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International Journal of Electrical and 
Electronics Engineering Research (IJEEER) 

ISSN (P): 2250-155X; ISSN (E): 2278-943X 
Vol. 7, Issue 4, Aug 2017, 95-102 
© TJPRC Pvt. Ltd. 



Electrical and Electronics Engineering, Sri Ramakrishna Polytechnic College, Coimbatore, Tamil Nadu, India 
2 Electrical and Electronics Engineering, Alagappa Chettiar College of Engineering, Karaikudi, Tamil Nadu, India 


This paper provides a technique to minimize torque ripple in BLDC motor by using single current sensor. There 
are number of techniques avail to minimize torque ripple. This paper proposes hysteresis current controller. By using this 
controller torque ripple is greatly reduced in various speed and loading conditions. Simulation is carried out using 
MATLAB / SIMULINK. The results show that the performance of BLDC motor is quite satisfactory. 

KEYWORDS: Brushless DC Motor, Trapezoidal Type Machine, PM Synchronous Motor & Torque Ripple Minimization 



•Journal Publications • Research Consultancy 

Received: Jul 20, 2017; Accepted: Aug 05, 2017; Published: Aug 11, 2017; Paper Id.: I JEEERAUG201710 


Brushless DC motors BLDC are more popular in recent years due to its high efficiency, high power 
density, high torque to inertia ratio for a given machine size and simple control characteristics. The application 
range in various fields like automobile and robotics, in BLDC motor 120° mode of rectangular wave voltage 
commutation is used, due to motor armature resistance and inductance the current waveform is not exact wave 
during commutation. This causes undesirable torque ripple. Theoretical analysis for torque ripple is available in [1- 
3] .This torque ripple leads to visible vibrations, acoustic noise and error in sensor less motor drives. The torque 
ripple varies with speed and may reach 50% of the average torque. 

Torque ripple exists due to cogging, imperfection of back emf waveforms, supply current ripple from 
PWM inverters and phase current commutation. Many technologies have developed for minimizing torque ripple. 
The cogging torque can be minimized by skewing the stator teeth or by changing the magnet’s dimension and 
position [3].An alternative approach for minimizing torque ripple, Current control is adopted in many ways 
because, current control is simple and effective method. For current control, PWM or hysteresis controls are 
adopted. In [4-11] phase current control is implemented during phase current commutation in a BLDC motor using 
phase current sensors. 

This paper proposes a simple current control method to restrain the commutation torque ripple in the 
various speed ranges with a single current sensor. This control system has very simple configuration and reliable 
performance. Complex control strategies for BLDC motor are sensitive to variation in parameters, magnetic 
saturation and also makes less reliable for entire system. For domestic or simple applications where the operating 
parameters are not frequently varies, then the control strategies required for BLDC motor should also be simple. 
This simple control system will be available at low cost and uses simple structure. 


editor @tjprc. org 

Original Article 


D.Gopalakrishnan &. V.Gopalakrishnan 


In ideal condition BLDC motor produces a traphizoidal back emf and excited with rectangular current wave form, 
due to this reason torque is uniform and ripple free. The ideal back emf and current wave form is shown in the figure 2, 
assume, the per phase resistance and inductance are equal. The self and mutual inductance are constant irrespective of rotor 
position. The rotor induced current are neglected and the damper winding are also not present. 

The Voltage Equation of the BLDC Motor can be expressed as 

Vi = Ri + L ^ +ei 

v2 — R 2 T L —— T ^2 

z z dt z 

^3 - ^3 + ^ + e 3 

( 1 ) 

( 2 ) 

( 3 ) 

In matrix form 

~ V 1 

V 2 


R 0 O' 
0 R 0 




l — M 0 0 

0 l-M 0 





e i 

e 2 

V 3 . 




- 0 0 l-M. 

d t 


e 3 . 

Where, R is the phase Resistance andi 1 ,i 2 d 3 are the phase current, e ± ,e 2 , e 3 are the back emf, l and M are the self 
and mutual inductance, of the individual coil. 

Due to the interaction between the stator current and magnetic field from rotor magnets, the electromagnetic 
torque has been developed. 

j< _ e lh + e 2^2 + e 3^3 

Where, co m is the angular speed of the machine. 

