Comparison of Performance of Brushless DC Drives underDirect Torque Control and PWM Current Control

Z. Q. Zhu, Y. Liu, D. HoweDepartment of Electronic and Electrical Engineering, The University of Sheffield

Mappin Street, Sheffield, SI 3JD, United Kingdom

Abstract Direct torque control (DTC) was originallysuccessfully developed for induction machine drives, and,more recently, to permanent magnet brushless AC (BLAC)drives. In this paper, the performance of DTC controlledbrushless DC (BLDC) drives is compared with that ofPWMcurrent controlled BLDC drives with and without currentshaping. The paper reports the simulation and experimentalinvestigation, as well as the analysis of torque waveformsand torque ripples. It shows that, in addition to well-knownfast torque response, the DTC controlled BLDC drive exhib-its significantly less low-frequency torque ripples than thePWM current controlled BLDC drive without current shap-ing, while it is easier to implement than the PWM currentcontrolled BLDC drive with current shaping.

I. INTRODUCTION

Numerous current control approaches have beenadopted to minimize the torque pulsation by generatingspecialized current reference to compensate torque rip-ples. For example, a solution to obtain a smooth torque ofBLDC motor over a wide speed range was proposed in[1]. The compensation and prediction terms were added tothe controller output. A new current control algorithmusing Fourier series coefficients was presented and com-pared with the conventional PWM methods in [2]. It re-duced the current ripples as well as the noise and vibra-tion. By attenuating the undesired pulsation, torque con-trol methods were also proposed for the BLDC motors.State feedback input-output linearization techniques wereused to select the outputs so that the torque-voltage rela-tionship was not only linearized but also optimized [3].Simulations show the high performance of the proposedscheme. The concept of direct torque control of a BLACdrive was extended in [4] to a BLDC drive to achieveinstantaneous torque control and the major differencesbetween the DTC ofBLDC drives and BLAC drives werepresented.

In this paper, the performance of BLDC drives underdirect torque control and PWM current control is com-pared. It will be shown that low-frequency torque ripplewhich would result with a conventional PWM currentcontrol can be eliminated automatically by optimizing thephase current waveform in accordance with the back-EMF waveform. Simulated results are presented and vali-dated by experiments.

II. CURRENT PWM CONTROL OF BLDC DRIVES

The common control algorithm for a permanent magnetBLDC motor is PWM current control. It is based on the

assumption of linear relationship between the phase cur-rent and the torque, similar to that in a brushed DC motor.Thus, by adjusting the phase current, the electromagnetictorque can be controlled to meet the requirement. It isvery simple and widely used in the many low-cost appli-cations [5]. However, the coupling characteristics be-tween the feed current and the resultant torque is actualnonlinear. In a BLDC drive system, the imperfection ofback EMF and the phase current commutations are themajor causes of the electromagnetic torque pulsation.

A. ConventionalPWM Current Control

The general structure of a current controller for aBLDC motor is shown in Fig. 1. The instantaneous cur-rent in the motor is regulated in each phase by a hysteresisregulator, which maintains the current within adjustablelimits. The rotor position information is sensed to enablecommutation logic, which has six outputs to control theupper and lower phase leg power switches. The currentreference is determined by a PI regulator, which main-tains the rotor average speed constant.

B. PWM Current Control with Current Shaping

In order to reduce torque ripples, it requires an ap-propriate current reference, which could be relativelycomplex and difficult to implement. In this section, forsimplifying explanation, a simple example of current con-trol with current shaping technique is presented. Fig.2shows the schematic ofPWM current control with currentshaping. In contrast to the conventional PWM currentcontrol, the current reference is generated according to thepre-determined back-emf waveform to maintain electro-magnetic torque constant. The hysteresis current regulatoradjusts the phase current according to the current refer-ence. The electromagnetic torque equation in BLDC driveis:

T =-(eaia + ebib + e,i, )a0a (1)

where co is the rotor mechanical speed, ea, eb and e, arethe back-emf of phase a , b and c, respectively. The ia, iband i, are the phase current of phase a, b and c, respec-tively.

Since the mechanical time constant is much biggerthan the electrical time constant, it can be deduced thatthe electromagnetic torque will keep constant when thephase currents are controlled as the inverse of back-emfwaveforms by assuming a constant rotor speed.

