Produção Nacional
Revisado por pares
Unipolar PWM predictive current‐mode control of a variable‐speed low inductance BLDC motor drive
2016; Institution of Engineering and Technology; Volume: 11; Issue: 5 Linguagem: Inglês
10.1049/iet-epa.2016.0421
ISSN1751-8679
AutoresRodolfo L. Valle, Pedro M. de Almeida, Andre A. Ferreira, Pedro G. Barbosa,
Tópico(s)Electric Motor Design and Analysis
ResumoIET Electric Power ApplicationsVolume 11, Issue 5 p. 688-696 Special Issue: Advances in Predictive Control of Variable-Speed Electric DrivesFree Access Unipolar PWM predictive current-mode control of a variable-speed low inductance BLDC motor drive Rodolfo L. Valle, Corresponding Author Rodolfo L. Valle rodolfo.lacerda@leopoldina.cefetmg.br Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, Brazil Electronics Department, Federal Centre of Technological Education of Minas Gerais, Leopoldina, BrazilSearch for more papers by this authorPedro M. de Almeida, Pedro M. de Almeida Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this authorAndre A. Ferreira, Andre A. Ferreira Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this authorPedro G. Barbosa, Pedro G. Barbosa Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this author Rodolfo L. Valle, Corresponding Author Rodolfo L. Valle rodolfo.lacerda@leopoldina.cefetmg.br Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, Brazil Electronics Department, Federal Centre of Technological Education of Minas Gerais, Leopoldina, BrazilSearch for more papers by this authorPedro M. de Almeida, Pedro M. de Almeida Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this authorAndre A. Ferreira, Andre A. Ferreira Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this authorPedro G. Barbosa, Pedro G. Barbosa Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, BrazilSearch for more papers by this author First published: 01 May 2017 https://doi.org/10.1049/iet-epa.2016.0421Citations: 27AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents the design and implementation steps of a digital predictive controller to regulate a low-inductance, three-phase, three-wire permanent magnet brushless DC motor currents. These types of motors are usually driven by multi-stage converters, switched at high frequencies, or use additional inductances to limit the current ripple. The motor's trapezoidal back electromotive force and rectangular currents waveforms make the design and the tuning process of linear controllers difficult. This task complexity increases when a wide speed range is considered. Digital predictive controllers are easily implemented in digital signal processors (DSPs), being successfully used to regulate currents of different types of power electronic converters. A unipolar pulse width modulation predictive controller is proposed here to regulate the rectangular currents of a brushless DC motor, without the need for any additional filter or converter. Experimental and simulation results using a 5 kW/48 V three-phase brushless DC (BLDC) motor are presented to demonstrate the feasibility of this proposal. It will be presented a methodology to compensate the conditioning and sampling circuits delays as well as the inverter's semiconductors voltage drop. The control algorithm was implemented in a TMS320F28335 DSP. 1 Introduction Permanent magnet synchronous motors (PMSM) and brushless DC (BLDC) motors have been widely used as traction engine for electric vehicle (EV) and hybrid electric vehicle [1]. These motors are named according to their back electromotive force (EMF) waveforms. Regardless their lower volume and weight, which are interesting features for embedded applications, they present low values of inductances, resulting in large current and torque ripples [2, 3]. Different converter topologies have been investigated in the literature to drive low inductance motors since they must be switched with high frequencies. In [4, 5], the authors use a two-stage drive, comprised of a buck-converter and a voltage source inverter, to control a BLDC motor. A large inductor limits the buck-converter current ripple while the voltage source inverter (VSI) is switched with a 200 kHz to regulate the motor torque. A similar structure, also based on two-stage converter, was used in [6] to control a inductance BLDC motor. Despite the limitation of the current through the semiconductor switches, the series inductor increases the cost, volume and weight of the drive. Besides the reduction of the current ripple and the precise torque control, the high switching frequency makes the use of multiple control hardware (field programmable gate array and digital signal