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A disturbance observer based approach to current control of PMSM drives for torque ripple reduction
2019 IFAC Workshop on 2019 IFAC Workshop on 2019 IFAC Workshop Control of Smart Gridon and RenewableAvailable Energy Systems online at www.sciencedirect.com Control of Smart Gridon and Renewable Energy Systems 2019 IFAC Workshop Control of Smart and Renewable Energy Systems 2019 Workshop on Jeju, IFAC Korea, JuneGrid 10-12, 2019 Jeju, Korea, JuneGrid 10-12, 2019 Control of Smart and Renewable Energy Systems Jeju, Korea, JuneGrid 10-12, 2019 Control of Smart and Renewable Energy Systems Jeju, Korea, June 10-12, 2019 Jeju, Korea, June 10-12, 2019
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IFAC PapersOnLine 52-4 (2019) 206–209
A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for torque ripple reduction A disturbance observer based approach to current control of PMSM drives for torque ripple reduction torque ripple reduction torque ripple reduction torque ripple reduction Yong-Hun Kim*, Kyunghwan Choi**, Yong-Hun Kyunghwan Choi**, Yong-Hun Kim*, Kim*, Kyunghwan Choi**, Seok-Kyoon Kim***, Kyung-Soo Kim** Yong-Hun Kim*, Seok-Kyoon Kim***, Kyung-Soo Kim** Kyunghwan Choi**, Yong-Hun Kim*, Kyunghwan Choi**, Seok-Kyoon Kim***, Kyung-Soo Kim** Seok-Kyoon Kim***, Kyung-Soo Seok-Kyoon Kim***, Kyung-Soo Kim** Kim** KAIST, Daejeon, Korea (e-mail: [email protected]). *Eco-friendly Smart Vehicle Research Center, KAIST, Daejeon, Korea (e-mail: [email protected]). *Eco-friendly Smart Vehicle Research Center, *Eco-friendlyofSmart VehicleEngineering, Research Center, KAIST, Daejeon, Korea (e-mail: [email protected]). **Department Mechanical KAIST, Daejeon, Korea (e-mail:[email protected]) *Eco-friendly Vehicle Research Center, KAIST, Daejeon, (e-mail: [email protected]). **Department ofSmart Mechanical Engineering, KAIST, Daejeon, KoreaKorea (e-mail:[email protected]) *Eco-friendly Smart Vehicle Research Center, KAIST, Daejeon, Korea (e-mail: Daejeon, [email protected]). **Department of Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department of Creative Convergence Engineering, Hanbat National University, Korea (e-mail: **Department of Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea (e-mail: (e-mail: **DepartmentofofCreative Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department Convergence Engineering, Hanbat National University, Daejeon, Korea [email protected])} ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea [email protected])} ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea (e-mail: (e-mail: [email protected])} [email protected])} [email protected])} Abstract: This paper paper deals deals with with the the reduction of of torque ripple ripple in aa PMSM PMSM (permanent (permanent magnet magnet Abstract: This Abstract: This paper deals with the reduction reduction of torque torque ripple in in a current PMSM ripple (permanent magnet synchronous motor) drive using disturbance observer based control. The is periodically synchronous motor) drive using disturbance observer based control. The ripple is Abstract: This paper deals with the reduction of ripple in PMSM (permanent magnet Abstract: This paper deals with the reduction of torque torque ripple back-EMF in PMSM (permanent magnet synchronous motor) drive using disturbance observer based control. Theaa current current ripple is periodically periodically synchronized to the position of the rotor in the form of distorted voltage. Therefore, the synchronous motor) drive using disturbance observer based control. The current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the synchronous motor) drive using disturbance observer based control. The current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking performance without a significant change of the controller by intensively increasing the disturbance this paper, a method is introduced to reduce the current ripple while maintaining reference tracking performance without change of the by increasing the disturbance this paper, aperformance method aais significant introduced to reduce the controller current ripple while maintaining reference tracking performance without significant change ofband the controller by intensively intensively increasing the disturbance suppression of the frequency corresponding to the current ripple. The proposed performance without aa significant change of the controller by increasing the disturbance suppression performance of corresponding to the ripple. The proposed performance without change ofband the controller by intensively intensively increasing the suppression performance of the the frequency frequency band corresponding to the current current ripple. Thedisturbance proposed method is verified that aa significant steady-state 58% ripple reduction in 500W SPMSM in the experiments. suppression performance of the frequency band corresponding to the current ripple. The method is verified that steady-state 58% ripple reduction in 500W SPMSM in the experiments. suppression performance of the frequency band corresponding the current The proposed proposed method is verified that a steady-state 58% ripple reduction in 500Wto SPMSM in the ripple. experiments. method verified that aa control; steady-state 58% ripple reduction in 500W SPMSM in the experiments. © 2019, is IFAC (International Federation ofripple Automatic Control) Hosting by Elsevier Ltd. All rights reserved. method is verified that steady-state 58% ripple reduction in 500W SPMSM in the experiments. Keywords: motor drive; torque reduction; disturbance observer; Keywords: Keywords: motor motor drive; drive; control; control; torque torque ripple ripple reduction; reduction; disturbance disturbance observer; observer; Keywords: motor drive; control; torque ripple reduction; disturbance observer; Keywords: motor drive; control; torque ripple reduction; disturbance observer;
