WO2000022723A1 - Method and device for controlling a brushless electric motor - Google Patents

Method and device for controlling a brushless electric motor Download PDF

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Publication number
WO2000022723A1
WO2000022723A1 PCT/DK1998/000442 DK9800442W WO0022723A1 WO 2000022723 A1 WO2000022723 A1 WO 2000022723A1 DK 9800442 W DK9800442 W DK 9800442W WO 0022723 A1 WO0022723 A1 WO 0022723A1
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WO
WIPO (PCT)
Prior art keywords
reference voltage
low
motor
generating
signal
Prior art date
Application number
PCT/DK1998/000442
Other languages
French (fr)
Inventor
Jesper Riber Rosholm
Jan Carøe AARESTRUP
Original Assignee
Danfoss Compressors Gmbh
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Danfoss Compressors Gmbh filed Critical Danfoss Compressors Gmbh
Priority to DE69822896T priority Critical patent/DE69822896T2/en
Priority to US09/807,587 priority patent/US6380707B1/en
Priority to BR9816046-0A priority patent/BR9816046A/en
Priority to AU94341/98A priority patent/AU9434198A/en
Priority to EP98947415A priority patent/EP1121753B1/en
Priority to PCT/DK1998/000442 priority patent/WO2000022723A1/en
Publication of WO2000022723A1 publication Critical patent/WO2000022723A1/en

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Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings

