IJSTE - International Journal of Science Technology & Engineering | Volume 3 | Issue 09 | March 2017 ISSN (online): 2349-784X Modeling of Direct Torque Control (DTC) of

BLDC Motor Drive

Addagatla Nagaraju Akkela Krishnaveni Lecturer Lecturer Department of Electrical Engineering Department of Electrical Engineering Government Polytechnic, Station Ghanpur, Warangal, Dr. B.R. Ambedkar Government Polytechnic, for Women, Telangana, India Karimnagar, Telangana, India

Abstract

Multilevel The position sensor-less direct torque and indirect flux control of brushless dc (BLDC) motor with non-sinusoidal back electromotive force (EMF) has been extensively investigated. In the literature, several methods have been proposed for BLDC motor drives to obtain optimum current and torque control with minimum torque pulsations. Most methods are complicated and do not consider the stator flux linkage control, therefore, possible high-speed operations are not feasible. In this study, a novel and simple approach to achieve a low-frequency torque ripple-free direct torque control (DTC) with maximum efficiency based on dq reference frame is presented. The proposed sensorless method closely resembles the conventional DTC scheme used for sinusoidal ac motors such that it controls the torque directly and stator flux amplitude indirectly using d-axis current. This method does not require pulse width modulation and proportional plus integral regulators and also permits the regulation of varying signals. Furthermore, to eliminate the low-frequency torque oscillations, two actual and easily available line-to-line back EMF constants (kba and kca) according to electrical rotor position are obtained offline and converted to the dq frame equivalents using the new line-to-line park’s transformation. Then, they are set up in the look-up table for torque estimation. The validity of the proposed sensor-less three-phase conduction DTC of BLDC motor drive scheme are verified through simulations results. Keywords: Direct torque control (DTC) permanent magnet synchronous motor (PMSM), brushless DC motor (BLDC) ______

I. INTRODUCTION

The permanent-magnet synchronous motor (PMSM) and brushless dc (BLDC) motor drives are used extensively in several high- performance applications, ranging from servos to traction drives, due to several distinct advantages such as high-power density, high efficiency, large torque to inertia ratio, and simplicity in their control. In many applications, obtaining a low-frequency ripple-free torque and instantaneous torque and even flux control are of primary concern for BLDC motors with non-sinusoidal back electromotive force (EMF). A great deal of study has been devoted to the current and torque control methods employed for BLDC motor drives. One of the most popular approaches is a generalized harmonic injection approach by numerical optimization solutions to find out optimal current waveforms based on back EMF harmonics to minimize mutual and cogging torque. Those approaches limit Fourier coefficients up to an arbitrary high harmonic order due to calculation complexity. Moreover, obtaining those harmonics and driving the motor by pulse width modulation (PWM) method complicates the real-time implementation. Optimal current references are not constant and require very fast controllers especially when the motor operates at high speed. Moreover, the bandwidth of the classical proportional plus integral (PI) controllers does not allow tracking all of the reference current harmonics. Since the torque is not controlled directly, fast torque response cannot be achieved. Also, the rotor speed is measured by an expensive position sensor.

Speed Control of Induction Motor The various methods available for the speed control of squirrel cage induction motor through semiconductor devices are given as under: 1) Scalar control. 2) Vector control (Field-Oriented Control, FOC). 3) Direct Torque Control (DTC). 4) AI based control.

II. SCALAR CONTROL

Despite the fact that “Voltage-Frequency” (V/f) is the simplest controller, it is the most widespread, being in the majority of the industrial applications. It is known as a scalar control and acts by imposing a constant relation between voltage and frequency. The structure is very simple and it is normally used without speed feedback. However, this controller does not achieve a good

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085) accuracy in both speed and torque responses, mainly due to the fact that the stator flux and torque are not directly controlled. Even though, as long as the parameters are identified, the accuracy in the speed can be 2% (expect in a very low speed), and the dynamic response can be approximately around 50ms.

III. DIRECT FIELD-ORIENTED CURRENT CONTROL

Figure 3.2 shows a direct field oriented control scheme for torque control using a current-regulated PWM inverter. For field orientation, controlling stator current is more direct than controlling stator voltage; the later approach must allow for the additional effects of stator transient inductances. With adequate dc bus voltage and fast switching devices, direct control of stator current can be readily achieved. The direct method relies on the sensing of air gap flux, using specially fitted search coils or Hall- effect devices. The drift in the integrator associated with the search coil is especially problematic at very low frequencies. Hall devices are also temperature-sensitive and fragile.

Direct field-oriented control of a current regulated PWM inverter induction motor drive.