1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION INTRODUCTION 1. INTRODUCTION Permanent Magnet Magnet 1. Synchronous motor (PMSM) (PMSM) has has been been Permanent Synchronous motor Permanent Magnet Synchronous motor (PMSM) hasrobots, been well received in applications such as drones, mobile Permanent Magnet Synchronous motor (PMSM) has been well received in applications such as drones, mobile robots, Permanent Magnet Synchronous motor (PMSM) has been well received in applications such as drones, mobile robots, and vacuum inpumps pumps for such decades of versatility versatility and well received applications as drones, mobile robots, and vacuum for decades of and well received in applications such as drones, mobile robots, and vacuum pumps for decades of versatility and performance. Particularly in electric and hybrid vehicles, and vacuum pumps for decades of versatility and performance. Particularly in electric and vehicles, and vacuum pumpsfor for of hybrid versatility and performance. Particularly in decades electric and hybrid vehicles, PMSM is responsible power sources ranging from 0.5 kW performance. Particularly in electric and hybrid vehicles, PMSM is responsible for power sources ranging from 0.5 kW performance. Particularly in electric and hybrid vehicles, PMSM is responsible forwith power sources rangingelectric from 0.5 kW to several hundred kW kW traction motors, power PMSM is responsible for power sources ranging from kW to several hundred traction motors, power PMSM isand responsible forwith power sources rangingelectric from 0.5 0.5 kW to several hundred kW with traction motors, electric power steering generators. to several hundred kW with traction motors, electric power steering and generators. to several kW with traction motors, electric power steering andhundred generators. steering and generators. steering and unwanted generators.properties Among the the unwanted properties of of the the motor, torque torque ripple ripple Among Among the unwanted properties of the tomotor, motor, torque ripple has been the subject of much research reduce the control has been the subject of much research to reduce the control Among the unwanted properties of the motor, torque ripple Among the unwanted properties of the motor, torque ripple has been the subject of much research to reduce the control accuracy in precision precision applications and to energy efficiency in has been the subject of much research reduce the control accuracy in applications and energy efficiency in has been the subject of much research to reduce the control accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple and noise. noise. Among them, the issues issues related to the the lifetime of large systems. There are many reasons to reduce torque ripple and Among them, the related to lifetime of large systems. There are many reasons to reduce torque ripple and noise. Among them, the issues related to the lifetimeand of the power device are most important (Rodriguez and noise. Among them, issues related to the lifetime of the power device are the most important (Rodriguez and and noise. the issues related to the and lifetime of the powerAmong device most important (Rodriguez and Amaratunga, 2008).them, Inare other words, torque ripple ripple current the power device are most important (Rodriguez and Amaratunga, 2008). In other words, torque and current the power device are most important (Rodriguez and Amaratunga, 2008). In other words, torque ripple and current noise are the the main main causes of shortening shortening the ripple lifetime ofcurrent power Amaratunga, 2008). In words, torque and noise are of the lifetime of power Amaratunga, 2008).causes In other other words, torque ripple and noise are the main causes of shortening the high lifetime ofcurrent power electronic devices. Particularly, in recent performance electronic devices. Particularly, in recent high performance noise are the main causes of shortening the lifetime of power noise are the main causes of shortening the lifetime of power electronic devices. Particularly, in recent high performance inverters, expensive film capacitors capacitors are applied applied to dc-link. dc-link. electronic devices. Particularly, in recent high performance inverters, expensive film are to electronic devices. Particularly, in recent high performance inverters, expensive film capacitors are applied to dc-link. Such charge discharge ofcapacitors the film film capacitor decreases the inverters, expensive film are to Such charge /// discharge the decreases the inverters, expensive film of areofapplied applied to dc-link. dc-link. Such charge discharge ofcapacitors the film capacitor capacitor decreases the performance and requires replacement parts (Wang and Such charge / discharge of the film capacitor decreases the performance and requires replacement of parts (Wang and Such charge / discharge of the film capacitor decreases the performance and requires replacement of parts (Wang and Blaabjerg, 2014). This is a particularly important issue for performance and requires replacement of parts (Wang and Blaabjerg, 2014). This is particularly issue for performance and requires ofimportant partsresearch (Wang and Blaabjerg, 2014). This hybrid is aareplacement particularly important issue into for electric vehicles and vehicles, and Blaabjerg, 2014). This is a particularly important issue for electric vehicles and hybrid vehicles, and research into Blaabjerg, 2014). This hybrid is aand particularly issue for electric vehicles and vehicles, isimportant and research into making robust capacitors batteries considered to be electric vehicles and hybrid vehicles, and research into making robust capacitors and batteries is considered to be electric vehicles and hybrid vehicles, and research into making robust capacitors and batteries is considered to be one of the biggest challenges to the commercialization of one of the biggest challenges to the commercialization of making robust capacitors and batteries is considered to be making robust capacitors and batteries is considered to be one of the biggest challenges to the commercialization of electric vehicles from 2000s. one of the challenges to electric from 2000s. one of vehicles the biggest biggest to the the commercialization commercialization of of electric vehicles fromchallenges 2000s. electric vehicles from 2000s. electric vehicles from 2000s. Torque ripple acts as a disturbance to the system in view of Torque ripple acts aa disturbance to the in of Torque ripplecontrol acts as as system, disturbance the system system in view view of the current whichto makes current control the current control system, which makes current control Torque ripple acts as a disturbance to the system in view of Torque ripple acts as a disturbance to the system in view of the current control system, which makes current control difficult (Yang et al., al.,system, 2017). which In order ordermakes to reduce reduce the control torque the current control current difficult (Yang et 2017). In to the torque the current control which current control difficult (Yang et been al.,system, 2017). In ordermakes toreduce reduce thecogging torque ripple, there have lots of studies to the difficult (Yang et al., 2017). In order to reduce the torque ripple, have been lots of studies to the difficult (Yang etin al., ordermotor reduce thecogging torque ripple, there there have been lots of In studies totoreduce reduce the cogging torque occurring the2017). motor: first, design. Second, ripple, there have been lots of studies to reduce the cogging torque occurring in the motor: first, motor design. Second, ripple, there have been lots of studies to reduce the cogging torque occurring the motor: first, motor design. Second, switching logic of ofin torque in the motor: first, motor design. Second, switching logic torque occurring occurring switching logic ofin the motor: first, motor design. Second, switching switching logic logic of of
inverters, inverters, and and third, third, control control law. law. However, However, researches researches on on inverters, and third, control law. However, researches on designing motor and switching logic are limited in terms of inverters, and third, control law. However, researches on designing motor and switching logic are limited in terms of inverters, and etthird, control law. researches designing motor and2013) switching logicHowever, are limited in terms on of cost. (Jezernik al., and switching logic are limited in terms of cost. (Jezernik et al., 2013) designing motor designing motor and2013) switching logic are limited in terms of cost. (Jezernik et al., cost. (Jezernik et al., 2013) cost. (Jezernik et al., 2013) While the output torque of aa machine machine is is physically physically related related to to While the torque of While the output output torquethe of acurrent machineripple is physically related to the stator current, is periodically periodically While the output torque of a machine is physically related to the stator current, the current ripple is While the output of acurrent machine isrotor physically related to the stator current, the is the periodically synchronized to torque the position position of the theripple in form of of the stator current, the current ripple is periodically synchronized to the of rotor in the form the stator current, the current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current current ripple is distorted back-EMF voltage. Therefore, the ripple is synchronized to the position of in form synchronized to the therotating position of the the rotor rotor in the the multiples form of of distorted back-EMF voltage. Therefore, theintegral current ripple is concentrated on frequency and distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotating frequency and integral multiples distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotating frequency and integral multiples in the rotating rotating speed in the the frequency frequencyand domain. (Mattavelli, concentrated on the rotating integral multiples in the speed in