Definitions

  • the present invention relates to a method and a device for controlling a brushless electric motor, preferably comprising a permanent magnet rotor and armature windings supplied with current from a DC-power supply via switching means controlled to selectively supply current to the armature windings.
  • the generating of commutation signals is performed in a simple manner taking advantage of the trapezoidal curve form of the back-electromotive forces which are compared to a low and high reference voltage, whereby these reference voltages are adjusted to achieve the correct timing of the commutation signals
  • measurement of the zero-crossings of the back-electromotive forces is avoided which can be complicated due to electrical noise
  • FIG. 1 diagrammatically shows a brushless motor provided with a control system in accordance with the invention
  • Figure 2 shows a more detailed circuit diagram of a preferred circuitry for generating a common reference voltage
  • Figure 3 shows a corresponding circuit diagram for detecting the electromotive forces in the windings
  • Figure 4 shows different signal wave forms at various points of the circuits shown in Figure 1-3.
  • Figure 5 shows a second embodiment of a diagram for generating a common reference voltage.
  • the brushless motor shown in Figure 1 comprises three armature windings U, V, W connected in a star configuration with a common midpoint P. Each winding U, V, W may be connected to the positive power supply or the negative power supply via transistors Q Q ⁇ or corresponding switching elements.
  • the power supply shown in Figure 1 consists of a controlled rectifier with smoothing inductor L and capacitor C. Regulating of the intermediate voltage U D c is performed by means of the controlled rectifier.
  • the switching elements Q Q 6 are controlled by a commutation generator in accordance with signals received from an electromotive-force detector in such a way that a rotating magnetic field is generated by the windings U, V, W to rotate the rotor of the motor, which preferably is a permanent magnet rotor.
  • back EMF back-electromotive force
  • the back-electromotive force detector generates commutation signals for the commutation generator by comparing the back-electromotive forces developed during operation in the windings U, V, W with a low and high reference voltage received from a low and high reference voltage generator.
  • the low and high reference voltages are preferably combined into a common reference signal U ⁇ M in order to simplify the circuitry in the back- electromotive force detector.
  • the low and high reference voltages are provided by simple resistive voltage dividers R1 , R2, R3 using the intermediate voltage U DC and controlled by switching transistors T1 , T2, which are controlled in accordance with a pulse width modulation signal and a synchronizing signal received from the commutation generator and the electromotive force detector, respectively.
  • the voltage U R2 is smoothed by a resistance-capacitor network R4, C1 to define the common reference signal U COM. More specifically the filter creates the mean value of the occasionally pulse width modulated voltage U R2 .
  • FIG. 1 shows the function of the control circuit shown in Figures 1-3 with reference to Figure 4 which shows different signal wave forms at various points of the circuit.
  • A, B and C show the input signals to the comparators COMP 1-3 in Figure 3.
  • the back EMF in the winding U has a trapezoidal wave form and is compared with the common reference signal U COM for generating commutation signals for the commutation generator.
  • the back EMF is superimposed on the midpoint voltage P.
  • the common reference signal U COM is equal to the high reference voltage and the back EMF in the winding U is rising until it reaches and passes the level corresponding to the high reference voltage at the time marked ti, at which point the comparator COMP 1 changes its output from low to high, thereby signalling to the commutation generator that the switching element Q 5 has to be switched off and the switching element Qi has to be switched on.
  • the common reference signal U COM is changed to be equal to the low reference voltage.
  • the next electromotive force crossing this low reference voltage is the back EMF from the winding W which crosses this low reference voltage at the time marked t 2 .
