A comparative analysis of torque ripple reduction techniques for sensor BLDC drive

Received Jul 16, 2021 Revised Jan 23, 2022 Accepted Jan 30, 2022 Brushless direct current motors (BLDC) are prominent due to their high efficiency and less maintenance. However, BLDC motor applications are limited due to the requirement of a complex controller, the existence of torque ripple, and high cost. This research work describes the comparative analysis of different control strategies of torque ripple reduction in BLDC motors and it discusses various topologies viz. cuk converter, simple voltage modulator scheme, charged capacitor, Z-source inverter, and QuasiZ source inverterbased toque ripple reduction techniques. The effectiveness of different control strategies has been verified using MATLAB Simulink and it helps to understand different control strategies for torque ripple reduction during the entire speed range. The analysis of MATLAB results reveal that the voltage modulation scheme reduces the torque ripple considerably during the entire speed range along with the noiseless operation of the BLDC motor when compared with other topologies.


INTRODUCTION
Direct current (DC) motors used in speed and position control applications are prone to wear and tear, and maintenance issues due to the presence of brushes. These issues are overcome with BLDC motors [1]. BLDC motors are becoming popular in industrial applications owing to their high efficiency, less maintenance, high speed, long life, less electromagnetic interference, and less noise operation [2]. These motors are employed in medical, power-driven and hybrid vehicles, industrial robots, defense, and aerospace industries. The brushless motor has hall sensors to provide electronic commutation. The dissimilarity in the phase current leads to torque ripples during commutation in the trapezoidal back emf motors [3].
The torque fluctuation in BLDC motors is generated due to cogging torque and imperfections of back emf [4]. This torque ripple causes vibrations and acoustic noises which leads to undesirable stresses in bearings, mountings of the drive systems [5]. The discontinuity in torque is imprudent for the constant torque applications and it affects the reliability of the drive system. The effect of ripple is negligible in the low-speed range as compared to the high-speed operations [4]. The cause for the production of torque ripple, the speed versus torque characteristics and the impact of commutation time on non-commutated phase current have been discussed in detail [4]. The two different current control commutation topologies viz., DC-link sensing and DC current sensing have been analysed. The result shows that the ripple can be reduced by the influence of inductance in the machine design. The expression for torque, the torque during conduction and the condition for minimum torque ripple have been analyzed in [5]. The relationship between speed and commutation time has been obtained for various values of speed [6]. The various control strategies for the torque ripple reduction have been listed in [7]. This includes comparison of different current and voltage control strategies of BLDC drive, features, emphasis, and applications of different control techniques. The torque ripple analysis and loss minimization techniques have been elucidated in detail [7]. A modified pulse width modulation (PWM) technique has been suggested to diminish the ripple owing to the mismatch between the energized and de-energized phase currents [8]. The PWM pulse duration is proportionate to the ratio of pulse duration to the commutation period. However, it has been observed that torque ripple reduction using PWM techniques can be used effectively for low-speed applications only [9].
A novel single ended primary inductor converter (SEPIC) with three-level neutral point converter (NPC) has been suggested to decrease the torque ripple during entire speed range [10]. The three-level converter reduces the torque ripple better than the two-level converter due to the application of half the supply voltage and reduces the harmonics which improves the efficiency. A Quasi-Z-source network has been proposed to diminish the torque ripple during the high-speed region [9]. The voltage is boosted using the Quasi-Z-source during the commutation period. A Z-source inverter (ZSI) has been suggested to diminish the ripple and to sense the end point of commutation [11]. A commutation time has been calculated using a comparator circuit with PWM without the calculation of commutation time [12].
A cuk converter control strategy [13] has been recommended during commutation to increase the supply voltage. The buck-boost mode regulates the input voltage using pulse amplitude modulation (PAM). A charged capacitor with two-phase modulation scheme has been stated [14] for the normal conduction and commutation periods. This avoids the need for mode selection circuit since the similar modulation technique has been used during the normal and commutation periods. A DC-link voltage modulator scheme has been reported to decrease the torque ripple [15]. This technique facilitates the commutating turn ON and turn OFF period and improves the DC-link supply during high speed. The ripple has been found to be diminished by a novel Integral variable structure control (IVSC) in which two-phase modulation is used [16]. A buck-boost converter has been used to regulate the phase current during commutation to minimize the ripple [17].
A single -input-dual-output (SIDO) converter is investigated [18] in which two voltage sources are used to supply the inverter and to increase the voltage during commutation. A novel topology using two-phase and three-phase conduction modes are mentioned to decrease the ripple throughout the regular and commutation period respectively [19]. A fuzzy logic based PI controller is proposed for the comparative analysis of BLDC motor [20]. A simple boost converter is mentioned in [21] to minimize the torque ripple with less storage elements.
The different optimization algorithms, analyses and applications have been discussed in [22]. A spider-based control algorithm has been suggested to minimize the ripple using a DC-link capacitor [23]. This algorithm restricts the use of large capacitor and switches and requires a simple and cost-effective BLDC drive. A. Alice Hepzibah et.al suggested an adaptive network-based fuzzy inference system (ANFIS) algorithm for a solar fed water pump system [24]. In this paper, various control approaches for the torque ripple reduction techniques are discussed. The variation on different parameters for the low-speed and high-speed ranges were analyzed. The simulation results provide adequate understanding of different control strategies of torque ripple reduction during the entire speed range.

