when the speed region determination unit 20 determines that the region is not near the zero speed (Flg_ZeroSpeed = 0), and updates the value otherwise. Do not process. The integrator 23 integrates the output according to the output of the acceleration storage unit 26, and calculates and outputs a predicted speed value.

  Assuming that the vehicle travels through zero speed from a region where the reverse speed is high, the output Flg_ZeroSpeed of the speed region determination unit 20 is 0 in the region where the reverse speed is high, that is, the output of the speed estimation unit 14 is valid. Yes. During this time, since there is speed, accurate speed estimation is possible. Based on this speed, acceleration is calculated and stored in the acceleration storage unit 26. When passing through the zero speed, updating of the value in the acceleration storage unit 26 is stopped. That is, the acceleration at the time of entering the near zero speed region is stored. In the near zero speed region, the speed is predicted based on the stored acceleration.

  According to the fifth embodiment, there are many systems that cannot obtain information such as the gradient, and when the worst condition is assumed, the acceleration that passes through the zero speed always decreases. In this embodiment, since the speed is predicted based on the acceleration in the vicinity of the zero speed, it is possible to maintain an appropriate acceleration in consideration of a running resistance such as a gradient.

(Sixth embodiment)
FIG. 10 is a configuration diagram of an electric vehicle drive control device according to the sixth embodiment of the present invention. For example, there is a system such as a train in which a plurality of electric vehicle drive control devices are mounted in one train. Now consider such a system. Also in the case of an electric vehicle, a plurality of electric vehicle drive control devices are mounted in a system that drives each wheel individually.

  The plurality of electric vehicle drive control devices control each inverter that drives each electric motor. In this case, the inverter frequencies of these inverters are made equal. As an example, the predicted speed values of the respective control units that drive and control the electric motor are made equal, and the inverter frequencies of the respective inverters are made equal.

  In FIG. 10, a single speed prediction unit 15 is provided for each control unit 28 of the electric vehicle drive control device. Information is transmitted between the speed prediction unit 15 and the control unit 28 by the information transmission unit 29.

  With this configuration, the predicted speed values in the respective control units 28 can be set to the same value. If the speed of the knitting is unique, but there is a difference in the predicted speed value of each control unit 28, this will cause a difference in the torque of the motor controlled by each control unit 28. As a result, torque generation in the composition becomes unbalanced, causing vibrations between vehicles in the composition and causing a great loss of riding comfort. As in the sixth embodiment, it is possible to suppress such vibration between vehicles by aligning the predicted speed values and making the torque generated by each motor uniform.

  The feature of the sixth embodiment is that the speed predicted values used in each control unit 28 are aligned. In the sixth embodiment, the unique speed prediction unit 15 is provided in the knitting, and each control unit 28 uses the value, thereby realizing that the speed prediction values used in each control unit 28 are aligned. Simply, even in a configuration in which each control unit 28 includes an independent speed prediction unit 15, it is possible to achieve substantially equivalent settings by setting the configuration and parameters of the speed prediction unit 15 to be the same. Thus, similarly, it is possible to suppress the unbalance of the torque generated between the vehicles and to suppress the vibrations between the vehicles.