  • This crossing makes the output from the comparator COMP 3 change from positive to negative, thereby indicating to the commutation generator that the transistor Q 4 has to be switched off and the transistor Q 6 has to be switched on, and at the same time changing the common reference voltage to the high reference voltage level.
  • Corresponding processes are performed at the times t 3 , t», t 5 , t 6 for one whole cycle for the system.
  • the comparators 1-3 in Figure 3 thus generate a three-bit-information signal which is sent to the commutation generator.
  • the information signal is 1-0-1 representing the signals from comparators COMP 1 , 2 and 3 respectively.
  • a look-up table contains stored commutation signals for the switches QrQ ⁇ -
  • the information signal 1-0-1 from the comparators is used as a key to the look up table, and here the corresponding commutation signals stored are ( Q 5 , Q 3 , d; Q 6 , Q 4 , Q 2 )-
  • commutation is activated each time a back EMF with positive slope crosses the high reference, and correspondingly each time a back EMF with negative slope crosses the low reference.
  • the synchronization signal for changing the common reference signal between the high reference voltage and the low reference voltage can be provided by a majority vote between the outputs from the comparators COMP 1-3.
  • the synchronization signal is thus given each time one of the comparators changes state.
  • the speed of the motor can be calculated from the number of state changes.
  • the synchronization signal is a speed dependent signal
  • the reference voltage U COM will also be speed dependent.
  • U C O M could be following the motor voltage on the phase U, V or W directly.
  • An advantageous feature of the invention is the establishment of a selfregulating commutation angle. Normally, commutation is done about 15 degrees after the back EMF has made a zero crossing. Determining when the 15 degrees are reached can be solved in different ways, e g by using a counter counting up to a limit value from the time a zero crossing is detected, or alternatively integrating the back EMF from zero-crossing up to a limit value These methods, however, places demands on the control circuitry as to calculative power and precision as to the commutation instants Even slight deviations from the optimal commutation angle mean loss in motor effiency However, by synchronizing the reference levels with the motor speed, a selfregulating commutation angle ⁇ (shown in Figure 4A) is achieved During fixed speed operation, the value of the commutation angle ⁇ will be a fixed value, if on the other hand, the motor current increases, the motor voltage will also increase and the commutation angle ⁇ will become smaller If the load decreases, the angle ⁇ will increase
  • Control of the switches Q Q ⁇ during normal operation can be done by means of PWM modulation
  • the switches are block commutated, i e there is no change in the duration of the on- times
  • a pulse-width-modulation scheme the effective voltages supplied to the windings U, V, W are reduced and correspondingly, the back-electromotive forces from the windings are reduced Accordingly, in this situation it is necessary to reduce the corresponding high reference voltage and low reference voltage correspondingly
  • This is provided by supplying sequentially the pulse-width-modulation signal used for pulse-width modulation of the switching transistors QrQ 6 , respectively, to the switching transistor T2 shown in Figure 2
  • the circuit described is simple, but has the drawback that the PWM switch T2 only pulls the voltage U R2 in one direction This

Abstract

The brushless electric motor (M) is provided with switching means (Q1 - Q6) for selectively supplying current to the armature windings (U, V, W) of the motor (M) from a DC-power supply (1) the switching means (Q1 - Q6) are controlled by measuring the back-electromotive forces developed in the windings (U, V, W) during operation and comparing these measurements with a high and low reference voltage, in such a way that each time a measured back-electromotive force with positive slope crosses the high reference voltage or a measured back-electromotive force with negative slope crosses the low reference voltage, a commutation signal is generated to commutate the switching means (Q1 - Q6), this provides a highly simplified control of the switching means.