MODELLING OF DIRECT TORQUE CONTROL (DTC) OF BLDC MOTOR DRIVE In a DTC drive, flux linkage and electromagnetic torque are controlled directly independently by the selection of optimum inverter switching modes. The selection is made to restrict the flux linkages and electromagnetic torque errors within the respective flux and torque hysteresis bands. The required optimal switching vectors can be selected by using so-called optimum switching-voltage vector look-up table. This can be obtained by simple physical considerations involving the position of the stator-flux linkage space vector, the available switching vectors, and the required torque flux linkage

TORQUE EXPRESSIONS WITH STATOR AND ROTOR FLUXES The torque expression for induction machine can be expressed in vector form as, 3 P T = ( ) ψ I (1) e 2 2 s s s s s s Where ψs = ψqs − jψds and Is = Iqs − jIds. In this equation, Is is to be replaced by rotor flux ψr. In the complex form, ψs and

ψr can be expressed as function of currents as,

ψs = LsIs + LmIr (2)

ψr = LrIr + LmIs (3) I Eliminating r from equation (4.2), we get Lm ψ = ψ + L′sIs (4) s Lr r 2 Where L′s = LsLr − Lm . The corresponding expression of Is is Lm Lm Is = ψ − ψ (5) Ls s LrL′s r Substituting equation (4.5) in (4.1) and simplifying yields

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085)

3 P Lm Te = ( ) ψ ψ (6) 2 2 LrL′s r s That is, the magnitude torque is 3 P Lm Te = ( ) |ψ ||ψ | sin γ (7) 2 2 LrL′s r s

Fig. 1: Stator flux, rotor flux, and stator current vectors on ds-qs plane (stator resistance neglected)

Where γ is the angle between the fluxes. Figure 4.1 shows the phasor (or vector) diagram for equation (4.6), indicating the vectors ψs, ψr, and Is for positive developed torque. If the rotor flux remains constant and stator flux is changed incrementally by stator voltage Vs as shown and the corresponding change of γ angle is ∆γ, the incremental torque ∆Te expression is given as 3 P Lm ∆Te = ( ) |ψ ||ψ + ∆ψ | sin ∆γ (8) 2 2 LrL′s r s s

IV. CONTROL STRATEGY OF DTC

The block diagram of direct torque control is shown in Figure 4.2 and Figure 4.3 explains the control strategy. The command ̂∗ ∗ stator flux ψ sand torque Te magnitudes are compared with the respective estimated values and the errors are processed through hysteresis-band controllers, as shown. The flux loop controller has two levels of digital output according to the following relations: Hψ = 1 for Eψ > +HBψ (9) Hψ = 1 for Eψ < −HBψ (10) ̂ ∗ Where 2HBψ= total hysteresis-band width controller. The circular trajectory of the command flux vector 훙 퐬 with the hysteresis band rotates in an anti-clockwise direction as shown in Figure 4.3(a). The actual stator flux 훙퐬 is constrained within the hysteresis band and it tracks the command flux in a zigzag path. The torque control loop has three levels of digital output, which have the following relations: HTe = 1 for ETe > +HBTe (4.11) HTe = −1 for ETe < −HBTe (4.12) HTe = 0 for − HBTe < ETe < +HBTe (13) The feedback flux and torque are calculated from the machine terminal voltages and currents. The signal computation block also calculates the sector number S(k) in which the flux vector 횿풔 lies. There are six sectors (each /3 angle wide), as in Figure 3(a).

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085)

Fig. 2: Direct torque control (DTC) block diagram

Fig. 4.3: (a) Trajectory of stator flux vector in DTC control,

Fig. 4.3: (b) Inverter voltage vectors and corresponding stator flux variation in time Δt.

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085)

The voltage vector table block in Figure 4.2 receives the input signals Hψ, HTe, and S(k) and generates the appropriate control voltage vector (switching states) for the inverter by lookup table, which is shown in table 4.1 (the vector sign is deleted). The inverter voltage vector (six active and two zero states) and a typical ψs are shown in Figure 4.3(b). Neglecting the stator resistance of the machine, we can write 푑 푉 = (ψ ) (4.14) 푠 푑푡 s

∆ψs = 푉푠. ∆푡 (15)

Which means that ψs can be changed incrementally by applying stator voltage 푉푠 for time increment Δt. The flux increment vector corresponding to each of six inverter voltage vectors is shown in Figure 3(b). The flux in machine is initially established to at zero frequency (dc) along the trajectory OA shown in Figure 4.3(a). With the rated flux, the command torque is applied and ∗ the Ψs vector starts rotating.

V. SIMULATION RESULTS

Simulation diagram of the position-sensorless direct torque and indirect flux control of BLDC motor.

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085)

Simulated indirectly controlled stator flux linkage trajectory under the sensorless three-phase conduction DTC of a BLDC motor drive when ir∗ds is changed from 0 to −5 A under 0.5 N·m load torque.

Actual q- axis and d-axis rotor reference frame back EMF constants versus electrical rotor position (kd(θre ) and kq(θre )).