For 120° mode six step motor controls, two phases are connected in series at each step. The instantaneous power 
is given by 

Pi= 0) m T e = 2EI (6) 

Where I = current amplitude and E is the induced back emf. 

Output torque can be expressed as 

T e = 2 KOI = 2 k t I (7) 

Where k t is motor torque constent. 

Impact Factor (JCC): 7.8965 

NAAS Rating: 3.19 

Low Cost BLDC Drive Using Single Current Sensor 


Analysis of Torque Ripple 

It is proposed in [10] that a single dc current sensor and a current deadbeat control scheme should be used to keep 
incoming and outgoing phase currents changing at the same rate during commutation. The study [10] presents a 
comprehensive analysis of the commutation torque ripple suppression method in brushless dc motor drives with only a 
single current sensor. BLDC motor is driven through 3 phase full bridge six step voltage source inverter. Each phase is 
energized for the interval of 120° electrical degree according to the rotor position. For providing current path in each step, 
one phase is energized as positive and another is energized as negative. 

For analysis of commutation mode, the commutation of the current through two phases will be considered. One 
phase will be switched off, the second phase will replace the switched off phase and the third phase will be remained 
conduction called non-commutated phase. 

Consider the commutation from phase 1 to phase2. The current transfer happens during the commutation interval 
in this analysis, current transfers from phase 1(+) to phase2(+). Phase3 (-) will be in the same condition. Phase 1 is called 
the outgoing phase, phase2 is called incoming phase and phase3 is called conducting phase. 

For ripple free uniform torque, the current in BLDC motor with traphizoidal back emf is rectangle in shape. 
Figure 2 shows the ideal phase current wave forms. In this, the incoming current i 2 takes the finite time to reach its 
maximum value, also the outgoing current ii takes a finite time to reach zero. 

Figure 3 shows the six step inverter, at each 60 electrical degree there will be 2 switches conducting at the same 
time. One from positive group i.e. upper arm and another from negative group i.e. lower arm. When phase 1 and phase3 
conducting, the upper arm switch SI and lower arm switch S4 will be in ON position. During commutation period switch 
SI turned OFF, the current will be decayed through the freewheeling diode D6 and the switch S4. This will take a short 
period which will occur at each step. In the next sequence switch S3 and switch S4 will be in ON position. Now phase2 
and phase3 are conducting. 


editor@tjprc. org 


D.Gopalakrishnan &. V.Gopalakrishnan 

Figure 3: Commutation of Phase Current from Phasel to Phase2 (A) Phasel 
Conducts, (B) Commutation Between Phasel, 2 (C) Phase2 Conducts 

Figure 4: Waveforms of Phase Currents during Commutation in Different Cases 

Slop of the curve is can be calculated from 

L d -±+Ri 1 +E 1 -(l^+Ri 3 + E 3 ) = 0 (8) 

L^ + Ri 2 +E ~(l ^+Ri 3 + E) = V dc (9) 

In practical situation, due to the phase resistance and inductance, the rate of rise of incoming current is not equal 
to the rate of drop of outgoing current. This mismatch produces torque ripple. Consider figure 4 (a) the current in the 
outgoing phase would reach zero before the current in incoming phase reach maximum value. 

— > — ( 10 ) 

d t d t 

Therefore the non commutated phase3 current will rise up slightly during commutation period. 

In figure 4(b) phasel rate of drop of outgoing current ips slower than the phase2 rate of rise of the incoming 

Impact Factor (JCC): 7.8965 

NAAS Rating: 3.19 

Low Cost BLDC Drive Using Single Current Sensor 


current i 2 . 

dq ^ di2 
d t d t 

( 11 ) 

Due to this mismatch a small dip appear in the phase3 during commutation period. Therefore overall torque 
produced in the motor has ripples. 

In figure 4(c) phase 1 rate of drop of outgoing current ips equal to phase2 rate of the rise of incoming current i 2 . 

dji _ ^i2 
d t d t 

( 12 ) 

In this condition no dip appears in the phase3 during commutation period. This leads to ripple free torque in 



Among the various PWM techniques, the hysteresis band current control is reliable and easy to implement. Also it 
has very fast response and effective current loop. The method does not need any knowledge of motor and load parameters. 
However, the current control with a fixed hysteresis band has the certain limitations that the PWM frequency varies within 
a band because peak-to-peak current ripple is required to be controlled at all points of the fundamental frequency wave. 