Description

METHOD AND DEVICE FOR CONTROLLING A BRUSHLESS ELECTRIC MOTOR.
TECHNICAL FIELD
The present invention relates to a method and a device for controlling a brushless electric motor, preferably comprising a permanent magnet rotor and armature windings supplied with current from a DC-power supply via switching means controlled to selectively supply current to the armature windings.
BACKGROUND ART
In this field it is known to control the switching means using the zero crossing of the back electromotive forces developed during operation in the windings of the motor as a reference and delaying the commutation relative to the zero crossings in different ways.
From US 5 640 073 it is known to use a delay of the back electromotive forces and to compare these delayed back electromotive forces with a sawtooth-wave reference voltage having a frequency proportional to the rotor speed and an amplitude whose center voltage is equal to the midpoint voltage. The amplitude of the sawtooth wave is adjusted in accordance with the rotor speed or rotor current in order to adjust the resulting delay of the commutation signals. The object of the provision of the sawtooth-wave signal is to make it possible to use a delay angle for the back electromotive forces, which is less than 90°, in order to provide a quick response to sudden load variations. When the rotor speed is below a predetermined speed, it may be necessary to increase the time constant for the delay of the back electromotive forces.
From US 5 506 487 a commutation method is known which does not use the detection of the zero-crossing. The three back electromotive forces are multiplexed onto one line and the polarity thereof is considered. A counter is counting up and down during periods with positive and negative multiplexed back-electromotive force respectively The counter counts until a predetermined value is reached, whereafter commutation is performed The predetermined value corresponds to the delay of the commutation after the zero-crossing of the back-electromotive force This method is relatively complicated and requires calculating power
The apparatus and method described in US 5327053 relate to solving a different problem, namely the detection of rotor position prior to starting up the motor The control of the motor after start up is based on a back-electromotive force zero- crossing commutation scheme which is not described in detail
DISCLOSURE OF THE INVENTION
It is the object of the present invention to provide a method and a device of the kind mentioned above of a simple nature, with which it is possible to control the motor with a selfregulating commutation angle without delay filters or time measurements and without the use of the mid point voltage of the motor, and this object is achieved with a method of said kind which according to the present invention comprises the steps set forth in the characterizing clause of claim 1 and a device of said kind which according to the present invention comprises the features set forth in the characterizing clause of claim 6 With this arrangement, the generating of commutation signals is performed in a simple manner taking advantage of the trapezoidal curve form of the back-electromotive forces which are compared to a low and high reference voltage, whereby these reference voltages are adjusted to achieve the correct timing of the commutation signals Furthermore, measurement of the zero-crossings of the back-electromotive forces is avoided which can be complicated due to electrical noise
Preferred embodiments of the method and apparatus are revealed in the subordinate claims 2-5 and 7-10, primarily aiming at simplifying the generation of the reference voltages BRIEF DESCRIPTION OF THE DRAWING
In the following detailed part of the present description, the invention will be explained in more detail with reference to the exemplary embodiments of a device for controlling a brushless electric motor according to the invention shown in the drawings, in which:
Figure 1 diagrammatically shows a brushless motor provided with a control system in accordance with the invention,
Figure 2 shows a more detailed circuit diagram of a preferred circuitry for generating a common reference voltage,
Figure 3 shows a corresponding circuit diagram for detecting the electromotive forces in the windings,
Figure 4 shows different signal wave forms at various points of the circuits shown in Figure 1-3, and
Figure 5 shows a second embodiment of a diagram for generating a common reference voltage.
DESCRIPTION OF THE OF THE PREFERRED EMBODIMENT
The brushless motor shown in Figure 1 comprises three armature windings U, V, W connected in a star configuration with a common midpoint P. Each winding U, V, W may be connected to the positive power supply or the negative power supply via transistors Q Qβ or corresponding switching elements. The power supply shown in Figure 1 consists of a controlled rectifier with smoothing inductor L and capacitor C. Regulating of the intermediate voltage UDc is performed by means of the controlled rectifier. The switching elements Q Q6 are controlled by a commutation generator in accordance with signals received from an electromotive-force detector in such a way that a rotating magnetic field is generated by the windings U, V, W to rotate the rotor of the motor, which preferably is a permanent magnet rotor. Measurement of the back-electromotive force (back EMF) is performed by measuring the voltage on the idle, currentless phase winding. The back-electromotive force detector generates commutation signals for the commutation generator by comparing the back-electromotive forces developed during operation in the windings U, V, W with a low and high reference voltage received from a low and high reference voltage generator. The low and high reference voltages are preferably combined into a common reference signal U∞M in order to simplify the circuitry in the back- electromotive force detector. Referring to Figure 2, the low and high reference voltages are provided by simple resistive voltage dividers R1 , R2, R3 using the intermediate voltage UDC and controlled by switching transistors T1 , T2, which are controlled in accordance with a pulse width modulation signal and a synchronizing signal received from the commutation generator and the electromotive force detector, respectively. Before delivery to the electromotive force detector, the voltage UR2 is smoothed by a resistance-capacitor network R4, C1 to define the common reference signal UCOM. More specifically the filter creates the mean value of the occasionally pulse width modulated voltage UR2.