frequency domain. (Mattavelli, concentrated on the rotating frequency and integral multiples in the rotating speed in the frequency domain. (Mattavelli, Tubiana et al, al, 2005 andinMohamed Mohamed and El-Saadany, El-Saadany, 2008) in the speed the domain. Tubiana et and and 2008) in the rotating rotating speed the frequency frequency domain. (Mattavelli, (Mattavelli, Tubiana et al, 2005 2005 andinMohamed and El-Saadany, 2008) Tubiana et al, 2005 and Mohamed and El-Saadany, 2008) Tubiana et al, 2005 and Mohamed and El-Saadany, 2008) In this study, a method is proposed to design a disturbance In this study, aa method is proposed to design aa disturbance In this study, method is proposed to design disturbance observer in order to reducing the torque ripple. In this study, a method is proposed to design a disturbance observer in to the In this study, a method is proposed to ripple. design a disturbance observer in order order to reducing reducing the torque torque ripple. observer observer in in order order to to reducing reducing the the torque torque ripple. ripple. 2. PMSM PMSM SYSTEM and and CONTROLLER DESIGN DESIGN 2. 2. PMSM SYSTEM SYSTEM and CONTROLLER CONTROLLER DESIGN 2. 2. PMSM PMSM SYSTEM SYSTEM and and CONTROLLER CONTROLLER DESIGN DESIGN 2.1 PMSM Model in a Synchronous Rotating d-q d-q Axis Axis 2.1 PMSM Model in a Synchronous Rotating 2.1 PMSM Model in a Synchronous Rotating d-q Axis 2.1 PMSM Model in a Synchronous Rotating d-q 2.1 Model Synchronous Rotating d-q Axis Axis (dqThe PMSM application ofinaa arotating rotating coordinate transformation The application of coordinate transformation (dqThe application of a rotating coordinate transformation (dqtransformation) subject to the the rotor rotor position derivatives (Kim (Kim The application of a rotating coordinate transformation (dqtransformation) subject to position derivatives The application of a rotating coordinate transformation (dqtransformation) subject to the rotor position derivatives (Kim et al., 2018) 2018) is is given given as follows: follows: transformation) subject to the rotor position derivatives (Kim et al., as transformation) subject to the rotor position derivatives (Kim et al., 2018) is given as follows: et given as et al., al., 2018) 2018) is is di given as follows: follows: d di L Ri u d did eL q iiq d L u d Rss id d d eL q iq dt Ld di R i L ud d s d e q q dt d R i L i ud di (1) L d dt Rss idd ee Lqq iqq u dd (1) Lddd di s d e q q d (1) dt q di dt q L L i R i u (1) di q e d d s q q e f q L dt ee L R u ee ff (1) Lqq di Ldd iidd Rss iiqq uq di dtqqq u qq L id R ee L d ss iiq ee ff d id q uq Lqqq dt L R e d d s q q e f dt dt i where and denote the d-q frame current. i q d iq denote the d-q frame current. where iid and denotes the the ee denotes where d and iq denote the d-q frame current. e denotes the i where and denote the d-q frame current. denotes the i electrical speed, with representing the number of pole p qq denote d e d and e i where the d-q frame current. denotes the i representing the number of pole electrical speed, with q d speed, e electrical with p of pole p representing the number electrical speed, with representing the number of pole p electrical speed, with p representing the number of pole
2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 responsibility IFAC 229Control. Peer review© of International Federation of Automatic Copyright ©under 2019 IFAC 229 Copyright © 2019 IFAC 229 10.1016/j.ifacol.2019.08.179 Copyright © 2019 IFAC 229 Copyright © 2019 IFAC 229
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pairs. The control inputs of ud and u q are the input voltages, and the generated torque Te is given as Te
3 p ( f iq ( Ld Lq )id iq ) 22
where K p , x Lx ,0 c and K i , x Rx ,0c are P- and I- gains of (2)
the PI controller and fˆx (t ) , x d , q , represent the estimated disturbances defined as
2.2 Design of the disturbance observer based controller
fˆx ,1 (t ) : x ,1 (t ) x ,1 x ,1 Lx ,0ix (t )
The PMSM model can be rewritten as Lx ,0
did Rs ,0ix v x u x f x , dt vd Lq ,0eiq
(7)
x ,1 (t ) x ,1 x ,1 (t ) x2,1 x ,1 Lx ,0ix (t ) x ,1 x ,1 Rx ,0ix (t ) u x , PI (t ) , x d , q
x d,q (3)
d fˆx ,2 (t ) : x ,2 fˆx ,1 (t ) d x ,2 x ,2 nx ,2
vd Ld ,0eid f e
d d x ,2 x ,2 1 x ,2 n x ,2
Where x d , q, t 0 with the nominal parameters of Rs ,0 , Ld ,0 , Lq ,0 , and PM ,0 . f x represents the uncertainties and
x ,2
disturbances caused by the unmodeled dynamics and parameter mismatch; vx , x d , q , denote the calculated cross-coupling terms and back-EMF; and e is the measurement of e .
d fˆx (t ) : x ,3 fˆx ,2 (t ) d x ,3 x ,3 nx ,3
x ,3
(8)
fˆx ,1 , x d , q
(9)
d d 3 x ,3 1 x ,3 fˆx ,2 , x d , q n x ,3
where x ,( ) , x ,( ) , n x , ( ) , and d x , ( ) are disturbance observer gains to make the transfer function of disturbance to disturbance estimate as x ,1 s / nx ,2 1 s / nx ,3 1 s x ,1 s / d x ,2 1 s / d x ,3 1 Fˆx ( s ) , x d,q Fx ( s ) x ,1 s / nx ,2 1 s / nx ,3 1 1 x ,1 s s / d 1 s / d 1 x ,1 x ,2 x ,3
x ,1
(10)
where Fx ( s ) and Fˆx ( s ) are Laplace transforms of f x (t ) and fˆ (t ) . The proposed controller can be designed considering x
following sensitivity functions M x s
Fig. 1. Proposed current control algorithm structure
output error Ex ( s) : Fx ( s ) input disturbance
The overall structure of the proposed current control scheme is illustrated in Fig. 1.
