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Transcript

A New Cost Effective Sensorless Commutation Method for Brushless DC Motors Without Phase Shift Circuit and Neutral Voltage Dec, 2008 高等伺服控制報告 授課老師： 王明賢 教授 學 生 ： 楊智淵 南台科大電機系 OUTLINE ABSTRACT I. INTRODUCTION II. MATHEMATICAL MODELS OF EACH COMMUTATION STATE III. PROPOSED ZCP DETECTION APPROACH BY AVERAGE LINE TO LINE VOLTAGE IV. ANALYSIS OF THE COMMUTATION ERROR V. EXPERIMENTAL EVALUATION VI. CONCLUSION REFERENCES 2 Abstract This paper presents the analysis, design, and implementation of a high performance and cost effective sensorless control scheme for the extensively used brushless dc motors. In an effort to decrease cost and increase ease of implementation, the commutation signals are obtained without the motor neutral voltage, multistage analog filters, A/D converters, or the complex digital phase shift (delay) circuits which are indispensable in the conventional sensorless control algorithms. In the proposed method, instead of detecting the zero crossing point of the nonexcited motor back electromagnetic force (EMF) or the average motor terminal to neutral voltage, the commutation signals are extracted directly from the specific average line to line voltages with simple RC circuits and comparators. 3 In contrast to conventional methods, the neutral voltage is not needed; therefore, the commutation signals are insensitive to the common mode noise. Moreover, the complex phase shift circuit can be eliminated. Due to its inherent low cost, the proposed control algorithm is particularly suitable for cost sensitive products such as air purifiers, air blowers, cooling fans, and related home appliances. Theoretical analysis and experiments are conducted over a wide operating speed range and different back EMF waveforms to justify the effectiveness of the proposed method. 4 I. INTRODUCTION DURING the last two decades, a lot of research on sensorless control techniques for brushless dc motors (BLDCMs) have been conducted. This research can be divided into four categories. Detection of the zero crossing point (ZCP) of the motor terminal to neutral voltage with a precise phase shift circuit. Back electromagnetic force (EMF) integration method. Sensing of the third harmonic of the back EMF. Detection of freewheeling diode conduction and related extended strategies . 5 The neutral voltage is required for comparison with the non-conducted back EMF or the average terminal voltage, in which it will introduce a high common-mode noise. Since the zero crossing points of the conventional back EMF method are inherently leading 30 electric degrees of the ideal commutation points, a precise velocity estimator and a phase shift circuit (algorithm) are needed to process the zero crossing signals so that accurate commutation points can be determined. 6 Instead of detecting the motor terminal to neutral voltage, the estimated commutation signals are extracted directly from the specific average line to line voltage of a BLDCM using simple single-stage low pass filters and low cost comparators. That is, the estimated commutation signals are well in phase with the ideal commutation points. Unlike conventional solutions, the proposed method does not require additional virtual motor neutral voltage, complex phase shift circuits, or precise speed estimators. 7 II. MATHEMATICAL MODELS OF EACH COMMUTATION STATE Fig. 1 shows the equivalent circuit of a BLDCM and the inverter topology. 8 Fig. 2 illustrates the relationship among the back EMF waveform of an ideal BLDCM, the armature current, the commutation signals (H1–H3), and the switching signals (S1–S6) for the inverter. According to the polarity of the armature current as illustrated in Fig. 2, the terminal voltage of each phase can be divided into three sub-sections, i.e., positive, negative, and nonconducted. 9 10 Fig. 3 illustrates the equivalent circuits of each commutation state for phase-“a ” over one electric cycle, and the same results can be obtained for the other two phases. 11 States I and II: Armature Current is Positive: Fig. 3(a) and (b) illustrate the equivalent circuit of the commutation states (I and II) where the armature current is positive. If the conduction voltage caused by the power switches and the diodes is negligible, then the terminal voltage can be obtained according to the switching status of the power switch S1 12 States IV and V: Armature Current is Negative: Fig. 3(c) and (d) illustrate the equivalent circuit of the commutation states (IV and V) where the armature current is negative. Since the switch S2 is turned on, the motor terminal is connected to the power ground. Therefore, the terminal voltage will be kept low despite the switching status of the upper legs 13 