In the following, the function of the control circuit shown in Figures 1-3 will be explained with reference to Figure 4 which shows different signal wave forms at various points of the circuit. A, B and C show the input signals to the comparators COMP 1-3 in Figure 3. As shown in A, the back EMF in the winding U has a trapezoidal wave form and is compared with the common reference signal UCOM for generating commutation signals for the commutation generator. The back EMF is superimposed on the midpoint voltage P. Starting from the left in A, the common reference signal UCOM is equal to the high reference voltage and the back EMF in the winding U is rising until it reaches and passes the level corresponding to the high reference voltage at the time marked ti, at which point the comparator COMP 1 changes its output from low to high, thereby signalling to the commutation generator that the switching element Q5 has to be switched off and the switching element Qi has to be switched on. At the same time, the common reference signal UCOM is changed to be equal to the low reference voltage. The next electromotive force crossing this low reference voltage is the back EMF from the winding W which crosses this low reference voltage at the time marked t2. This crossing makes the output from the comparator COMP 3 change from positive to negative, thereby indicating to the commutation generator that the transistor Q4 has to be switched off and the transistor Q6 has to be switched on, and at the same time changing the common reference voltage to the high reference voltage level. Corresponding processes are performed at the times t3, t», t5, t6 for one whole cycle for the system.
Following the explanation above, the comparators 1-3 in Figure 3 thus generate a three-bit-information signal which is sent to the commutation generator. Just after time ti the information signal is 1-0-1 representing the signals from comparators COMP 1 , 2 and 3 respectively. Inside the commutation generator, a look-up table contains stored commutation signals for the switches QrQβ- The information signal 1-0-1 from the comparators is used as a key to the look up table, and here the corresponding commutation signals stored are ( Q 5, Q 3, d; Q 6, Q4, Q 2)- As can be seen from Figure 4, commutation is activated each time a back EMF with positive slope crosses the high reference, and correspondingly each time a back EMF with negative slope crosses the low reference.
The synchronization signal for changing the common reference signal between the high reference voltage and the low reference voltage can be provided by a majority vote between the outputs from the comparators COMP 1-3. The synchronization signal is thus given each time one of the comparators changes state. As every state change is caused by a back EMF which is crossing either the high or low reference, the speed of the motor can be calculated from the number of state changes. As the synchronization signal is a speed dependent signal, the reference voltage UCOM will also be speed dependent. Alternatively, UCOM could be following the motor voltage on the phase U, V or W directly. Thus, the high and low reference automatically adapt to the motor speed enabling commutation also at a very low motor speed, where the amplitude of the generated back EMF is limited and detection of zero-crossings normally are problematic due to electrical noise.
An advantageous feature of the invention is the establishment of a selfregulating commutation angle. Normally, commutation is done about 15 degrees after the back EMF has made a zero crossing. Determining when the 15 degrees are reached can be solved in different ways, e g by using a counter counting up to a limit value from the time a zero crossing is detected, or alternatively integrating the back EMF from zero-crossing up to a limit value These methods, however, places demands on the control circuitry as to calculative power and precision as to the commutation instants Even slight deviations from the optimal commutation angle mean loss in motor effiency However, by synchronizing the reference levels with the motor speed, a selfregulating commutation angle α (shown in Figure 4A) is achieved During fixed speed operation, the value of the commutation angle α will be a fixed value, if on the other hand, the motor current increases, the motor voltage will also increase and the commutation angle α will become smaller If the load decreases, the angle α will increase, hereby keeping the optimum commutation timing The invention thus gives a selfregulating commutation angle α which is fixed related to the rotor speed and changes value, if changes in the load are occurring
Control of the switches Q Qθ during normal operation can be done by means of PWM modulation However, in this exemplary embodiment of the invention, the switches are block commutated, i e there is no change in the duration of the on- times However, during start up of the motor it may be appropriate to control the switching transistors Q Q6 in accordance with a PWM scheme in order to limit the current in the windings of the motor When using such a pulse-width-modulation scheme, the effective voltages supplied to the windings U, V, W are reduced and correspondingly, the back-electromotive forces from the windings are reduced Accordingly, in this situation it is necessary to reduce the corresponding high reference voltage and low reference voltage correspondingly This is provided by supplying sequentially the pulse-width-modulation signal used for pulse-width modulation of the switching transistors QrQ6, respectively, to the switching transistor T2 shown in Figure 2 The circuit described is simple, but has the drawback that the PWM switch T2 only pulls the voltage UR2 in one direction This leads to minor inaccuracies in the timing of the commutations It would be preferable to regulate the voltage UCOM around a center voltage (corresponding to UR2) which could be raised or lowered, giving more dynamic regulation possibilities A circuit for generating the voltage UCOM m said way is shown in Figure 5 The low reference voltage is generated with a signal on transistor T3 while T4 is off The high reference signal requires T3 to be off, whereas T4 is modulated with PWM. If T4 is switched on, the voltage on the basis of T5 decreases, and T5 starts conducting. The voltage UR6 is now essentially determined by the resistors R9 and R6 (R5»R9 and R6).
Although the invention has been described in connection with a preferred embodiment thereof, it will be understood that various changes may be performed without departing from the following claims, such variations comprising among other things using the high reference voltage and the low reference voltage without the change between the two levels and supplying those voltages to separate comparators, whereby the system shown in the drawings has to be changed in such a way that six comparators are used for comparing the back-electromotive forces with the two different reference voltage levels. Also, the invention could be used with a voltage stiff intermediate circuit as known in the art. This, however, would necessitate measurement of the phase voltages. Other modifications might involve using a motor with another number of windings than three, although this is preferred.