processor, DSP) necessary, adds complexity to the controller's implementation and does not allow the use of insulated gate bipolar transistors (IGBTs). In [7], a inductance BLDC motor is driven by a three-level inverter. Multilevel converters allow the increase of the DC voltage level since four MOSFETs are series connected in each VSI branch. At the same time, the use of fast switches, like MOSFET, permits high switching frequency, up to 150 kHz. In spite of the lower current ripple, the DC-link midpoint voltage control is one of the biggest challenges when implementing a three-level converter. Several non-ideal conditions, such as time delays, dead-time, among others, make the midpoint DC-link voltage control too complicated for low inductance motors applications. In a similar manner, the low motor's inductance values also make the current controllers design for the PMSM and BLDC motors challenging. Different types of controllers have been proposed in the literature where the aim is to design regulators with high cut-off frequencies to assure small errors over the wide range of the motor speed variation [8]. The successful model predictive control (MPC) applications in processing industries associated with high-performance DSPs development have encouraged researchers and engineers to apply MPC to control more complex and fast dynamic systems [9]. Rodriguez and Cortes [10] have demonstrated the MPC algorithms effectiveness when controlling different types of power electronics converters and plants. As the semiconductor switches are turned on and off many times per cycle, it is possible to choose a combination of active switches to optimise a cost function or to force the error, between the reference and controlled variables, to go to zero in a finite number of sampling periods. In [11-14], predictive current control algorithms are applied to different motor drives. They can be grouped into: (i) two-configuration, (ii) direct and (iii) pulse width modulation (PWM) predictive techniques [13]. The two-configuration predictive control uses a modulator to apply two different inverter branches configurations during the commutation period minimising the current error. The direct predictive controller estimates the current future value for each inverter's output voltage vector. Then, a cost function is used to determine the voltage vector which minimises the current error [14]. The last type is the PWM predictive control (PPC). It calculates, at the present time, the necessary change in the control signal that makes the current track its reference at the next sample [13]. The PPC has the advantage of not requiring an optimisation algorithm. Therefore, it is less computationally complex and exhibits the fastest dynamic response among aforementioned predictive controllers. Based on the previous considerations, the PWM predictive is an interesting and promising option to regulate the currents of low inductance BLDC motors. On the other hand, the PPC main drawbacks are: (i) steady-state errors; (ii) effectiveness compromised under parametric uncertainties, as well as, delays and non-linearities if not taken into account during the controller design [15]. These constraints may restrict the PCC application. In [16], the authors added an integral action to eliminate the current error. However, it changes the BLDC motor dynamical behaviour reducing the compensated system stability margins. This work main contribution is the design of a fast current predictive control applied to a 5 kW/48 V three-phase three-wire brushless DC motor with a low winding inductance (). The control algorithm is implemented without the cost function minimisation to ensure a fast dynamic for the controller. A simple methodology, based on the current waveform behaviour, is proposed to compensate the drive steady-state error without the need of additional controller. It is used a single-stage two-level IGBT-inverter to drive the BLDC motor. The conduction mode of the BLDC motor allows to control the VSI as a full bridge DC–DC converter, increasing the equivalent switching frequency up to 100 kHz, while each IGBT is commutated with 50 kHz, reducing the current ripple without the need of connection of any additional series inductance or converter stage. This paper is organised as follows: Section 2 presents the BLDC drive analysis showing that the current flows only between two phases of the motor at every time period. This feature allows to control the three-phase BLDC drive as a full-bridge DC–DC converter, and the use of an unipolar PWM strategy to increase its output equivalent switching frequency. Section 3 addresses the design steps of the proposed