Modified Field Oriented Control for Smooth Torque ... - IEEE Xplore

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Freescale Semiconductor, Inc - AMPG, Roznov pod Radhostem, Czech Republic e-mail: [email protected]@freescale.com.
Modified Field Oriented Control for Smooth Torque Operation of a BLDC Motor Marek Lazor, Marek Stulrajter Freescale Semiconductor, Inc - AMPG, Roznov pod Radhostem, Czech Republic e-mail:

[email protected]@freescale.com

and power per volume ratio are higher than in the PMSM with the same copper losses. Six-step commutation control is the most common control technique suitable for BLDC motors. Despite the power density being 15% higher than in the PMSM, the commutation control principle introduces a significant ripple in produced torque. This torque ripple occurs six times per one electrical revolution and is the essential property of the six-step commutation strategy. Therefore, there is an effort to fmd some control strategy for the BLDCM that will reduce torque ripple and keep all the advantages of this type of motor drive. The research for an optimal control strategy is based on an idea of the fmding optimal current waveforms reflecting the shape of the back-EMF of BLDC machines with surface mounted PMs. Several methods have been presented, analytically derived and proven by simulation results [2,3]. A unique and optimal solution that constrains the quadratic minimization problem has been clearly expressed in closed form in [4], however, this approach did not incorporate iron losses. An extended Park's transformation approach, by means of the so-called pseudo-dq axes reference frame, has been presented in [5,6]. Various current excitation strategies have been investigated in the past, and a modified field oriented control with a closed control loop is presented in [7]. A new BLDC control strategy based on a specific current harmonics injection approach is presented in this paper. The complete mathematical model is described and verified on a simulation model. Simulation results of the proposed approach are analyzed and compared with the conventional six-step control strategy considering phase commutation.

Abstract-this paper describes a novel approach to field oriented control of a BLDC

(Brushless

Direct-Current)

motor producing a significantly reduced torque ripple. This paper presents a standard mathematical model of a BLDC motor in the abc reference frame which is suitable for simulation

of

the

six-step

control

strategy,

and

a

mathematical model of a BLDC motor in the dq reference frame suitable for standard and modified field oriented control strategies. An extended dq transformation, in other words

a

Park's-Iike

transformation,

is

described

and

implemented in the simulation model. Simulation results of all the control strategies are evaluated and compared. Keywords-modified field oriented control, BLDC motor, smooth torque, extended Park's transformation.

I.

INTRODUCTION

Efficient and effective motor control with smooth torque operation is an important feature for many specific applications in industry. Plenty of motor control developers and engineers work on new and sophisticated control strategies for permanent magnet (PM) motors in order to increase the efficiency and eliminate the torque ripple. In general, PM motors can be divided into two main categories, namely, the Permanent Magnet Synchronous Motor (PMSM) with a sinusoidal back­ EMF, and the Brushless Direct Current Motor (BLDCM or BLDC motor) with a trapezoidal back-EMF. The difference in shape of the back-EMF is a result of the arrangement, shape and magnetization of the PMs, stator windings distribution, the number of stator slots and their skew [I]. PMSMs are well known for their high efficiency, smooth generated torque, low rotor inertia, high dynamic properties and a high ratio between power and weight. High-performance control of PMSM machines is characterized by a smooth rotation over the entire speed range and full torque control at a zero speed. To achieve such control, a vector control technique is used, also referred to as a field-oriented control (FOC). A certain drawback of the PMSMs in comparison with the BLDCM is the higher price, due to the quasi-sinusoidal conductor density distribution and the higher precision rotor position sensor. Nowadays, due to the cost-reduction trends in industry, a cost-effective solution is also required in the field of electric motors and motor control. BLDC motors are becoming strong players in applications such as fans, pumps and commercial compressors thanks to their high power density, a simpler construction which leads to a lower price and the possibility of easy control with lower accuracy sensor or even without sensor. Power density

978-1-4799-3721-9/14/$31.00 mOl41EEE

II.

TORQUE PRODUCTION

In general, synchronous torque can be expressed as: Te

.

=

d0

Nz dt

.

= Z

dJ.jJ de

e({)r) z({)r) ----:0:.

=

(1)

where N is the number of turns of stator windings, i is the phase current,

JWW"ffl'N\-

I

----- � -----+----- - - - - t-

--

I 1 ______ I

- - - t+---�"'4------___j_--Il:::-____ :l ____l

---t --

-----r-----

'--____---"-______--'---______'---__ -- __---"-____-----.l 0.1

.-------,--,---�--�

- - - - - � - - - - - � - ----

--

0.05

J1 --

-0.15 '------�--'--" 0.2 5 0.05 0.1 0.15 02 o .