States III and VI: Armature is Open (Nonconducted): Fig. 3(e) and (f) illustrate the equivalent circuit of the commutation states (III and VI) where the armature is open. Since the armature is disconnected from the voltage source, the terminal voltage can be expressed as the summation of the armature back EMF and the neutral voltage 14 If the switch of the upper leg is conducted (e.g., S3 is on), the neutral voltage can be expressed as According to (6) and (7), the neutral voltage can be written as 15 If the switch of the upper leg is not conducted (e.g., S3 is off), the neutral voltage can be expressed as 16 17 Substituting (14) into (8) and (11), the motor neutral voltage can be rewritten as Substituting (12) and (13) into (5), the terminal voltage of a BLDCM which has an ideal trapezoidal back EMF waveform can be expressed as 18 Equation (18) represents the case where the back EMF waveform is perfectly sinusoidal 19 Note that each motor terminal is placed between the upper diodes, which are connected to the dc source, and the lower diodes of the inverter, which are connected to the ground. It can be expected that the maximum and minimum terminal voltages will be fixed between Vdc and 0. Fig. 4 shows the measured terminal voltage and the corresponding switching signals. It is found that the waveforms are in accordance with the theoretical analysis. 20 III. PROPOSED ZCP DETECTION APPROACH BY AVERAGE LINE TO LINE VOLTAGE The major problem of the conventional back EMF sensing techniques is that they require noisy motor neutral voltage and a fixed phase shift circuit. Since the noisy motor neutral voltage will introduce the common mode noise into the sensorless circuit, a low pass filter is indispensable. On the other hand, the fixed phase shift function over a wide speed range is hard to implement with analog circuits. In order to cope with the aforementioned problems, the proposed method extracts the commutation points directly from the motor terminal voltages with simple comparators and a single stage low pass filter. 21 If the terminal voltages are expressed in the average form (i.e., duty ratio), the switching states in (3), (4), (17), and (18) can beeliminated. The terminal voltages are rewritten as follows. States I and II: Armature Current is Positive: States III and VI: Armature is Open (Nonconducted): States III and VI: Armature is Open (Nonconducted): 22 According to (19)–(21), the ideal average terminal voltages for all three phases with different duty ratios are illustrated in Fig. 5. Fig. 5. Ideal average terminal voltages under different duty ratios. 23 The measured instantaneous (upper trace) and average (lower trace) terminal voltages as the duty ratio is increased from 10%,to 50%, to 100% are shown in Fig. 6. Fig. 6. Measured instantaneous (first trace) and average (second trace) terminal voltages under different duty ratios. (a) Duty ratio = 10%. (b) Duty ratio = 50%. (c) Duty ratio = 100%. 24 According to the average terminal voltage derived in (19)–(21), the average line to line voltage Vac can be expressed 25 Equation (23) reveals that the zero crossing points of the average line to line voltage will occur at 30 and 210 electric degrees. According to (22) and (23), Fig. 7 shows the phase relationship among the ideal back EMF, the average terminal voltage, and the average line to line voltage of phase “a ” and phase “c .” It is clear to see that the average line to line voltage Vac lags 30 electric degrees compared with the back EMFea , namely the zero crossing points of the line to line voltage are in phase with the ideal commutation signals. Fig. 7. Phase relationship among the back EMF, the average terminal voltage,and the average line to line voltage. 26 Table (I) summarizes the three specific line to line voltages for the proposed sensorless commutation approach. 27 • Fig. 8(a) illustrates the practical circuit for implementing the proposed approach to obtain the commutation signals (namely the virtual Hall effect signals H1~H3 ). • Consequently, the circuit needed in the proposed approach is much simplercompared with that needed in the conventional circuit shown in Fig. 8(b). Fig. 8. Proposed and conventional sensorless commutation circuits. (a) Proposed cost effective sensorless commutation circuit. (b) Conventional sensorlesscommutation circuit. 