Claims

1. Method for controlling a brushless electric motor (M) provided with switching means (Qi-Qβ) for selectively supplying current to the armature windings (U, V, W) of the motor (M) from a DC-power supply (1), characterized by comprising the steps of:
measuring the back-electromotive forces developed during operation in the windings (U, V, W) of the motor,
generating a low reference voltage and a high reference voltage,
comparing said back-electromotive forces with said low and high reference voltages for generating commutation signals each time a measured back- electromotive force with positive slope crosses the high references voltage, and/or a measured back-electromotive force with negative slope crosses the low reference voltage, and
using said commutation signals to commutate the switching means (QrQe).
2. Method in accordance with claim 1, characterized by comprising the step of generating the low reference voltage and the high reference voltage as a common reference voltage signal (UCOM) constituted by a mainly square wave signal formed to correspond to the low reference voltage when comparing with a back-electromotive force with negative slope and to correspond to the high reference voltage when comparing with a back-electromotive force with positive slope.
3. Method in accordance with any of the preceding claims, characterized by comprising the step of generating the high and low reference voltages proportional to the voltage applied to the windings or proportional to the speed of the motor.
4. Method in accordance with any of the preceding claims, characterized by comprising the step of using pulse width modulation of the switching means (Q Q6) during start up of the motor and generating the high and low reference voltages or the common reference voltage signal (UCOM) by pulse width modulation of voltages proportional to the DC-power supply voltage used by the switching means (QrQe) for supplying current to the windings (U, V, W) of the motor.
5. Method in accordance with any of the preceding claims 2-4, cha racterized by comprising the steps of:
generating a control signal as a logic function of the result of the comparing of the electromotive forces and the reference voltage signal (UCOM), and
using said control signal to switch the common reference voltage signal between the low reference voltage and the high reference voltage.
6. Device for controlling a brushless electric motor provided with switching means (QrQ.6) for selectively supplying current to the armature windings (U, V, W) of the motor from a DC-power supply (1), characterized by comprising
means (4) for measuring the back-electromotive forces developed during operation in the windings (U, V, W) of the motor
means (2) for generating a low and a high reference voltage, and
means for comparing said back-electromotive forces with said low and high reference voltages and generating commutation signals each time a measured back-electromotive force with a negative gradient crosses the low reference voltage, or a measured back-electromotive force with a positive gradient crosses the high reference voltage, said commutation signal being supplied to a commutation generator (3) controlling said switching means (Q Q6).
7. Device in accordance with claim 6, characterized by the means (2) for generating the low and high reference voltages comprising means for generating a common reference voltage signal (UCOM) having a mainly square wave form, the common reference voltage signal (UCOM) being equal to the low reference voltage whenever comparing a back-electromotive force with a negative gradient and equal to the high reference voltage whenever comparing with a back-electromotive force with a positive gradient.
8. Device in accordance with claim 6 or 7, characterized by comprising means for generating the low and high reference voltages proportional to the voltage applied to the motor windings (U, V, W) or proportional to the speed of the motor.
9. Device in accordance with claim 6, 7 or 8, c h a r a c t e r i z e d by comprising means for driving the switching means (Qi-Qε) in a pulse width modulation scheme during start up of the motor and the means (2) for generating low and high reference voltages comprising means (T2) for pulse-width modulation of voltages proportional to the DC-power supply voltage supplied to the switching means (QrQ6), using the same pulse-width-modulation signals, and means for low pass filtering the resulting low and high reference voltages.
10. Device in accordance with claim 7, 8 or 9, c h a r a c t e r i z e d by comprising means for synchronizing the common reference signal (UCOM) with the commutation signals, said means for synchronizing comprising logic circuits supplied with the commutation signals and supplying a switching signal to switch the common reference signal between the low and high reference voltages.
PCT/DK1998/000442 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor WO2000022723A1 (en)

Priority Applications (6)

Application Number Priority Date Filing Date Title
DE69822896T DE69822896T2 (en) 1998-10-12 1998-10-12 METHOD AND DEVICE FOR CONTROLLING A BRUSHLESS ELECTRICAL ENGINE
US09/807,587 US6380707B1 (en) 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor
BR9816046-0A BR9816046A (en) 1998-10-12 1998-10-12 Process and device for controlling a brushless electric motor
AU94341/98A AU9434198A (en) 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor
EP98947415A EP1121753B1 (en) 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor
PCT/DK1998/000442 WO2000022723A1 (en) 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/DK1998/000442 WO2000022723A1 (en) 1998-10-12 1998-10-12 Method and device for controlling a brushless electric motor

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WO2000022723A1 true WO2000022723A1 (en) 2000-04-20

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US (1) US6380707B1 (en)
EP (1) EP1121753B1 (en)
AU (1) AU9434198A (en)
DE (1) DE69822896T2 (en)
WO (1) WO2000022723A1 (en)

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EP1121753A1 (en) 2001-08-08
US6380707B1 (en) 2002-04-30

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