The performance of the developed sensorless technique is demonstrated by simulation, and then, it is implemented using TMS320LF2407A DSP

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Abstract—This paper presents the analysis, design, and imple- mentation of a cost-effective sensorless control technique for a low- cost four-switch, three-phase inverter brushless dc motor drive.

The proposed sensorless technique is based on the detection of zero crossing points (ZCPs) of three voltage functions that are derived from the filtered terminal voltages and . Six commutation instants are provided that coincide to ZCPs of voltage functions.

Hence, there is no need for any 30 or 90 phase delay that is prevalent in conventional sensorless methods. Two low-pass filters are used for elimination of high-frequency noises and calculation of average terminal voltages. Also, a direct phase current control method is used to control the phase currents in the four-switch inverter. An analytical study on position estimation error is dis- cussed, and a correction method for some typical applications is suggested. The performance of the developed sensorless technique is demonstrated by simulation, and then, it is implemented using TMS320LF2407A DSP. Experimental results are provided to con- firm the simulations.

Index Terms—Brushless dc (BLDC) motor drive, four-switch in- verter, phase shift, sensorless control.

I. INTRODUCTION

Permanent-magnet brushless dc (BLDC) motor is increas- ingly being used in automotive, computer, industrial, and household products because of its high efficiency, high torque, ease of control, and lower maintenance. A BLDC motor is designed to utilize the trapezoidal back EMF with square-wave currents to generate the constant torque [1]. A conventional BLDC motor drive is generally implemented via a six-switch, three-phase inverter and three Hall-effect position sensors that provide six commutation points for each electrical cycle. Cost minimization is the key factor in an especially fractional horse- power BLDC motor drive for home applications. It is usually

Manuscript received January 27, 2008; revised April 17, 2008. Current version published December 09, 2008. This paper was presented in part at the IEEE International Conference on Electrical Machines and Systems (ICEMS’07), Seoul, Korea, October 8–11, 2007. Recommended for publication by Associate Editor K.-B. Lee.

A. Halvaei Niasar is with the Iran University of Science and Technology (IUST), Tehran 16846-13114, Iran and also with the Department of Elec- trical Engineering, Faculty of Engineering, University of Kashan, Kashan 87317-51167, Iran (e-mail: [email protected]).

A. Vahedi is with Iran University of Science and Technology, Tehran 16846- 13114, Iran (e-mail: [email protected]).

H. Moghbelli is with Isfahan University of Technology, Isfahan 84154, Iran, and also with the Department of Science and Mathematics, Texas A&M Univer- sity at Qatar, Doha 23874, Qatar (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2008.2002084

achieved by elimination of the drive components such as power switches and sensors. Therefore, effective algorithms should be designed for the desired performance. Recently, a four-switch, three-phase inverter (FSTPI) topology has been developed and used for a three-phase BLDC motor drive. Reduction in the number of power switches, dc power supplies, switching driver circuits, losses and total price are the main features of this topology. However, in the four-switch topology, conventional control schemes are not effective for current regulation. Leeet al. [2] developed a new and effective current control scheme to obtain 120 rectangular currents based on the independent control of the phases’ current.

Manufacturing cost of a BLDC motor drive can be reduced more by elimination of position sensors and by developing feasible sensorless methods. Furthermore, sensorless control is the only choice for some applications where these sensors cannot function reliably because of the harsh environments.

The major sensorless methods published in the literature can be classified as follows [3], [4]: back EMF sensing techniques, flux estimation method, stator inductance variations method, observers, and intelligent control methods. The sensorless techniques utilizing the back EMF voltage include: 1) terminal voltage sensing; 2) third-harmonic back EMF voltage sensing;

and 3) freewheeling diode conduction current sensing. Sensor- less techniques based on back EMF are the most popular due to their simplicity, ease of implementation, and lower cost [5]–[7], which lead to the manufacture of the commercial sensorless ICs [8]. There are many papers that utilize back EMF voltage and detection of the zero crossing point (ZCP). A 30 phase delay between ZCPs and commutation instants is usually carried out via a speed-dependent phase shifter, a lookup table, or by using a hardware fixed-phase shifter. It needs more hardware or complicated software that may lead to computational errors.

Some authors tried to develop a frequency-independent phase shifter to overcome the mentioned problem [9].