28 IV. ANALYSIS OF THE COMMUTATION ERROR A. Phase Delay by the Low Pass Filter and the Armature Impedance B. Voltage Spikes by the Residual Current 29 A. Phase Delay by the Low Pass Filter and the Armature Impedance The phase delay angles caused by the input low pass filter and the armature impedance shown in Fig. 9(a) and (b) can be expressed as Since the 30 (or 90 ) phase shift circuit shown in Fig. 8(b) is not required in the proposed approach, the corner frequency fc of the input low pass filter can be easily determined by the maximum motor speed RPMmax and the switching frequency fs , in which the value of fc can be chosen as 30 The phase delay caused by the armature impedance can be neglected in most small to mid-sized BLDCMs due to the fact that the value of the resistance is usually much larger than the inductance. The current loop compensator can be used to overcome the delay caused by the armature impedance, however, it is not needed in most home appliance applications since it is only required in very high speed applications. 31 B. Voltage Spikes by the Residual Current The voltage spikes shown in Figs. 4 and 6 are created by the residual current when the armature current is blocked by the power switches. The voltage spike is the main cause for the commutation error in the conventional back EMF integration method and the window-captured back EMF method (detecting back EMF during the silent period) . 32 Fig. 9. Illustration of various commutation errors. (a) Low pass filter. (b) Armature impedance. (c) Effect of the voltage spike. 33 V. EXPERIMENTAL EVALUATION Fig. 10 shows the block diagram of the proposed sensorless control method. The system can be divided into several subblocks, including a velocity command generator, an open loop starting process, a line to line voltage based virtual Hall effect signal circuit, an electric commutation table, and a PWM generator. Fig. 10. Block diagram of the overall system. 34 Fig. 11. Structure of the employed BLDCMs. (a) Type I (segmented magnet), trapezoidal back EMF. (b) Type II (ring magnet), sinusoidal back EMF. 35 Fig. 12. Measured back EMF waveforms of employed BLDCMs. (a) Type Imotor. (b) Type II motor. 36 Fig. 13. Measured commutation signals under different duty ratios and back EMF waveforms (from top to bottom: average terminal voltage V a, average terminal voltage Vc , average line to line voltage Vac , estimated commutation signal, signal from Hall effect sensor). (a) Duty ratio = 10%, type I motor. (b) Duty ratio= 50%, type I motor. (c) Duty ratio = 100%, type I motor. (d) Duty ratio = 10%, type II motor. 37 It can be seen that the signal from the conventional solution strongly depends on the operating speed; the mismatch angle is leading 21.8 in 10% full-speed . Fig. 14. (a) Duty ratio = 10%. 38 Lagging 14.4 in 50% full-speed. Fig. 14. (a) Duty ratio = 50%. 39 lagging 22.8 in full speed. Fig. 14. (a) Duty ratio = 100%. 40 The large commutation error is mainly caused by the multistage filters; thereforea speed dependent phase compensation algorithm is usually indispensable. Compared with the conventional solution, the proposed method is not only easier to design and implement, but also exhibits better performance. 41 VI. CONCLUSION Unlike conventional back EMF based sensorless commutation methods which focus on detection of the ZCP of the motor terminal to neutral voltage, a novel sensorless commutation method based on the average line to line voltage is proposed in this study. Both theoretical analysis and experimental results verify that satisfactory performance can be achieved with the proposed sensorless commutation method. Compared with the conventional solutions, the proposed method has several advantages, including the following. 42 Elimination of the motor neutral voltage: Elimination of the fixed phase shift circuit: Since the amplitude of the line to line voltage is significantly larger than the phase voltage, even a small back EMF can be effectively detected. Namely, a lower open loop starting speed can be achieved. Insensitive to the back EMF waveform: The proposed specific average line to line voltage inherently lags 30 electric degrees compared with the phase back EMF. Moreover, experimental results have revealed that thephase relationship is insensitive to operating speed and load conditions. Low starting speed: The neutral voltage is not required in the proposed method, only the three motor terminal voltages need to be detected. Compared with the third-harmonic detection method, the proposed method can be used for a BLDCM with nonideally trapezoidal or sinusoidal back EMF waveforms, since most BLDCMs do not have ideal back EMF waveforms. Cost effective: Because the speed estimation algorithm and the complex phase shift circuits are not required, the costly digital signal processor controller is not needed. Using a simple starting process, the proposed method can be easily interfaced with the low cost commercial Hall effect sensor based commutation ICs. Consequently, the proposed method is particularly suitable for cost sensitive applications such as home appliances and related computer peripherals. 43 REFERENCES 44 45