Sx s
(11) control input U x (s) : N x ( s ) measurement noise
Because the current ripple is the consequence of the disturbances f x , the controller should be designed to reject the disturbance. The control input is designed:
Lx ( s )
output I x (s) : E x ( s ) output error
u x (t ) u x , pi (t ) vx (t ) fˆx (t ),
Fig. 2 illustrates the effect of adopting the proposed controller (4) – (9). The control tracking error caused from disturbance M x ( s ) is 3 ~ 5 dB reduced on high speed ripple
x d , q (4)
frequency region. This implies additional design through adopting n x , ( ) , and d x , ( ) gives additional disturbance
where PI-control inputs u x , pi (t ) , x d , q are defined as u x , PI K p , x ex K i , x ex dt ex
rejection performance especially on torque ripple frequency region. The values of the machine parameters are arranged in Table. 1. The selected control gains are also arranged in Table. 2.
, x d , q (6)
i ix * x
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Fig. 2. Load disturbance sensitivity M q ( s ) : The frequency response of tracking error caused from disturbance
Fig. 4. Loop transfer function Lx ( s )
Fig. 3 shows the noise effect on control input S q ( s ) . High frequency above 1kHz are not amplified by additional frequency shapers n x , ( ) , and d x , ( ) in (8) and (9).
Therefore, the proposed control is designed to reduce the torque ripple additionally from the basic disturbance observer based control approach (7) by applying additional frequency shaper (8) and (9) considering the significant torque ripple is centred on specific frequency range.
Robust stability of the control system must be checked. By securing sufficient robust margins, the control system can be designed safely. Fig. 4 displays the loop transfer function Lq ( s ) and phase margin. The designed control loop is stable
Table 1. Machine parameters Ld [H]
value
because the phase margin is secured to 68.7deg.
Lq [H]
Rs []
f [Wb/m2 ]
1.26e-4 1.346e-4 3.15e-2
1.09e-2
Table 2. Control gains
value
value
c
1,x
1,x
1.26e-4
62.8
20.0
d 2, x
n2,x
d 3, x
n3, x
3.77e2
1.27e2
6.28e2
1.88e3
3. EXPERIMENT RESULTS In this section, the experiment results are illustrated in order to show the additional performance by adding (8) and (9) compared to (7). Fig. 3. Noise disturbance sensitivity S x ( s ) : The frequency
Fig. 5. illustrate the FFT of the 0A tracking control output when motor is rotating at speed of 1500RPM (poles = 6). The significant cogging ripples are centred around 75Hz. However, the peak value at 75Hz are decreased when applying the proposed controller. Fig. 6 shows the timedomain current output of Fig. 5. It can be seen that the proposed method gives lower standard deviation current outputs.
response of noise amplification effect on control input. Note that, the proposed control system has better disturbance attenuation, while the sensitivity and robustness are well maintained compare to the base disturbance observer which only applying (7) but not (8) and (9).
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Property for Electric Power Steering Applications. Energies, 11(5), p.1224. Jezernik, K., Korelič, J., and Horvat, R. (2013). PMSM sliding mode FPGA-based control for torque ripple reduction. IEEE Transactions on Power Electronics, 28(7), 3549-3556. Mattavelli, P., Tubiana, L. and Zigliotto, M. (2005). TorqueRipple Reduction in PM Synchronous Motor Drives Using Repetitive Current Control. IEEE Transactions on Power Electronics, 20(6), pp.1423-1431. Mohamed, Y. and El-Saadany, E. (2008). A Current Control Scheme With an Adaptive Internal Model for Torque Ripple Minimization and Robust Current Regulation in PMSM Drive Systems. IEEE Transactions on Energy Conversion, 23(1), pp.92-100. Rodriguez, C. and Amaratunga, G. (2008). Long-Lifetime Power Inverter for Photovoltaic AC Modules. IEEE Transactions on Industrial Electronics, 55(7), pp.25932601. Wang, H. and Blaabjerg, F. (2014). Reliability of Capacitors for DC-Link Applications in Power Electronic Converters—An Overview. IEEE Transactions on Industry Applications, 50(5), pp.3569-3578. Yang, J., Chen, W., Li, S., Guo, L. and Yan, Y. (2017). Disturbance/Uncertainty Estimation and Attenuation Techniques in PMSM Drives—A Survey. IEEE Transactions on Industrial Electronics, 64(4), pp.32733285.
Fig. 5. FFT of the output q-axis current signal.
ACKNOWLEDGEMENT This research was supported by a grant (17TLRP-C13544601, Development of Hybrid Electric Vehicle Conversion Kit for Diesel Delivery Trucks and its Commercialization for Parcel Services) from Transportation & Logistics Research Program (TLRP) funded byMinistry of Land, Infrastructure and Transport of Korean government.
Fig. 6. The output q-axis current signal of Fig. 5.
4. CONCLUSIONS In this study, by applying additional modification to the existing disturbance observer based feedback controller, the torque ripple of the PMSM control system is reduced. Although this software approach cannot make a significant improvement, it is meaningful that the approach does not require additional costs. The standard deviation of the current output is reduced to 62% level and, the cogging current ripple is decreased -5dB in the experiment.