unipolar PWM predictive current controller. Initially, the current controller is designed to track the changes in the reference signal in one sampling period. However, due to the computational limitations, the algorithm is applied in two consecutive sampling periods to overcome the hardware constraints. In Section 4, it is analysed how the uncertainties and variations of the motor parameters affect the system absolute stability. The theoretical analyses are validated by experimental results. Section 5 describes the methodology to compensate the delays and non-linearities of the motor drive in the unipolar PPC algorithm. Section 6 presents the laboratory prototype. Experimental results are used to demonstrate the feasibility of the proposed control strategy. Section 7 presents some concluding remarks. 2 The BLDC motor drive Fig. 1a shows the schematic diagram of the BLDC motor drive based on a three-phase VSI. The voltages , and represent the phase-to-neutral back EMF while R and L are the resistance and inductance of the BLDC phase winding, respectively. This system is intended to be embedded on a small-scale EV. In Fig. 1a, coloured lines indicate the phases which are conducting a non-zero current during the operation period depicted inside Fig. 1b highlighted rectangle. Fig. 1Open in figure viewerPowerPoint Variable speed BLDC drive a Simplified schematic diagram b Back EMF (continuous lines) and currents (dashed lines) waveforms At a first glance, the back EMF trapezoidal waveform shown in Fig. 1b can be viewed as a disadvantage. However, the power density and torque increase ∼15% for the same current level. This feature also simplifies the position sensors placement in the machine stator since it will be only necessary to identify six different positions of the BLDC rotor [2]. Another advantage is related to the BLDC motor drive controller design. Considering that, during each rad, the current flows only by two phases of the motor, it is not necessary to design three but only one current controller to regulate a ‘pseudo’ current calculated by (1)where is the magnitude of the ‘pseudo’ current synthesised by the VSI [17-19]. Notwithstanding, having in mind the operation of the motor inside the highlighted sector of Fig. 1b, it is possible to use two different PWM switching strategies to control the VSI output voltage and current [20]. In the bipolar PWM pattern, the modulating signal is compared with an up-down counter to generate the PWM signals, whereas the output voltage is switched between and . On the other hand, the unipolar PWM pattern uses two triangular carrier waves, phase shifted by rad between them, to generate the PWM signals and as shown in Figs. 2a and b, respectively. The output voltage is switched between 0 and with a frequency two times higher than the frequency of the triangular carrier wave (Fig. 2c). Fig. 2d depicts the ‘pseudo’ current waveform. Fig. 2Open in figure viewerPowerPoint Unipolar PWM pattern waveforms a Modulating signal and triangular carrier waves b PWM signals ( and ) c VSI output voltage () d Synthesised ‘pseudo’ current () It is important to emphasise that the operation strategy described in this section allows the control of the three-phase BLDC drive as a full-bridge DC–DC converter, increasing the inverter output equivalent switching frequency by using an unipolar PWM pattern. Consequently, it is also possible to employ different types of predictive controllers, which were originally developed for DC–DC converters. This characteristic is not a disadvantage, but in fact, an interesting and promising field to be explored. The technique presented here can also be easily applied to any multiphase BLDC motors in which the conduction mode is , where P is the number of the motor phases. In this case, the inverter branches may be controlled as full-bridge DC–DC converters. In the next section, it will be shown how the waveforms of Fig. 2, as well as the duty cycle d[k], can be used to derive a predictive control law to regulate the the BLDC motor currents. 