Most of the sensorless methods for a six-switch inverter BLDC motor drive are not directly applicable to the four-switch inverter. The main reason is that in the four-switch topology, some methods detect less than six points, and other commutation instants must be interpolated via software. So far, there are few researches on sensorless control of a four-switch inverter, three-phase BLDC motor drive. Lately, Linet al.[10] proposed a new sensorless control method for the four-switch topology.

Based on the experimental results, they found that two crossing points between terminal voltages A and B coincide to two commutation instants, and other four commutation instants

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3080 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 6, NOVEMBER 2008

Fig. 1. Four-switch inverter, BLDC motor drive, and equivalent circuit of the BLDC motor.

Fig. 2. Signal waveforms of a BLDC motor.

are attained via interpolation and shift delay software. Halvaei Niasar et al.[11] introduced three new error functions in the four-switch inverter topology where their ZCPs are 30 before the commutation points. Therefore, a 30 shift delay should be carried out. This paper presents a low-cost sensorless approach for the four-switch inverter topology, which does not need any phase shift. The proposed approach uses the ZCPs of three voltage functions (line-to-line voltages), so that they coincide to six commutation points. Theoretical analysis, simulations, and several experiments are conducted to demonstrate the feasibility of the proposed sensorless method [12].

II. ANALYSIS OF AFSTPI-BLDC MOTORDRIVE

Fig. 1 shows the configuration of a four-switch inverter in- cluding the equivalent circuit of a three-phase BLDC motor. The typical mathematical model of the BLDC motor is represented as follows:

(1) where , , , , and represent the voltage, back EMF, phase current, self-inductance, and mutual inductance of phase x, respectively (x=a,b,c). Fig. 2 shows phase back-EMF, current waveforms, and Hall-effect sensor signals of a three-phase

Fig. 3. Voltage functions and phase back EMF voltages waveforms in a four- switch, BLDC motor drive.

TABLE I

COMMUTATIONLOGICWITHRESPECT TOVOLTAGEFUNCTIONS

Fig. 4. Simulation block diagram of the sensorless-controlled, four-switch BLDC motor drive.

TABLE II BLDC MOTORPARAMETERS

BLDC motor drive in ideal case. During each operation mode, only two phases are conducting and the third phase is inac- tive. To drive the motor with maximum and constant torque, the phase currents should be rectangular. However, in a four-switch inverter, the generation of 120 conducting current profiles is inherently difficult [2]. Hence, in order to use the four-switch inverter topology for a three-phase BLDC motor, a direct phase

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Fig. 5. Simulation results: terminal voltages, voltage functions, virtual Hall signals, and phase current waveforms of the developed sensorless control method. (a) At speed of 30 r/min. (b) At speed of 220 r/min.

current (DPC) control approach is used, i.e., the currents of phases A and B in two modes II and V are controlled via independent current regulators. Therefore, the back EMF voltage of phase C does not disturb the phase currents. Based on the independent switching of two phases A and B, current profiles are similar to the currents of a six-switch inverter BLDC motor drive.

III. SENSORLESSCONTROL OF ANFSTPI-BLDC MOTOR

DRIVEBASED ONVOLTAGEFUNCTIONS

Terminal voltages of a BLDC motor in the four-switch inverter with respect to the mid-point of the dc bus are as follows:

(2) Three voltage functions (VFs) are derived from two terminal voltages and as

(3) Fig. 3 shows the waveforms of voltage functions and phase back EMF voltages. Neglecting the voltage drop on the stator impedance, voltage functions lag 30 inherently rather than phase back EMF voltages, which means that the ZCPs of VFs coincide to commutation instants. Using simple comparators

circuits, zero crossings of VFs are detected, and the virtual Hall sensor signals , and are generated that can be used for current commutation. Table I summarizes the relation between virtual Hall sensor signals and the corresponding operation modes.