REFERENCES Kim, Y., Seo, H., Kim, S. and Kim, K. (2018). A Robust Current Controller for Uncertain Permanent Magnet Synchronous Motors with a Performance Recovery 232
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IFAC PapersOnLine 52-4 (2019) 206–209
A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for A disturbance observer based approach to current control of PMSM drives for torque ripple reduction A disturbance observer based approach to current control of PMSM drives for torque ripple reduction torque ripple reduction torque ripple reduction torque ripple reduction Yong-Hun Kim*, Kyunghwan Choi**, Yong-Hun Kyunghwan Choi**, Yong-Hun Kim*, Kim*, Kyunghwan Choi**, Seok-Kyoon Kim***, Kyung-Soo Kim** Yong-Hun Kim*, Seok-Kyoon Kim***, Kyung-Soo Kim** Kyunghwan Choi**, Yong-Hun Kim*, Kyunghwan Choi**, Seok-Kyoon Kim***, Kyung-Soo Kim** Seok-Kyoon Kim***, Kyung-Soo Seok-Kyoon Kim***, Kyung-Soo Kim** Kim** KAIST, Daejeon, Korea (e-mail: [email protected]). *Eco-friendly Smart Vehicle Research Center, KAIST, Daejeon, Korea (e-mail: [email protected]). *Eco-friendly Smart Vehicle Research Center, *Eco-friendlyofSmart VehicleEngineering, Research Center, KAIST, Daejeon, Korea (e-mail: [email protected]). **Department Mechanical KAIST, Daejeon, Korea (e-mail:[email protected]) *Eco-friendly Vehicle Research Center, KAIST, Daejeon, (e-mail: [email protected]). **Department ofSmart Mechanical Engineering, KAIST, Daejeon, KoreaKorea (e-mail:[email protected]) *Eco-friendly Smart Vehicle Research Center, KAIST, Daejeon, Korea (e-mail: Daejeon, [email protected]). **Department of Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department of Creative Convergence Engineering, Hanbat National University, Korea (e-mail: **Department of Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea (e-mail: (e-mail: **DepartmentofofCreative Mechanical Engineering, KAIST, Daejeon, Korea (e-mail:[email protected]) ***Department Convergence Engineering, Hanbat National University, Daejeon, Korea [email protected])} ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea [email protected])} ***Department of Creative Convergence Engineering, Hanbat National University, Daejeon, Korea (e-mail: (e-mail: [email protected])} [email protected])} [email protected])} Abstract: This paper paper deals deals with with the the reduction of of torque ripple ripple in aa PMSM PMSM (permanent (permanent magnet magnet Abstract: This Abstract: This paper deals with the reduction reduction of torque torque ripple in in a current PMSM ripple (permanent magnet synchronous motor) drive using disturbance observer based control. The is periodically synchronous motor) drive using disturbance observer based control. The ripple is Abstract: This paper deals with the reduction of ripple in PMSM (permanent magnet Abstract: This paper deals with the reduction of torque torque ripple back-EMF in PMSM (permanent magnet synchronous motor) drive using disturbance observer based control. Theaa current current ripple is periodically periodically synchronized to the position of the rotor in the form of distorted voltage. Therefore, the synchronous motor) drive using disturbance observer based control. The current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the synchronous motor) drive using disturbance observer based control. The current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking current ripple is concentrated on the rotation frequency and integral multiples in the frequency domain. In this paper, a method is introduced to reduce the current ripple while maintaining reference tracking performance without a significant change of the controller by intensively increasing the disturbance this paper, a method is introduced to reduce the current ripple while maintaining reference tracking performance without change of the by increasing the disturbance this paper, aperformance method aais significant introduced to reduce the controller current ripple while maintaining reference tracking performance without significant change ofband the controller by intensively intensively increasing the disturbance suppression of the frequency corresponding to the current ripple. The proposed performance without aa significant change of the controller by increasing the disturbance suppression performance of corresponding to the ripple. The proposed performance without change ofband the controller by intensively intensively increasing the suppression performance of the the frequency frequency band corresponding to the current current ripple. Thedisturbance proposed method is verified that aa significant steady-state 58% ripple reduction in 500W SPMSM in the experiments. suppression performance of the frequency band corresponding to the current ripple. The method is verified that steady-state 58% ripple reduction in 500W SPMSM in the experiments. suppression performance of the frequency band corresponding the current The proposed proposed method is verified that a steady-state 58% ripple reduction in 500Wto SPMSM in the ripple. experiments. method verified that aa control; steady-state 58% ripple reduction in 500W SPMSM in the experiments. © 2019, is IFAC (International Federation ofripple Automatic Control) Hosting by Elsevier Ltd. All rights reserved. method is verified that steady-state 58% ripple reduction in 500W SPMSM in the experiments. Keywords: motor drive; torque reduction; disturbance observer; Keywords: Keywords: motor motor drive; drive; control; control; torque torque ripple ripple reduction; reduction; disturbance disturbance observer; observer; Keywords: motor drive; control; torque ripple reduction; disturbance observer; Keywords: motor drive; control; torque ripple reduction; disturbance observer;