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Speed commnd Current reference

Fig. 1. Schematic of conventional PWM current control.

Speed comad Current reference

Fig. 2. Schematic ofPWM current control with current shaping.

Fig. 3. Schematic ofDTC BLDC drive.

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III. DIRECT TORQUE CONTROL OF BLDC DRIVES

Similar to the concept of DTC for BLAC drives [6],the DTC strategy of BLDC drives is based on the flux-linkage observers. The stator flux-linkage vector can beobtained from the measured stator voltages, uS, and cur-

rents, is . The magnitude and position of the stator flux-linkage can be calculated, respectively. The electromag-netic torque equation for a BLAC motor can be expressedin the stationary reference frame as:

T 2p(vI sa is6- Vs,63s) (2)

where p is the number of poles.For a surface-mounted BLDC motor with non-

sinusoidal back-emfs, the electromagnetic torque equationcan be expressed as:

3 p dV dYifipT =_-1V2 ra isa + iS.i (3)

where 0e is the rotor electrical angle. VIra and Y'rj3 are

the rotor flux-linkage in the oc-axis and the f-axis of thestationary reference frame, respectively, which can becalculated as:

IV. SIMULATED AND EXPERIMENTAL RESULTS

The current and torque control methods with singleswitch chopping mode for BLDC drives are validated bysimulation and experiment for a surface-mounted perma-nent magnet BLDC motor, whose parameters are given inappendix. The simulation model is developed using Mat-lab/Simulink, and is used to predict the electromagneticperformance of the drives. The main elements of the ex-perimental drive system are shown in Fig. 4. The controlsystem is composed of DAC boards, ADC boards, atransducer board, a TMS320C3 1 DSP, on which the con-trol algorithms are implemented, and a rotor positionboard, which is simply an interface between the DSP andthe rotor position sensor, which is an incremental encoder.Each DAC board has four 12-bit digital-to-analogue con-verter (AD767) channels, which are used to output pa-rameters such as the rotor speed and stator phase current.Its output port provides gate drive signals for the powerswitching devices. Each ADC board has four 12-bit ana-logue-to-digital converter (AD678) channels and a 12-bitdigital input parallel port. In addition, there are currenttransducers (LEM LA25-NP) and voltage transducers(LEM LV25-P). The phase currents and voltages aremeasured and sampled by the transducer board and ADCboard, respectively.

(4)

(5)

where L, is the stator winding inductance. Since equation(2) can be regarded as a particular case of equation (3),when the back-emf waveform is sinusoidal, and repre-sents the fundamental component of the electromagnetictorque. When the back-emf waveform is non-sinusoidal,in general, equation (3) should be used for torque calcula-tion.

In a BLAC drive, the voltage space vectors can be rep-resented by 3 digits, which fully represent all the states ofthe inverter switches. In a BLDC drive, however, sincethe upper and lower switches in a phase leg may both besimultaneously off, irrespective of the state of the associ-ated freewheel diodes, 6 digits are required, one digit foreach switch. The voltage space vectors in the oc-f refer-ence frame for a BLDC drive have a 30° phase differencerelative to those for a BLAC drive. Two non-zero voltagespace vectors now bound each section of the vector circle,while in a BLAC drive each section is centered on a non-zero voltage space vector. Fig. 3 shows a schematic of aDTC BLDC drive, which is essentially the same as thatfor a DTC BLAC drive, except for the switching table andtorque estimation.

In summary, the main difference between the DTC ofBLDC and BLAC drives are in the torque estimation andthe representation of the inverter voltage space vectors.The control algorithms for the demand torque, the statorflux-linkage and the output voltage vectors can be estab-lished in a similar manner to those for BLAC drives.

Fig. 4. Schematic ofBLDC drive system.

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0.0125 0.025 0.0375Time (s)

Fig. 5. Back-emf waveforms of the motor.