3 Unipolar PWM predictive current controller design The BLDC drive current control must quickly respond to changes on the motor load assuring an acceptable torque ripple. Therefore, the predictive control is a suitable technique to meet the aforementioned requirements. Due to the fact that the operation sector shift does not affect the ‘pseudo’ current behaviour, the control strategy development will only address the operation within the highlighted rectangle depicted in Fig. 1b. Therefore, neglecting the resistance of the motor winding () and taking into consideration the output voltage and current waveforms shown in Figs. 2c and d, the following relation can be written for the ‘pseudo’ current (2)where is the period between and in which is ; is the period between and in which is 0; is the sampled period; ; and are, respectively, the ‘pseudo’ current rise and fall rates, which are given by (3)and (4)where L is the motor per phase inductance and . It was considered that the mechanical time constant is greater than in (3) and (4). Therefore, the back EMF value, which depends on the shaft speed, was assumed constant during a switching period. Substituting (3) and (4) into (2), isolating d[k] and making yields (5)where is the reference current, d[k] is the duty cycle for the unipolar PWM pattern between the intervals and . The duty cycle range is . However, there are some operation modes, for example the regenerative breaking, where the control variable may assume negative values. Therefore, making , it is possible to rewrite (5) as follows (6)where is the modulation index for the unipolar PWM signal generator. The modulation index m[k] is the control signal calculated by the PWM predictive controller in the instant that is sent to the VSI modulator to force the ‘pseudo’ current track the reference current in the next sample period . Sometimes, due practical limitations, it is not possible to sample, execute the algorithm and act as fast as shown in Fig. 2. To overcome this constraint, (6) is applied to two consecutive periods resulting in the following control law (7)where is the reference current and m[k + 1] is the modulation index for the period between and . That is, (7) returns the modulation index for the instant to force the VSI output current to track its reference after two samples. One constraint of the proposed methodology takes place when the motor resistance is not negligible. In this case, the predictive current law given by (7) lose its effectiveness and the design steps presented in this section should be revalidated considering the effect of this parameter. 4 Absolute stability analysis According to the previous developments, the predictive control algorithm regulates the BLDC currents in such a way that the reference signal is tracked after two samples. However, the uncertainties or variations on the motor parameters may compromise the algorithm effectiveness given in (7). Neglecting the harmonics generated by the switched operation of the VSI, the following dynamic equation can be written for the active branches shown in Fig. 1a(8)where and . Applying the zero-order hold (ZOH) [21] to discretize (8), the following state-space representation is obtained (9)where (10)and (11)Substituting and into (9) and applying the -transform in the resulting difference equation yields (12)In the same way, applying the -transform in the difference equation of the PWM predictive controller given by (7) returns (13)The subscript ‘c’ associated to and in (13) was introduced here to differentiate the estimated parameters used in the control law from the real ones. From (12) and (13), it is possible to draw the control block diagram depicted in Fig. 3a. Assuming the BLDC voltage E is effectively compensated by the feed-forward signal , the following closed-loop transfer function can be written (14) Fig. 3Open in figure viewerPowerPoint Compensated system poles locus under parametric variation a Variable speed BLDC drive (PPC and BLDC) block diagram b Assuming and varying R c Assuming R = 0 and varying L Considering and , the discrete transfer function (14) is reduced to . In this way, the PPC can be viewed as a discrete case of state feedback controller in which the compensated poles are placed in the origin of the complex z-plane. The Jury's stability criterion is very useful to determine whether the uncertainties on affect the compensated system pole location by moving it to the instability region [21]. Thus, to guarantee that the poles of (14) are inside the unit circle, the follow inequality must remain true (15)The inequality in (15) is reduced to when . This condition implies that the compensated system will be unstable if the parameter exceeds twice the value of the motor inductance L. The discrete closed-looped function in (14) can also be used to investigate how the motor parameters R and L affect the compensated system poles location. On the other hand, parametric errors due to measurement or variations on the motor operation point may lead the designer to pick wrong values when tuning the predictive controller. Figs. 3b and c show the locus of the poles considering the variations on the motor resistance and inductance, respectively. As can be seen the poles do not remain exactly at the origin of