The block diagram of the electric vehicle drive control apparatus concerning the 1st Embodiment of this invention. The block diagram of the speed estimation part in the 1st Embodiment of this invention. The characteristic view of the starting characteristic when not considering driving resistance in the speed estimation part in the 1st Embodiment of this invention. The characteristic diagram of the starting characteristic at the time of considering driving resistance in the speed estimation part in the 1st Embodiment of this invention. The block diagram of the speed estimation part in the electric vehicle drive control apparatus concerning the 2nd Embodiment of this invention. The characteristic view of the starting characteristic in the state without running resistance in the 2nd Embodiment of this invention. The block diagram of the speed estimation part in the electric vehicle drive control apparatus concerning the 3rd Embodiment of this invention. The block diagram of the speed estimation part in the electric vehicle drive control apparatus concerning the 4th Embodiment of this invention. The block diagram of the speed estimation part in the electric vehicle drive control apparatus concerning the 5th Embodiment of this invention. The block diagram of the electric vehicle drive control apparatus concerning the 6th Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Pantograph, 2 ... Wheel, 3 ... Filter reactor, 4 ... Filter capacitor, 5 ... Inverter, 6 ... Current detector, 7 ... Induction motor, 8 ... Current command calculating part, 9 ... Voltage command calculating part, 10 ... Coordinate Conversion unit, 11 ... PWM circuit, 12 ... coordinate conversion unit, 13 ... integrator, 14 ... speed estimation unit, 15 ... speed prediction unit, 16 ... slip frequency reference calculation unit, 17 ... switch, 19 ... adder, 20 ... speed region determination unit, 21 ... subtractor, 22 ... acceleration prediction calculation unit, 23 ... integrator, 24 ... variable load inertia conversion unit, 25 ... inertia correction unit, 26 ... acceleration storage unit, 27 ... acceleration calculation unit, 28 ... Control part, 29 ... Information transmission part

Claims (7)

A speed estimation unit that estimates the speed of the motor based on an applied voltage or current of an electric motor driven by an inverter and obtains a speed estimated value, and at least a boarding rate, a gradient, and the number of driving motors in addition to the torque command of the motor A speed prediction unit that predicts the speed of the electric motor based on one of the above and obtains a speed estimation value, and performs vector control using the speed prediction value when the rotation speed of the motor is near zero speed, and in other regions An electric vehicle drive control device comprising: a control unit that performs vector control using the estimated speed value. 2. The electric vehicle drive control device according to claim 1, wherein the electric vehicle is a railway vehicle, and the gradient information is acquired from an automatic train control device, an automatic train stop device, and a navigation device. The electric vehicle drive control device according to claim 1, wherein the electric vehicle is an electric vehicle, and the gradient information is acquired from a car navigation device. A speed estimator that estimates the rotational speed of the motor based on the applied voltage and current of the motor driven by the inverter and obtains a speed estimated value, and the minimum acceleration that can be assumed in operation of the vehicle in addition to the torque command of the motor A speed prediction unit that predicts the speed of the motor based on the above and obtains a predicted speed value, and performs vector control using the predicted speed value when the rotation speed of the motor is near zero speed, and the speed in other areas An electric vehicle drive control device comprising: a control unit that performs vector control using an estimated value. An acceleration calculation unit that calculates the acceleration of the rotation speed of the motor driven by the inverter, and an acceleration calculated by the acceleration calculation unit immediately after the rotation speed of the motor shifts from a region not near zero speed to a region near zero speed. An acceleration storage unit that stores a calculated value, a speed estimation unit that estimates the rotation speed of the motor based on an applied voltage or current of the motor, and a predicted speed value based on a torque command or an acceleration stored in the acceleration storage unit A speed prediction unit to calculate, and a control unit that performs vector control using the speed prediction value when the rotation speed of the motor is near zero speed, and performs vector control using the speed estimation value in other regions. An electric vehicle drive control device comprising: A plurality of electric motors driven by an inverter in the same vehicle or knitting, a speed estimation unit for estimating a rotational speed of the motor based on an applied voltage or current of the electric motor to obtain a speed estimated value, and a torque command of the electric motor A speed prediction unit that predicts a speed of the electric motor based on a minimum acceleration that can be assumed in the operation of the vehicle and obtains a speed prediction value; and when the rotation speed of the motor is near zero speed, the speed prediction value is used. A control unit that performs vector control and performs vector control using the speed estimation value in other areas, and equalizes the inverter frequency of each inverter that drives the motor at that time. Electric vehicle drive control device. 7. The electric vehicle drive control device according to claim 6, wherein the predicted speed values of the respective control units that drive and control the electric motor are made equal, and the inverter frequencies of the respective inverters are made equal.

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