MATHEMATICAL MODELLING OF BLDC MOTOR
The mathematical modelling of electrical machines gives the relation between its electromagnetic torque and other electrical and mechanical quantities. It is mainly used to obtain the performance parameters of a machine. The equivalent circuit of the BLDC drive system is shown in Figure 1.
It is assumed that the phase resistances = = and the self -inductances ( ) and mutual inductances ( ) are constant. The expression for phase voltages is given by (1).
The stator voltage equation is given by, Figure 2 shows the trapezoidal back emf, phase currents and gate pulses for the equivalent circuit of the BLDC motor. Table 1 gives the various parameters of the converter control circuit used in this paper.

ANALYSIS OF TORQUE RIPPLE IN A BLDC DRIVE
The torque equation is given by (6).
Where, = developed electromagnetic torque (Nm) = Rotor angular velocity (rad/sec) The BLDC motor has three phases in which two phases are supplied with positive and negative energies and third phase is floating. The BLDC motor operated with six step commutations. Let, phase 'a' is positively energised, phase 'b' is negatively energised and phase 'c' is de-energised.
Before commutation, the expression for the developed torque is (8).
After Commutation, the torque expression is given by (9). Hence the current will remain constant for the condition of (14).

= −
The condition for minimum torque ripple can be obtained by adding the (10), (11) and (12) and simplifying, The (15) gives the minimum torque ripple condition [25]. The duty cycle ( ) expression during the conduction period is given by (16).

ANALYSIS OF DIFFERENT TORQUE RIPPLE REDUCTION TOPOLOGIES
In this paper, various control approaches for the torque ripple reduction techniques have been explored. The effect of varying different parameters on torque ripple for the entire speed range has been analyzed. This paper discusses various topologies such as cuk converter, simple voltage modulator scheme, charged capacitor, Z-Source inverter, and Quasi-Z source inverter-based toque ripple reduction techniques.

Cuk converter topology
The cuk converter in Figure 3 is suggested [13] to improve the input voltage during the commutation interval. The switch and diode are used as the mode selection circuit. The normal conduction is enabled when the switch is off and diode is forward biased to drive the BLDC drive through the DC supply voltage. During this mode of operation, the inverter input voltage can be controlled by the speed and current control strategy without the PWM scheme. The switch is closed and diode is open during commutation and the converter is operating in boost mode. In this condition, the DC input voltage can be increased by adding the capacitor voltage.
The proposed strategy performance is verified under rated conditions shown in Table1 of a BLDC motor drive with a speed of 1500 rpm and torque of 2 Nm. This topology has many advantages such as reduction in torque ripple, PAM technique evades the voltage spikes during turn on and off switches and simple modulation scheme. Figure 4 shows the charged capacitor topology [14]. The capacitor charges through the diode by keeping switch 1 off and 2 on during normal interval. This charged voltage is added with the supply voltage during commutation period by turning on 1 and turning off 2 . In this method the input voltage is boosted using charged capacitor during commutation period. This topology does not require DC-DC converter, uses two-phase modulation during both the conduction periods and the voltage stress can be reduced without the use of inductors.