the complex z-plane. By the analysis of the aforementioned figures, it is possible to conclude that, variations of the resistance does not affect significantly the poles location, while changes in L can make the system unstable. From Fig. 3c, considering , the compensated system will present an underdamped characteristic until , when it will become unstable. In contrast, for , the compensated system will show an overdamped characteristic. An interesting condition to be investigated takes place at the end of the highlighted rectangle of Fig. 1b. During a short overlapping period, the three phases of the VSI are active and the equivalent phase inductance is reduced to (3/4) L. Thus, replacing L by (3/4) L in (12) and substituting into (13), the poles of the compensated system move to , as shown in Fig. 3c. Although this condition happens six times per cycle, the poles remain inside the unity circle and (14) stays stable. Figs. 4a–c show the experimental step response of the ‘pseudo’ current when the parameter is chosen equal to L, 1.5L and 0.5L, respectively. The reference current signal is changed from 15 to 20 A. As predicted by the previous analysis, the choice of produces an underdamped current response (Fig. 4b), while for an overdamped current response is obtained (Fig. 4c). Ideally, when (Fig. 4a), the current tracks its reference signal in two sampling periods. Fig. 4Open in figure viewerPowerPoint Behaviour of the ‘pseudo’ current for a step change on the reference signal from 15 to 20 A a b c All the results presented in this section were obtained using a motor which parameters are , and . The VSI switching frequency is 50 kHz and the DC link voltage 48 V. More details about the variable speed BLDC drive prototype are presented in Experimental results. 5 Driver parameters compensation Despite the good dynamic performance and robustness of the predictive controller, the currents synthesised by the VSI exhibit steady-state errors due to non-linear effects such as blanking-time, voltage drops on the semiconductor switches, delay time of pulse drive and sampling delay time [13]. In the following sections is presented how the aforementioned undesired effects can be easily compensated in the PPC algorithm [22]. 5.1 The blanking time In practice, due to the finite turn-on and turn-off times, the active switch of each VSI branch is turned off before the other is turned on. This time delay is chosen in a way to avoid a short-circuit or cross-conduction current through the VSI branches [20]. As a consequence, the output voltage of each VSI branch is reduced or increased, depending on the direction of the current flow, by following factor (16)where is the blanking time; is the inverter output voltage increasing or decreasing factor, and N is the negative terminal of the VSI. Therefore, having in mind the unipolar PWM switching pattern, the rates and can be recalculated substituting by and into (3) and (4), respectively, to correct the predictive control law given by (7), where . 5.2 The delay time of pulse drive Figs. 5a–c show the pulse drive delay time effect on the VSI output voltage and current. The current is sampled every time the main triangular carrier waveform reaches its peak value as shown in Fig. 5c. This choice provides a good noise immunity on the current sensor signal since the average value of the ‘pseudo’ current is sampled without the need of any passive filter. Fig. 5Open in figure viewerPowerPoint Pulse drive delay effect on the ‘pseudo’ current synthesise by the VSI a Inverter output voltage b Real and delayed currents c Triangular carrier Comparing the drawings (dashed and solid lines) are shown in Fig. 5, it is possible to conclude that the delay time will cause an offset error on the ‘pseudo’ current. A possible solution is to calculate a correction factor for the sampled current as follows (17)where is the delay time of pulse drive; is the current fall rate of . Since is negative, the addition of the factor in the sample current will force the predictive control law (7) to correct the index m[k + 1] to compensate the undesired offset on the synthesised current. 5.3 The sampling delay time The delay time of the sampling and the conditioning circuits produce an offset error on the sampled current similar to that shown in Fig. 5b. As in the previous case, this delay time can be compensated by adding a factor in the sample current given by (18)where is the delay time of the sampling and conditioning circuits. 