25.------,------,-------,-�--_,--�__.

�: I �

----

I ______1_

-----+-----

0.1

�1

Modified FOe

I

0.24

0.05

SIMULATION RESULTS

The proposed approach with the modified FOC has been verified on a simulation model employing a BLDC motor with an almost ideal trapezoidal shape of back­ EMF. The normalized functions of the back-EMF have been determined by (8). Harmonics higher than 19th have been neglected.

o



-;= 3i---:---T-----:I --=====;l

0.2

.0'"

-10

I

0.23

L-____---'-__ - ____"---__ -- __---"-______-"---____---.J o 0.05 0.1 0.15 0.2 0.25 Time [51

02 . 5

(21)

-5

0.22

Fig. 6 compares the dq feedback currents on the output of the BLDC model (with significant perturbation of the magnitude) and on the output of extended transfonnation (modified currents) with unalterable magnitude. As can be seen, the extended transfonnation provides current feedback significantly smoother than the standard FOC. This behavior can also be clearly observed in the current error signal entering the PI controllers, Fig. 7.

Fig. 4 Modified field oriented control strategy

VI.

I O�.-......r-

Fig. 6 Feedback currents in dq reference frame

eqn.14,15

A.

-----

Time [5]

0.15

0.2

0.4

0.25

0.2

Fig. 5 Voltages in the dq reference frame after decoupling

Fig. 5 represents the decoupled voltages in the dq frame which supply the model of the motor. Inverter nonlinearities are not taken into account because space

o

-

- - - r -

---0.23

'--------cL =�.:-' ---------:-L :------ :"- :------� O .05 0. 15 0. 1 0.25 0 0.2

lime [sl

Fig. 8 Electromagnetic and load torque

183

To express the power requirements for each control strategy, it is appropriate to evaluate the root mean square (RMS) value of currents with the following equation:

Fig. 8 shows the produced electromagnetic torque and applied load torque, including a detail of the torque behavior in the steady state. As can be seen, a very smooth torque behavior with minimized torque ripple is achieved.

IIOO

...j IRMS

Comparison of control stategies

B.

Keeping the same simulation conditions, such as the same commands for the desired angular velocity, same load torque commands and the same parameters of the BLDe motor, the six-step commutation strategy, the standard Foe and proposed modified Foe (MFOC) focusing on produced torque, the total harmonic distortion of the current, and the power rating can all be compared. One period of the current waveforms of all the control strategies is shown in Fig.9. 3

Tripple

D-

--Foe --MFoe -- SIX-S TEP

� 0.95

f-

- - - - - - - r- ------- r --

-2

- - - - - - - � - - - - - - - � - --

Q

_3L0.225

0.23

0.235

Time

[s]

Their harmonic spectrum is analyzed using a fast Fourier transformation and the graphical interpretation is shown in Fig. 10.

.

2 5 2

� :;

15

"

--

.

u

o

7 9 11 Harmonic order

. 13

• 15

17

--------------

0.23

19

The amount of distortion in a phase current in the machine is quantified by the total harmonic distortion (THO), which is defined by: THD%

·2 h=2,3 ,4 .... 1h

=

.

11

100%

--Foe --MFoe --SIX-STEP

I --------------

0.235

Time

[s]

0.24

--

0.245

TABLE 1. STMULAnON RESULTS



Fig. 10 Harmonic contents of the phase currents

JIOO

---I I

0.5

_.

-

As seen in Fig. 11, produced torque with the Six-step control strategy has a significant torque ripple due to the phase current commutation which occurs six-times per one electrical revolution. Electromagnetic torque produced during the Foe control has also some ripple in the torque caused by the rippled back-EMF (Fig. 3). Significantly reduced ripple in produced electromagnetic torque has been achieved by the proposed modified Foe by injecting the right current harmonics (Fig.6 - detail). The results achieved are summarized in Table 1.

3



---

Fig. 11 Produced electromagnetic torque of three different control strategies

Fig. 9 Current waveforms of three different control strategies





0.225

0.245

0.24

9

Q�

�________�______�_________L�

______

(24)

Te_avg

1.05

'" .... Q) :0

-1

Te max - Te min

1.1 ,------�--,____--�__,

� 0

.c

_

-

where Te max and Te min are the maximum and minimum instantaneous values, -and Te_avg is the average value of produced torque.

c :0 " Q)