1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION INTRODUCTION 1. INTRODUCTION Permanent Magnet Magnet 1. Synchronous motor (PMSM) (PMSM) has has been been Permanent Synchronous motor Permanent Magnet Synchronous motor (PMSM) hasrobots, been well received in applications such as drones, mobile Permanent Magnet Synchronous motor (PMSM) has been well received in applications such as drones, mobile robots, Permanent Magnet Synchronous motor (PMSM) has been well received in applications such as drones, mobile robots, and vacuum inpumps pumps for such decades of versatility versatility and well received applications as drones, mobile robots, and vacuum for decades of and well received in applications such as drones, mobile robots, and vacuum pumps for decades of versatility and performance. Particularly in electric and hybrid vehicles, and vacuum pumps for decades of versatility and performance. Particularly in electric and vehicles, and vacuum pumpsfor for of hybrid versatility and performance. Particularly in decades electric and hybrid vehicles, PMSM is responsible power sources ranging from 0.5 kW performance. Particularly in electric and hybrid vehicles, PMSM is responsible for power sources ranging from 0.5 kW performance. Particularly in electric and hybrid vehicles, PMSM is responsible forwith power sources rangingelectric from 0.5 kW to several hundred kW kW traction motors, power PMSM is responsible for power sources ranging from kW to several hundred traction motors, power PMSM isand responsible forwith power sources rangingelectric from 0.5 0.5 kW to several hundred kW with traction motors, electric power steering generators. to several hundred kW with traction motors, electric power steering and generators. to several kW with traction motors, electric power steering andhundred generators. steering and generators. steering and unwanted generators.properties Among the the unwanted properties of of the the motor, torque torque ripple ripple Among Among the unwanted properties of the tomotor, motor, torque ripple has been the subject of much research reduce the control has been the subject of much research to reduce the control Among the unwanted properties of the motor, torque ripple Among the unwanted properties of the motor, torque ripple has been the subject of much research to reduce the control accuracy in precision precision applications and to energy efficiency in has been the subject of much research reduce the control accuracy in applications and energy efficiency in has been the subject of much research to reduce the control accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple accuracy in precision applications and energy efficiency in large systems. There are many reasons to reduce torque ripple and noise. noise. Among them, the issues issues related to the the lifetime of large systems. There are many reasons to reduce torque ripple and Among them, the related to lifetime of large systems. There are many reasons to reduce torque ripple and noise. Among them, the issues related to the lifetimeand of the power device are most important (Rodriguez and noise. Among them, issues related to the lifetime of the power device are the most important (Rodriguez and and noise. the issues related to the and lifetime of the powerAmong device most important (Rodriguez and Amaratunga, 2008).them, Inare other words, torque ripple ripple current the power device are most important (Rodriguez and Amaratunga, 2008). In other words, torque and current the power device are most important (Rodriguez and Amaratunga, 2008). In other words, torque ripple and current noise are the the main main causes of shortening shortening the ripple lifetime ofcurrent power Amaratunga, 2008). In words, torque and noise are of the lifetime of power Amaratunga, 2008).causes In other other words, torque ripple and noise are the main causes of shortening the high lifetime ofcurrent power electronic devices. Particularly, in recent performance electronic devices. Particularly, in recent high performance noise are the main causes of shortening the lifetime of power noise are the main causes of shortening the lifetime of power electronic devices. Particularly, in recent high performance inverters, expensive film capacitors capacitors are applied applied to dc-link. dc-link. electronic devices. Particularly, in recent high performance inverters, expensive film are to electronic devices. Particularly, in recent high performance inverters, expensive film capacitors are applied to dc-link. Such charge discharge ofcapacitors the film film capacitor decreases the inverters, expensive film are to Such charge /// discharge the decreases the inverters, expensive film of areofapplied applied to dc-link. dc-link. Such charge discharge ofcapacitors the film capacitor capacitor decreases the performance and requires replacement parts (Wang and Such charge / discharge of the film capacitor decreases the performance and requires replacement of parts (Wang and Such charge / discharge of the film capacitor decreases the performance and requires replacement of parts (Wang and Blaabjerg, 2014). This is a particularly important issue for performance and requires replacement of parts (Wang and Blaabjerg, 2014). This is particularly issue for performance and requires ofimportant partsresearch (Wang and Blaabjerg, 2014). This hybrid is aareplacement particularly important issue into for electric vehicles and vehicles, and Blaabjerg, 2014). This is a particularly important issue for electric vehicles and hybrid vehicles, and research into Blaabjerg, 2014). This hybrid is aand particularly issue for electric vehicles and vehicles, isimportant and research into making robust capacitors batteries considered to be electric vehicles and hybrid vehicles, and research into making robust capacitors and batteries is considered to be electric vehicles and hybrid vehicles, and research into making robust