5.4 Voltage drop of the semiconductor switches Similarly to blanking-time, the voltage drop of the semiconductor switches reduces the VSI output voltage. The polarity and the value of the voltage drop will depend on the direction of the current flow and on which switches are active. Considering the active branches depicted in Fig. 1a, it is possible to calculate new values for output voltage as (19)where is the voltage drop in each active switch. To simplify the compensation factor, the voltage drop of all semiconductors switches is considered equals. Substituting (19) into (3) and (4), respectively, it is possible to recompute the predictive control law taking into account the voltage drops in the semiconductor switches. 6 Experimental results Fig. 6a shows the block diagram of a variable speed BLDC motor drive prototype built in the laboratory to demonstrate the feasibility of the proposed predictive control. In this figure, the phase selector block diagram is also responsible for determining the branches of the VSI which will be activated during each rad sector of the operation cycle. Fig. 6b shows the picture of the BLDC motor manufactured by Golden Motor Inc. whose main parameters are given in Table 1. Fig. 6c shows the picture of the three-phase VSI built with SEMiX101GD066HDS Semikron® module. This system is intended to be embedded into a small EV which the electrical energy will be supplied by a lithium-ion battery. Table 1. BLDC motor characteristics Parameter Value rated power 5 kW rated voltage 48 V rated current 100 A maximum efficiency 89.1% resistance per phase 6.2 mΩ inductance per phase 14.8 μH 0.0125 V/rpm number of poles 8 weight 11 kg maximum torque 13.92 Nm rated speed 3532 rpm Fig. 6Open in figure viewerPowerPoint Experimental setup a BLDC current controller block diagram b Picture of the BLDC motor and load (DC generator) c Picture of the three-phase inverter and auxiliary circuitries The control algorithm of the BLDC motor as well as the detection rotor position and speed algorithms were implemented in a TMS320F28335 DSP from Texas Instruments Inc. Fig. 7a shows the steady-state three-phase current waveforms of the BLDC while Fig. 7b shows the harmonic spectrum of phase ‘a’ current. The reference ‘pseudo’ current signal is 15 A and the ripple of the synthesised current is 6 A. Figs. 8a and b show the current waveforms and the phase ‘a’ harmonic spectrum, respectively, when a bipolar PWM predictive controller is used [23]. Although both controllers synthesise currents with the same steady-state value, the current ripple of the bipolar controller (Fig. 8a) is 280% higher than the ripple produced by the unipolar. Fig. 7Open in figure viewerPowerPoint Unipolar PWM three-phase currents of BLDC motor (, ) a Steady-state PWM waveforms b Harmonic spectrum of phase ‘a’ current Fig. 8Open in figure viewerPowerPoint Bipolar PWM three-phase currents of BLDC motor (, ) a Steady-state PWM waveforms b Harmonic spectrum of phase ‘a’ current The comparison of Figs. 7b and 8b shows that the lower-order switching harmonics of the unipolar strategy come in side bands around 100 kHz, whereas the switching harmonics of the bipolar strategy arise around 50 kHz. Thus, considering the commutation frequency is the same in these two strategies, the unipolar PWM predictive current controller will result in a better torque response [24] since the current ripple is reduced and the frequency of the switching harmonics is two times higher than the commutation frequency of the VSI (50 kHz). Incorporating the compensating factors (16), (17), (18) and (19) into (7) yields the following the compensated predictive control law (20)where , , and can be obtained experimentally and their values are given in Table 2. Table 2. Delays and voltage drop of the BLDC drive Parameter Value blanking time 600 ns sample delay time 1.2 μs delay time of pulse drive 600 ns voltage drop of switches 1.45 V Fig. 9 shows the step response of the current of the phase ‘a’ for the predictive control laws given by (7) and (20), without and with the parametric compensation, respectively. In these figures, the red dashed line indicates the instant in which the ‘pseudo’ reference current is varied from 15 to 30 A. As expected, the current of the BLDC tracks its reference signal in a fast way, two sampling periods, regardless of the control algorithm and the instant in which the reference signal is changed. The comparison between the current waveforms depicted in Figs. 9a and b demonstrates that the methodology proposed in this work compensates the steady-state error without affecting the transient response of the system. Fig. 9Open in figure viewerPowerPoint Phase ‘a’ BLDC current for a step change in the reference signal from 15 to 30 A a Without parametric compensation b With parametric compensation Figs. 