IV. SIMULATIONRESULTS

Fig. 4 shows the overall block diagram of the sensorless-controlled, four-switch inverter BLDC motor drive in Simulink. A high-torque, low-speed BLDC motor with 16 poles is used for simulation and its parameters are given in Table II. The speed control block provides the current reference. In the current control block, the currents of two phases A and B are regulated via two independent hysteresis controllers with a hysteresis band of 0.05 A. In the power inverter block, proper phase voltages are generated and applied to the BLDC motor using the developed duty cycles. The zero crossing detector block detects the ZCPs of the voltage functions and then develops virtual position Hall signals for sensorless control. Two second-order Butterworth low-pass filters with passband frequency of 700 rad/s are used to eliminate the high-frequency components of PWM voltages.

Fig. 5 shows the estimated operation mode, voltage signals, and phase currents at speeds of 30 and 220 r/min where the phase currents are rectangular. The filtered terminal voltages are used to determine the voltage functions. There are some glitches on the current due to the position estimation error, which are dis- cussed in the following section.

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Fig. 6. Analysis of the estimation error. (a) Voltages signals. (b) Estimation error due to the voltage drop on the stator impedance. (c) Current commutation via virtual Hall signals. (d) Phase delay of low-pass filters.

V. ANALYSIS OF THEPOSITIONESTIMATIONERROR

The position estimation error of the developed sensorless method is generated by a voltage drop on the stator impedance, phase delay of the filters, and voltage measurement, which are explained as follows.

A. Voltage Drop on the Stator Impedance

The developed voltage functions inherently lag 30 from phase back voltages, as mentioned earlier. It is due to the fact that the voltage functions contain the line back EMF voltages.

However, the voltage drop on the stator impedance shifts the ZCPs of the voltage functions from those of the corresponding line back EMF voltages. The estimation error due to stator impedance is analyzed for all operation conditions, and analytic relations are developed as follows. For simplicity, the voltage drop on the stator inductance ( ) is ignored, which means that the current commutation is considered ideal. It is a true assumption in most small- to mid-sized BLDC motors because the resistance voltage drop is usually much larger than the inductance voltage drop. Fig. 6(a) illustrates a close look at the voltage waveforms of phase A. The zero crossing of is used for current commutation of phase A. There is an inherent delay angle ( ) between the signal and the line back EMF voltage . The voltage function from (2) and (3) can be revised as

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In mode I, as shown in Fig. 2, phases B and C are conducting

the current and then . Hence, by

neglecting the term , the line back EMF voltage is obtained as

(5) Therefore, at ZCP of (at = ′), the line back EMF voltage has the value ofRI. The estimation error can be obtained easily from the similarity of two triangles OAH and OA′H′shown in Fig. 6(a) as follows:

(6) where , and are the load torque, torque constant, back EMF constant, and the rotor speed, respectively.

Equation (6) implies that as long as the load torque is increasing, the estimation error also increases, and while the speed is increasing, the estimation error decreases. Fig. 6(b) shows variations of the estimation error for different speed and load conditions. At high speed, the estimation error reduces to 4 . However, at low speed and under heavy loads, the estimation error increases, in which the operation of the sensorless algorithm is limited to a certain speed. To obtain this limitation by using Fig. 6(c), the phase back EMFs and currents in the interval

can be represented as

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Fig. 7. Hardware schematic of the sensorless-controlled, four-switch BLDC motor drive based on TMS320LF2407A DSP.

Hence, the air gap power during interval is obtained as (8)

To have a reliable sensorless operation at low speeds, a sufficient condition is that the instant output power of the motor should be positive (in forward motoring case). Equation (8) shows that the estimation error must satisfy . For the BLDC motor used in this study and by substituting the motor parameters into (6), the low limit point of the speed is obtained about 40 r/min in full-load condition. Although this limit point may be a bit higher due to the voltage drops on power switches, diodes, and also the neglected term . Therefore, the voltage drop on the stator impedance is the main source of the estimation error at low speed range.

B. Phase Delay of the Low-Pass Filters

Designing the proper filters is important for zero crossing detection of the voltage functions, because the terminal voltages are PWM signals. In this paper, two second-order Butter- worth low-pass filters are designed [13]. To adjust the filters, the measured PWM voltages have been processed in Matlab, and the passband frequency of the filters have been set to 100 Hz (with 0.1 dB attenuation). Fig. 6(d) shows the phase delay versus frequency for the designed filters. The phase delay at two frequencies of 6.5 Hz ( ) and 35 Hz (

) are 1.5 and 5 , respectively.