Z source inverter topology
The shoot through state of ZSI in Figure 5 is a forbidden state in voltage and current source inverters because of output voltage distortion and higher current rating which may damage the circuit. But in ZSI, this shoot through state is possible and it improves the performance of power conversion. In this topology, a novel non-commutated phase current stabilization and commutation end point detection were proposed [11]. The zero-crossing point of back electromotive force (EMF) can be obtained by comparing all phase voltages with zero reference voltage. The ZSI improves the DC voltage utilization, enhances the safety and reliability of the system. This method avoids the need of additional current sensors for the commutation end point detection and does not require extra resistances and inductances. Figure 5. ZSI based BLDC drive system for torque ripple reduction

Quasi-Z source inverter topology
The torque ripple during the high-speed operation can be reduced using high gain and smooth reliability characteristics of the Quasi-Z-source inverter [9]. The PWM technique is employed to regulate the speed and the torque ripple. During the non-shoot-through state, the metal oxide semiconductor field effect transistor (MOSFET) is open and 1 and 2 supplies the energy to the load and capacitor 1 stores the energy. During shoot-through state, the MOSFET is closed and the capacitor 2 supplies the load. The boosted voltage can be obtained from the inductor currents 1 and 2 . The switch over from DC supply to Quasi-Z-source network can be accomplished using a power selection circuit and a switch as shown in Figure 6. This reduces the commutation interval delay of the Quasi-Z-source network. This topology is applicable for fans and servo motor systems, and it gives high reliability and improved efficiency.

DC-link voltage modulator scheme
The DC-link Voltage Modulator (DVM) scheme uses switches 1 and 2 , capacitors 1 and 2 , an inductor and diode for the reduction of torque ripple [15]. During normal conduction period 1 is off and

RESULTS AND DISCUSSIONS
This paper compares the various control topologies for the torque ripple reduction. The analysis of stator current and torque ripple is discussed in detail. The torque, speed and stator current of the conventional and cuk converter-based torque ripple reduction techniques are shown in Figures 8 (a) and 8 (b). Figure 9 (a) shows the zoom view of torque waveforms for 500 rpm of 5 Nm load torque whereas and Figure 9 (b) illustrates the torque waveform with 1500 rpm using cuk converter respectively. The 7.2% of non-commutated phase current fluctuation is reduced than the traditional strategy. The high-frequency interference issues of MOSFET switch can be reduced by varying the inverter input voltage by PAM scheme during the normal conduction period. The torque ripple using charged capacitor method is shown in Figures 10 (a) and (b) for the 500 rpm and 1500 rpm with 2 Nm load torque respectively. The ripple is reduced compared to the traditional method using the boosted DC-link voltage. The current and torque ripple are reduced 20% more than the conventional method. The ZSI topology reduces the current ripple considerably than the other torque ripple reduction techniques. The non-commutated current fluctuation as shown in Figures 11 (a) and 11(b) can be reduced by 8.4% which is 23% more than the conventional method in heavy load conditions. The ZSI improves the DC voltage utilization, enhances the safety and reliability of the system. This method avoids the need for additional The PWM modulation scheme is simplified compared to three-phase modulation techniques and reduces the number of MOSFET switches and its driver circuit. The torque ripple waveforms are obtained for 2 Nm load torque with 500rpm speed using Q-ZSI is depicted in Figure 12 (a). The torque ripple for the high-speed range of 1500 rpm is revealed in Figure 12 (b). The torque ripple is reduced by 6.5% during high speed and 8.7% during low speed. The switch over from DC supply to Quasi-Z-source network can be accomplished using a power selection circuit and a switch. This reduces the commutation interval delay of the Quasi-Z-source network. This topology is applicable for fans and servo motor systems, and it gives high reliability and improved efficiency.
The torque waveforms using DVM converter during 500 rpm and 1500 rpm in Figures 13 (a) and 13 (b) shows that the torque ripple reduction is 6% which is better than other topologies. The analysis of MATLAB result shows that the voltage modulation scheme has a better torque ripple reduction than other topologies. This method diminishes the torque ripple during entire speed range with the noise less operation of BLDC motor. Table 2 shows the torque ripple analysis for the different topologies.

CONCLUSION
This paper encompasses the comparative analysis of various control techniques for the torque ripple reduction topologies such as cuk converter, simple voltage modulator scheme, charged capacitor, Z-Source inverter, and Quasi-Z source inverter have been deliberated. Each strategy has its own advantages and disadvantages from different perspectives. The cuk converter topology has resulted in 7.5% of torque ripple minimization during high-speed region and 11% of torque ripple minimization in low-speed region whereas charged capacitor method has resulted in 20% of torque ripple reduction. The DVM method gives better performance than all other topologies by providing 5.5% of torque ripple reduction during high-speed region. The simulation results validates that the DVM has a better torque ripple reduction during entire speed range with the noise-less operation of BLDC motor with less components. ISSN: 2088-8694 