10a and b show the current of the phase ‘a’ considering the operation of the BLDC motor at 500 and 2000 rpm, respectively. The mechanical load was adjusted to force the BLDC motor to drain the same ‘pseudo’ current in both cases. The comparison of the waveforms shows that the current is not fully rectangular in the second case. This behaviour is due to the fact that the back EMF is not thoroughly trapezoidal for the operation of the motor at high speeds since the airgap magnetic flux does not vary abruptly. As a consequence, there will be an error between the real back EMF and the estimated one. Fig. 10Open in figure viewerPowerPoint Steady-state current waveform for the operation of the BLDC at a 500 rpm b 2000 rpm One way to improve the current waveform is shown in Fig. 10b can be achieved by measuring and storing the points of the back EMF waveform, for different motor speeds, by addressing these points as a function of the rotor position during the machine operation. However, from Fig. 3a, assuming that voltage E (real back EMF) is not entirely compensated by the feed-forward signal (estimated EMF), due to the aforementioned error, it is possible to write a disturbance transfer function which poles will be at the same location as those given in (14). Therefore, if the estimation error of the back EMF is bounded, the current of the compensated system will present a stable behaviour since the poles of the disturbance transfer function are placed inside the unity circle [21]. Finally, an outer speed loop is added and the ECE-15 (European Driving Cycle 15) is used to investigate the performance of the predictive current controller. Fig. 11a shows the BLDC reference signal and speed (upper curves) and the phase ‘a’ current (bottom curve). In Fig. 11b, the ECE-15 was modified replacing the smooth variations of the speed reference signal by step changes. Both results demonstrate that the predictive current control of the BLDC drive presents a quick response, assuring a good speed tracking. Fig. 11Open in figure viewerPowerPoint Speed BLDC control: reference signal and motor speed (upper curves) (vert. scale: 500 rpm/div), phase ‘a’ BLDC current (bottom curve) a European driving cycle (ECE-15) benchmark b Modified European driving cycle benchmark 7 Conclusion This paper proposed a novel PWM predictive controller to regulate the currents of a low inductance 5 kW/48 V three-phase three-wire brushless DC motor. The key idea is to control the three-phase VSI as a full-bridge DC–DC converter which allows increasing the inverter output equivalent frequency switching up to 100 kHz while each individual switch is commutated with 50 kHz. This strategy made it possible to use an IGBT-based VSI to drive the BLDC. It also made possible the predictive algorithm optimisation due to the fact that it is only necessary to run one control algorithm to regulate a ‘pseudo’ current. Furthermore, it avoids the cumbersome cost function minimisation. Despite of the simple processing requirement, the robustness and reliability of the predictive controller is strongly influenced by model mismatches and parameter variation. An analysis of the absolute stability was performed under parametric uncertainties. A methodology to eliminate the steady-state error due to blanking time, pulse driver delay, sampling delay and switches voltage drop was presented and incorporated in the modified predictive control law. The experimental results obtained with a laboratory prototype were presented to validate the theoretical analyses. The performance of the predictive current controller was tested for different motor speeds, demonstrating a fast response and a good current tracking. The unipolar PWM strategy resulted in a better frequency response since the current ripple was reduced and the switching harmonic frequency was doubled. 8 Acknowledgment The authors thank FAPEMIG, CNPq, INERGE and SEMIKRON for the financial support and semiconductor donation for this work. 9 References 1Asano, K., Inaguma, Y., Ohtani, H., et al: ‘ High performance motor drive technologies for hybrid vehicles’. 2007 Power Conversion Conf.-Nagoya, 2007 2Krishnan, R.: ‘ Permanent magnet synchronous and brushless DC motor drives’ ( CRC Taylor & Francis, 2010) 3Krah, J.