C. Measurement Errors

The sensorless algorithm developed in this study is based only on the filtered terminal voltages and . Therefore, the accuracy of the measured voltages directly affects the accuracy of the position estimation. Using exact components to make the low-pass filters also reduces the position estimation. Pro- viding the virtual Hall position signals via hardware eliminates the quantization error due to the analog-to-digital (A/D) conver- sion.

Fig. 8. Main control flowchart of the system software.

Fig. 9. Measured back EMF voltages of the employed BLDC motor.

All error sources mentioned in this section cause the estimated commutation instants to lag rather than real commutation instants, and there is no room for compensation. Determi- nation of voltage functions and corresponding virtual Hall signals can be carried out through the software to solve the mentioned problem. Calculated voltage functions are compared with the proper thresholds. This approach advances the commutation that can compensate any phase delay. However, it increases the amount of calculations and leads to more complex algorithms, which is against the objectives of employing an inexpensive and simple sensorless control algorithm for a FSTPI-BLDC motor drive. For some cost-sensitive applications such as fan, blowers, etc., where the load increases when speed increases, the proposed sensorless algorithm (without error compensation in the software) is feasible and can be implemented via an inexpensive microcontroller.

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Fig. 10. Measured instantaneous and filtered terminal voltagesV andV at (a) 60 r/min and (b) 220 r/min. Voltage functions waveforms at (c) 60 r/min and (d) 220 r/min.

VI. DSP IMPLEMENTATION OF THESENSORLESSTECHNIQUE

A. System Hardware Structure

Fig. 7 shows the schematic diagram of the hardware system, where the system is controlled via a DSP controller TMS320LF2407A [14]. DSP commands are isolated and am- plified via HCPL A316J gate drivers and the phase currents are measured via LA55-P current transducers. The sensorless technique developed in this study uses the measured terminal voltages, where the Hall-effect linear transducer LV25-P is used. Determination of the voltage functions and making the virtual position signals are carried out via hardware. Therefore, it is possible to employ the capabilities of the capture unit in the event manager module of DSP.

B. Software Organization

The developed software is based on four modules: system initialization, protection, startup, and run modules, as shown in Fig. 8. The first step for the development of the software is to initialize all peripherals on the DSP board, which includes the initialization of PWM ports, timer interrupt, and A/D converters.

The second module checks the safety of the drive. In the third module, a startup procedure for the sensorless control is provided. Open-loop starting is a practical control procedure to run the BLDC motor without position sensors that is accomplished by providing a rotating stator field with a certain frequency pro- file [15]. This method should be started from a certain initial rotor position. However, for a motor with no reluctance variation around the air gap, determination of the rotor initial position is impossible, and consequently, the forced alignment of the rotor must be implemented. In this paper, after energizing two phases A and B (mode II) for enough time, the next commutation signals advancing the switching pattern by an electrical 60 angle is given. After that one electrical evolution elapsed, the sensorless closed-loop control is run.

C. Experimental Results

Fig. 9 shows the measured phase back EMF voltages where the rising edge of position signal is simultaneous with the flat part of the back EMF voltage . Fig. 10(a) and (b) shows the instantaneous and the filtered terminal voltages at two speeds of 60 r/min (360 electrical r/min) and 220 r/min (1760 electrical

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Fig. 11. Developed virtual position signals under different conditions. (a) At 60 r/min and no load. (b) At 60 r/min under 70% full load. (c) At 220 r/min and no load. (d) At 220 r/min under 70% full load.

r/min). The dc bus voltage is 60 V, whereas the voltage sensors are set such that the voltage range 35 to 35 V is converted to 0–3.3 V into DSP. Therefore, the voltage scale in Fig. 10 is 70/3.3 = 21v/v.Fig. 10(c) and (d) shows the corresponding voltage functions waveforms at 60 and 220 r/min, respectively, that have the same amplitude. Fig. 11 shows the estimated position signals at different conditions that indicate that the estimated signals in all conditions are together at 120 . At no-load condition, the estimation error is 4 and 4.5 at low and high speeds, respectively. Due to the increase of rotational losses at high speed for the BLDC motor used, there is actually not a no-load condition. Therefore, at high speed with no-load condition, there is some estimation error. The estimation error under 70% full-load condition at low and high speeds are 24 and 14 . The measured estimation errors confirm the simulation and also the proposed analysis error.