The PWM current controller acts once a cycle, controlling the duty cycle of the chopper. The chopper is a variable 
voltage source with average current control. Instantaneous current control is not exercised in the PWM current controller. 

Figure 5: Block Diagram of Hysteresis Current Controller 

In between two consecutive switching, the current can exceed the maximum limit; if the PWM controller is 
sampled and held once a switching cycle, then the current is controlled on an average but not on an instantaneous basis. 
The hysteresis controller overcomes such a drawback by converting a voltage source into a fast acting current source. The 
current is controlled within a narrow band of excursion from its desired value in the hysteresis controller. The hysteresis 
window determines the allowable or preset deviation of current Figure 5 shows the block diagram of hysteresis current 
controller which is generate the gating signals for inverter switches. 

The DC link current i d is measured and compared with preset value of reference current. The error is fed to a 
comparator with a preset hysteresis band. Switching of the devices (SI off) occurs when the line current exceeds a preset 
value corresponding to the desired line current i d . The reverse switches (SI on) occur when the line current reaches less 


editor@tjprc. org 


D.Gopalakrishnan &. V.Gopalakrishnan 

than desired i d . 

hysteresis upper band 

Hysteresis current control is simple to implement and produces a very good quality of wave form. The switching 
pattern gives as 

If Ai d > H SI is off 

A i d < H SI is on 


Mainly Torque ripples occur during commutation period only. In voltage source inverter, commutation between 
the three phases is occurred six times per electrical revolution. As a result, output current ripples are generated during 
commutation period, this leads to torque ripples. This output current ripple reflects ripples in input DC link. A current 
sensor is placed in the DC link to measure the input current value. Measured current is feed to hysteresis current controller. 
Whenever the input current ripple above the pre set value in the hysteresis current controller, corresponding outgoing 
switch is driven by switching pulse which was generated by hysteresis controller instead of switch off. Pulse generated by 
the hysteresis controller is extended up to the incoming current reaches 80% of its maximum value. 

By using this technique, in un commutated phase current ripple is minimized, therefore torque ripple is minimized in 
motor output. 


To verify the effectiveness of the proposed technique, simulation using MATLAB Simulink is carried out. Motor 
parameters are 4 pole, 24V, 200W and 1500 rpm. Simulation results of the phase currents, de-link current and torque ripple 
are illustrated in the speed range of 1200 rpm. 

For easy comparison, switching algorithm is implemented for two phases only. Therefore in the six step sequence, 
four are controlled by new algorithm and two are uncontrolled. Proposed algorithm effectively neutralizes the mismatched 
phase current during commutation period and minimizes the commutation torque ripple over entire speed range..By using 
this technique torque ripple is minimized up to 65 percentages. The inverter’s line current is shown in figure 8. The stator 
phase current wave form is shown in figure 9. The rotor toque is shown in figure 10. 

Impact Factor (JCC): 7.8965 

NAAS Rating: 3.19 

Low Cost BLDC Drive Using Single Current Sensor 


Figure 7: MATLAB Simulation of Conventional Six Switch Fed Single Current Sensor BLDC Motor Drive 

Figure 9: Phase Current 


Voltage 24V 

Power 200W 


editor @tjprc. org 


D.Gopalakrishnan &. V.Gopalakrishnan 

Phase Resistance 
Phase Inductance 
Torque constant 
Back EMF constant 


0.19 Ohm 
0.517 mH 
0.11 Nm/A 

This paper has presented an analytical study of torque ripple and DC link current sensing using single current 
sensor. In this paper torque ripples of BLDC motor drive with hysteresis current controller loop is carried out and it is 
compared with, without hysteresis current controller fed BLDC drive. Simulation results shows that current ripple and 
torque ripple are minimized which enhances the drive performance. The results show that the dynamic performance of the 
motor is quite satisfactory for various speed conditions. 


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Reduction,” International Conference on Electrical Engineering and Informatics, pp. 1-6, 17-19 July, Bandung, Indonesia, 

Impact Factor (JCC): 7.8965 

NAAS Rating: 3.19