-O., Holtz, J.: ‘High-performance current regulation and efficient PWM implementation for low-inductance servo motors’, IEEE Trans. Ind. Appl., 1999, 35, (5), pp. 1039– 1049 (doi: https://doi.org/10.1109/28.793364) 4Fang, J., Zhou, X., Liu, G.: ‘Instantaneous torque control of small inductance brushless dc motor’, IEEE Trans. Power Electron., 2012, 27, (12), pp. 4952– 4964 (doi: https://doi.org/10.1109/TPEL.2012.2193420) 5Fang, J., Zhou, X., Liu, G.: ‘Precise accelerated torque control for small inductance brushless dc motor’, IEEE Trans. Power Electron., 2013, 28, (3), pp. 1400– 1412 (doi: https://doi.org/10.1109/TPEL.2012.2210251) 6Li, H., Zheng, S., Ren, H.: ‘Self-correction of commutation point for high-speed sensorless bldc motor with low inductance and nonideal back emf’, IEEE Trans. Power Electron., 2017, 32, (1), pp. 642– 651 (doi: https://doi.org/10.1109/TPEL.2016.2524632) 7De, S., Rajne, M., Poosapati, S., et al: ‘Low-inductance axial flux bldc motor drive for more electric aircraft’, IET Power Electron., 2012, 5, (1), pp. 124– 133 (doi: https://doi.org/10.1049/iet-pel.2010.0329) 8Chau, K., Chan, C., Liu, C.: ‘Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles’, IEEE Trans. Ind. Electron., 2008, 55, (6), pp. 2246– 2257 (doi: https://doi.org/10.1109/TIE.2008.918403) 9Mohamed, T., Bevrani, H., Hassan, A., et al: ‘Decentralized model predictive based load frequency control in an interconnected power system’, Energy Convers. Manage., 2011, 52, (2), pp. 1208– 1214 (doi: https://doi.org/10.1016/j.enconman.2010.09.016) 10Rodriguez, J., Cortes, P.: ‘ Predictive control of power converters and electrical drives’ ( John Wiley & Sons, 2012), vol. 40 11Wang, X., Wang, X., Fu, T., et al: ‘Predictive instantaneous torque control for disc coreless permanent magnet synchronous motor with the current source chopper’, IEEE Trans. Power Electron., 2015, 30, (12), pp. 7100– 7112 (doi: https://doi.org/10.1109/TPEL.2015.2388705) 12Sozer, Y., Torrey, D.A., Mese, E.: ‘Adaptive predictive current control technique for permanent magnet synchronous motors’, IET Power Electron., 2013, 6, (1), pp. 9– 19 (doi: https://doi.org/10.1049/iet-pel.2012.0155) 13Morel, F., Lin-Shi, X., Rétif, J.-M., et al: ‘A comparative study of predictive current control schemes for a permanent-magnet synchronous machine drive’, IEEE Trans. Ind. Electron., 2009, 56, (7), pp. 2715– 2728 (doi: https://doi.org/10.1109/TIE.2009.2018429) 14Arashloo, R.S., Salehifar, M., Romeral, L., et al: ‘A robust predictive current controller for healthy and open-circuit faulty conditions of five-phase bldc drives applicable for wind generators and electric vehicles’, Energy Convers. Manage., 2015, 92, pp. 437– 447 (doi: https://doi.org/10.1016/j.enconman.2014.12.075) 15Alexandrou, A.D., Adamopoulos, N.K., Kladas, A.G.: ‘Development of a constant switching frequency deadbeat predictive control technique for field-oriented synchronous permanent-magnet motor drive’, IEEE Trans. Ind. Electron., 2016, 63, (8), pp. 5167– 5175 (doi: https://doi.org/10.1109/TIE.2016.2559419) 16Na, W., Park, T., Kim, T., et al: ‘Light fuel-cell hybrid electric vehicles based on predictive controllers’, IEEE Trans. Veh. Technol., 2011, 60, (1), pp. 89– 97 (doi: https://doi.org/10.1109/TVT.2010.2087045) 17Fakham, H., Djemai, M., Busawon, K.: ‘Design and practical implementation of a back-emf sliding-mode observer for a brushless dc motor’, IET Electric Power Appl., 2008, 2, (6), pp. 353– 361 (doi: https://doi.org/10.1049/iet-epa:20070242) 18Dixon, J.W., Leal, L.: ‘Current control strategy for brushless dc motors based on a common dc signal’, IEEE Trans. Power Electron., 2002, 17, (2), pp. 232– 240 (doi: https://doi.org/10.1109/63.988834) 19Berendsen, C.-S., Champenois, G., Bolopion, M.: ‘Commutation strategies for brushless dc motors: influence on instant torque’, IEEE Trans. Power Electron., 1993, 8, (2), pp. 231– 236 (doi: https://doi.org/10.1109/63.223976) 20Mohan, N., Undeland, T., Robbins, W.: ‘ Power electronics: converters, applications, and design, number v. 1 power electronics: converters, applications, and design’ ( John Wiley & Sons, 2003) 21Åström, K.J., Wittenmark, B.: ‘ Computer-controlled systems: theory and design’ ( Courier Corporation, 2013) 22Cortés, P., Kazmierkowski, M.P., Kennel, R.M., et al: ‘Predictive control in power electronics and drives’, IEEE Trans. Ind. Electron., 2008, 55, (12), pp. 4312– 4324 (doi: https://doi.org/10.1109/TIE.2008.2007480) 23Damasceno, A., Braga, H., Barbosa, P.: ‘ Battery charge system based on bidirectional dc-dc converter employing a digital current-mode controller for photovoltaic applications’. Proc. of Brazilian Power Electronics Conf., 2007, pp. 388– 394 24Song, J.-H., Choy, I.: ‘Commutation torque ripple reduction in brushless dc motor drives using a single dc current sensor’, IEEE Trans. Power Electron., 2004, 19, (2), pp. 312– 319 (doi: https://doi.org/10.1109/TPEL.2003.823177) Citing Literature Volume11, Issue5May 2017Pages 688-696 FiguresReferencesRelatedInformation
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