Fig. 12 shows the current waveforms at different conditions where the current scale is 6 A/V. The motor is started using the open-loop startup algorithm, as mentioned earlier. Forced alignment takes about 1.2 s, as shown in Fig. 12(a), and the open-loop control is applied for one electrical cycle. It can be done for less

than one electrical cycle under lower load. Experimental results show that the developed sensorless algorithm can be applied at 30 r/min for no-load condition. Fig. 12(b) shows the current waveforms for no-load condition when the sensorless control is applied. It indicates that the rotational loss of the BLDC motor is considerable. Current waveforms under load condition at low and high speeds are shown in Fig. 12(c) and (d), respectively.

In both cases, the sensorless control of the currents as well as employing the DPC control method is successful.

VII. CONCLUSION

A low-cost BLDC motor drive is introduced in this study.

Cost saving is achieved by reducing the number of inverter power switches and also by elimination of the position Hall-effect sensors. For current commutation, virtual Hall signals are developed by a novel sensorless method using line-to-line voltages that are calculated from the measured terminal voltages. Simulation and experimental results verify the validity of the proposed sensorless method. The proposed error analysis shows that the voltage drop on the stator impedance is the main

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Fig. 12. Phase current waveforms using virtual position signals. (a) Motor startup. (b) At 220 r/min and no load. (c) At 60 r/min under 70% full load. (d) At speed 150 r/min under 70% full-load conditions.

error source especially at low speeds. Therefore, the developed sensorless method is suitable for applications when the load is increasing as the speed increases. The main advantages of the proposed method are as follows.

1) Full (six) commutation points are detected in the four- switch inverter drive. Therefore, extra phase-shifting circuits or interpolation in the software for prediction of other commutation points are not required.

2) Commutation points immediately follow the developed virtual Hall sensors. Therefore, 30 phase shifting as used in the methods based on back EMF voltage is not required.

3) Voltage functions are determined directly from the terminal voltages A and B without making the motor neutral point.

4) The proposed sensorless technique is independent of the back EMF waveform that can be applied to permanent- magnet synchronous [brushless ac (BLAC)] motors.

For low-cost applications, the implementation of the proposed method is easier and less expensive than that of other methods even with the sensorless methods based on back EMF voltage. Therefore, it is more attractive and cost-effective, and it can be implemented as integrated circuits (ICs).

REFERENCES

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Abolfazl Halvaei Niasar(S’04–M’09) was born in Kashan, Iran, in 1974. He received the B.S. degree from Isfahan University of Technology (IUT), Isfahan, Iran, in 1998, the M.S. degree from the University of Tehran (UT), Tehran, Iran, in 2000, and the Ph.D. degree from Iran University of Science and Technology (IUST), Tehran, Iran, all in electrical engineering

He is currently an Assistant Professor at the Department of Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran. His current research interests include DSP-based control systems, electric drives, permanent-magnet brushless dc motor drives, sensorless drives, and design of high speed motors.

Dr. Halvaei Niasar is a Member of the IEEE Power Electronics Society (PELS) and the IEEE Industry Applications Society (IAS).

Dr. Vahedi is a member of the Institution of Electrical Engineers (IEE) and the Society for Electrical Engineering (SEE).

Hassan Moghbelli(M’90) was born in Isfahan, Iran, in 1950. He received the B.S. degree from Iran Uni- versity of Science and Technology (IUST), Tehran, Iran, in 1973, the M.S. degree from Oklahoma State University, Stillwater, in 1978, and the Ph.D. degree 1989 from the University of Missouri-Columbia (UMC), Columbia, in 1989, all in electrical engineering.

He is currently an Assistant Professor at Isfahan University of Technology, Isfahan. He is also a Vis- iting Assistant Professor in the Department of Sci- ence and Mathematics, Texas A&M University at Qatar, Doha, Qatar. He has directed several projects in the area of electric drives, power systems, electric vehicles, hybrid electric and fuel cell vehicles, and railway electrification. His current research interests include electric drives, power electronics, and design of electric and hybrid electric vehicle.

Dr. Moghbelli is a member of the American Society of Mechanical Engineers (ASME) and the Society of Automotive Engineers (SAE).