Experimental estimated electromechanical torque under time-varying reference when ir∗ds = 0 under 0.5 N·m load torque

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Modeling of Direct Torque Control (DTC) of BLDC Motor Drive (IJSTE/ Volume 3 / Issue 09 / 085)

VI. CONCLUSION

In this thesis work, successfully simulated, the proposed position-sensorless three-phase conduction DTC scheme for BLDC motor drives that is similar to the conventional DTC used for sinusoidal ac motors where both torque and flux are controlled, simultaneously. This method provides advantages of the classical DTC such as fast torque response compared to vector control, simplicity (no PWM strategies, PI controllers, and inverse Park and inverse Clarke transformations), and a position-sensorless drive. It is shown that the BLDC motor could also operate in the flux-weakening region by properly selecting the d-axis current reference in the proposed DTC scheme. First, practically available actual two line-to-line back EMF constants (kba and kca) versus electrical rotor position are obtained using generator test and converted to the dq frame equivalents using the new line-to- line Park transformation in which only two input variables are required. Then, they are used in the torque estimation algorithm. Electrical rotor position required in the torque estimation is obtained using winding inductance, stationary reference frame currents, and stator flux linkages. Since the actual back EMF waveforms are used in the torque estimation, low-frequency torque oscillations can be reduced convincingly compared to the one with the ideal-trapezoidal waveforms having 120 electrical degree flat top. A look-up table for the three-phase voltage vector selection is designed similar to a DTC of PMSM drive to provide fast torque and flux control. Because the actual rotor flux linkage is not sinusoidal, stator flux control with constant reference is not viable anymore. Therefore, indirect stator flux control is performed by controlling the flux related d-axis current using bang-bang (hysteresis) control, which provides acceptable control of time-varying signals (reference and/or feedback) quite well.

REFERENCE

[1] Salih Baris Ozturk, and Hamid A. Toliyat, “Direct Torque and Indirect Flux Control of Brushless DC Motor” IEEE/ASME Transactions On Mechatronics, Vol. 16, No. 2, April 2011. [2] W. C. Gan and L. Qiu, “Torque and velocity ripple elimination of AC permanent magnet motor control systems using the internal model principle,” IEEE/ASME Trans. Mechatronics, vol. 9, no. 2, pp. 436–447, Jun. 2004. [3] D. Sun and J. K. Mills, “Torque and current control of high-speed motion control systems with sinusoidal-PMAC motors,” IEEE/ASME Trans. Mechatronics, vol. 7, no. 3, pp. 369–377, Sep. 2002. [4] T. S. Low, K. J. Tseng, T. H. Lee, K. W. Lim, and K. S. Lock, “Strategy for the instantaneous torque control of permanent-magnet brushless dc drives,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 137, no. 6,pp. 355–363, Nov. 1990. [5] D. Grenier, L. A. Dessaint, O. Akhrif, and J. P. Louis, “A park-like transformation for the study and the control of a nonsinusoidal brushless dc motor,” in Proc. IEEE IECON, Orlando, FL, Nov. 6–10, 1995, vol. 2, pp. 836–843. [6] T. Kim, H.-W. Lee, L. Parsa, and M. Ehsani, “Optimal power and torque control of a brushless dc (BLDC) motor/generator drive in electric and hybrid electric vehicles,” in Conf. Rec. IEEE IAS Annu. Meeting, 8–12 Oct. 2006, vol. 3, pp. 1276–1281. [7] F. Aghili, M. Buehler, and J. M. Hollerbach, “Experimental characterization and quadratic programming-based control of brushless motors,” IEEE Trans. Control Syst. Technol., vol. 11, no. 1, pp. 139–146, Jan. 2003. [8] S. J. Kang and S. K. Sul, “Direct torque control of brushless dc motor with non-ideal trapezoidal back-EMF,” IEEE Trans. Power Electron., vol. 10, no. 6, pp. 796–802, Nov. 1995. [9] S. K. Chung, H. S. Kim, C. G. Kim, andM. J. Youn, “A new instantaneous torque control of PM synchronous motor for high-performance direct drive applications,” IEEE Trans. Power Electron., vol. 13, no. 3, pp. 388– 400, May 1998. [10] L. Hao and H. A. Toliyat, “BLDC motor full-speed operation using hybrid slidingmode observer,” in Proc. IEEE APEC, Miami, FL, Feb. 9–13, 2003, vol. 1, pp. 286–293. [11] P. L. Chapman, S. D. Sudhoff, and C. A. Whitcomb, “Multiple reference frame analysis of non-sinusoidal brushless dc drives,” IEEE Trans. Energy Convers., vol. 14, no. 3, pp. 440–446, Sep. 1999. [12] M. Depenbrock, “Direct self-control of inverter-fed induction machine,” IEEE Trans. Power Electron., vol. 3, no. 4, pp. 420–429, Oct. 1988. [13] S. B. Ozturk and H. A. Toliyat, “Direct torque control of brushless dc motor with non-sinusoidal back-EMF,” in Proc. IEEE IEMDC Biennial Meeting, Antalya, Turkey, May 3–5, 2007, vol. 1, pp. 165–171. [14] P. J. Sung, W. P. Han, L. H. Man, and F. Harashima, “A new approach for minimum-torque-ripple maximum-efficiency control of BLDC motor,” IEEE Trans. Ind. Electron., vol. 47, no. 1, pp. 109–114, Feb. 2000. [15] L. Zhong, M. F. Rahman, W. Y. Hu, and K. W. Lim, “Analysis of direct torque control in permanent magnet synchronous motor drives,” IEEE Trans. Power Electron., vol. 12, no. 3, pp. 528–536, May 1997

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