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Fig. 5 shows the phase and line back-emf waveformsof the motor. The simulated and measured waveforms ofphase current and electromagnetic torque using conven-tional PWM current control are given in Figs.6 and 7,respectively. It can be seen that the phase current is flattop with 120° elec. conduction period and the electro-magnetic torque exhibits significant low-frequency torquepulsations. Figs.8 and 9 compare the simulated and meas-ured results of phase current and electromagnetic torque

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V'ra ::::::: Vsa -Ls isa

Vf r,6 Vf s,6 Ls is,6

using a PWM current control with current shaping, re-spectively. As will be seen, the phase current reference isgenerated according to the pre-determined back-emfwaveform. The phase current follows the current refer-ence by a current controller, which eliminates the low-frequency torque ripples. Fig. 10 shows the simulatedphase winding terminal to ground voltage, phase voltage,phase current and electromagnetic torque when the directtorque control is employed. The corresponding experimentresults are given in Fig.11. In general, good agreement isachieved between simulated and measured results. It willbe seen that the phase current waveform inherently fol-lows the inverse of the back-emf waveform within each60° elec. sector of the 120° elec. conduction period so asto maintain the electromagnetic torque constant. The highfrequency torque ripple exists in the simulated results dueto the low winding inductances and PWM events. How-ever, the low frequency torque ripple, which would haveresulted with a conventional current control, has beeneliminated by automatically optimizing the phase currentwaveform in accordance with the back-emf waveform. Inaddition, comparing current control with current shaping,direct torque control is potentially more attractive since itis easier to implement with faster torque response.

REFERENCES

[1] C. S. Berendsen, G. Champenois and A. Bolopion, "Commutationstrategies for brushless DC motors: influence on instant torque,"IEEE Transactions on Power Electronics, Vol.8, No.2, April 1993pp.231-236.

[2] T. S. Kim; S. C. Ahn and D. S. Hyun, "A new current control algo-rithm for torque ripple reduction of BLDC motors," The 27th An-nual Conference of the IEEE Industrial Electronics Society, IECON01, Vol.2, 29th Nov.-2nd Dec. 2001, Denver, CO, USA, pp.1521-1526

[3] D. Grenier, S. Yala, 0. Akhrif and L. A. Dessaint, "Direct torquecontrol ofPM AC motor with non-sinusoidal flux distribution usingstate-feedback linearization techniques," Proceedings of the 24thAnnual Conference of the IEEE Industrial Electronics Society, IE-CON98, vol.3, 31st Aug.-4th Sept.1998, Aachen, Germany, pp.1515-1520.

[4] Y. Liu, Z. Q. Zhu and D. Howe, "Direct torque control of brushlessDC drives with reduced torque ripple," IEEE Transactions on In-dustry Applications, vol.4 1, No.2, March/April, 2005, pp.599-608.

[5] T. J. E. Miller, Brushless permanent-magnet and reluctance motordrives, Oxford: Clarendon Press, 1989.

[6] L. Zhong, M. F. Rahman, W. Y. Hu and K. W. Lim, "Analysis ofdirect torque control in permanent magnet synchronous motordrives," IEEE Transitions on Power Electronics, Vol. 12, No.3,May, 1997, pp.528-536.

IV. CONCLUSIONS

The performance of direct torque controlled perma-nent magnet BLDC drive has been compared with that ofPWM current controlled drives with and without currentshaping. Owing to inherently torque control rather thancurrent control, a direct torque controlled BLDC driveexhibits significantly less low-frequency torque ripplesthan the PWM current controlled BLDC drive withoutcurrent shaping, while it is easier to implement with bettertorque control ability than the PWM current controlledBLDC drive with current shaping, as validated by bothsimulations and measurements.

APPENDIX

SPCIFICATION OF SURFACE-MOUNTED PM BRUSHLESS MOTORNumber of poles, p 10DC link voltage (V) 36Phase resistance (Q) 0.35Self-inductance (mH) 3.9Mutual-inductance (mH) -0.0023Rated speed (rpm) 400PM excitation flux-linkage (Wb): 0.0794

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(a) Phase current

050 0.0125 0.025 0.0375 0.05

Time (s)

(b) Electromagnetic torqueFig. 8. Current PWM control with current shaping (simulated).

(a) Phase current Time (12.5ms/div)X(a) Phase current

Time (12.5ms/div)

(b) Electromagnetic torqueFig. 9. Current PWM control with current shaping (measured).

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