capacitors and batteries is considered to be one of the biggest challenges to the commercialization of one of the biggest challenges to the commercialization of making robust capacitors and batteries is considered to be making robust capacitors and batteries is considered to be one of the biggest challenges to the commercialization of electric vehicles from 2000s. one of the challenges to electric from 2000s. one of vehicles the biggest biggest to the the commercialization commercialization of of electric vehicles fromchallenges 2000s. electric vehicles from 2000s. electric vehicles from 2000s. Torque ripple acts as a disturbance to the system in view of Torque ripple acts aa disturbance to the in of Torque ripplecontrol acts as as system, disturbance the system system in view view of the current whichto makes current control the current control system, which makes current control Torque ripple acts as a disturbance to the system in view of Torque ripple acts as a disturbance to the system in view of the current control system, which makes current control difficult (Yang et al., al.,system, 2017). which In order ordermakes to reduce reduce the control torque the current control current difficult (Yang et 2017). In to the torque the current control which current control difficult (Yang et been al.,system, 2017). In ordermakes toreduce reduce thecogging torque ripple, there have lots of studies to the difficult (Yang et al., 2017). In order to reduce the torque ripple, have been lots of studies to the difficult (Yang etin al., ordermotor reduce thecogging torque ripple, there there have been lots of In studies totoreduce reduce the cogging torque occurring the2017). motor: first, design. Second, ripple, there have been lots of studies to reduce the cogging torque occurring in the motor: first, motor design. Second, ripple, there have been lots of studies to reduce the cogging torque occurring the motor: first, motor design. Second, switching logic of ofin torque in the motor: first, motor design. Second, switching logic torque occurring occurring switching logic ofin the motor: first, motor design. Second, switching switching logic logic of of
inverters, inverters, and and third, third, control control law. law. However, However, researches researches on on inverters, and third, control law. However, researches on designing motor and switching logic are limited in terms of inverters, and third, control law. However, researches on designing motor and switching logic are limited in terms of inverters, and etthird, control law. researches designing motor and2013) switching logicHowever, are limited in terms on of cost. (Jezernik al., and switching logic are limited in terms of cost. (Jezernik et al., 2013) designing motor designing motor and2013) switching logic are limited in terms of cost. (Jezernik et al., cost. (Jezernik et al., 2013) cost. (Jezernik et al., 2013) While the output torque of aa machine machine is is physically physically related related to to While the torque of While the output output torquethe of acurrent machineripple is physically related to the stator current, is periodically periodically While the output torque of a machine is physically related to the stator current, the current ripple is While the output of acurrent machine isrotor physically related to the stator current, the is the periodically synchronized to torque the position position of the theripple in form of of the stator current, the current ripple is periodically synchronized to the of rotor in the form the stator current, the current ripple is periodically synchronized to the position of the rotor in the form of distorted back-EMF voltage. Therefore, the current current ripple is distorted back-EMF voltage. Therefore, the ripple is synchronized to the position of in form synchronized to the therotating position of the the rotor rotor in the the multiples form of of distorted back-EMF voltage. Therefore, theintegral current ripple is concentrated on frequency and distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotating frequency and integral multiples distorted back-EMF voltage. Therefore, the current ripple is concentrated on the rotating frequency and integral multiples in the rotating rotating speed in the the frequency frequencyand domain. (Mattavelli, concentrated on the rotating integral multiples in the speed in frequency domain. (Mattavelli, concentrated on the rotating frequency and integral multiples in the rotating speed in the frequency domain. (Mattavelli, Tubiana et al, al, 2005 andinMohamed Mohamed and El-Saadany, El-Saadany, 2008) in the speed the domain. Tubiana et and and 2008) in the rotating rotating speed the frequency frequency domain. (Mattavelli, (Mattavelli, Tubiana et al, 2005 2005 andinMohamed and El-Saadany, 2008) Tubiana et al, 2005 and Mohamed and El-Saadany, 2008) Tubiana et al, 2005 and Mohamed and El-Saadany, 2008) In this study, a method is proposed to design a disturbance In this study, aa method is proposed to design aa disturbance In this study, method is proposed to design disturbance observer in order to reducing the torque ripple. In this study, a method is proposed to design a disturbance observer in to the In this study, a method is proposed to ripple. design a disturbance observer in order order to reducing reducing the torque torque ripple. observer observer in in order order to to reducing reducing the the torque torque ripple. ripple. 2. PMSM PMSM SYSTEM and and CONTROLLER DESIGN DESIGN 2. 2. PMSM SYSTEM SYSTEM and CONTROLLER CONTROLLER DESIGN 2. 2. PMSM PMSM SYSTEM SYSTEM and and CONTROLLER CONTROLLER DESIGN DESIGN 2.1 PMSM Model in a Synchronous Rotating d-q d-q Axis Axis 2.1 PMSM Model in a Synchronous Rotating 2.1 PMSM Model in a Synchronous Rotating d-q Axis 2.1 PMSM Model in a Synchronous Rotating d-q 2.1 Model Synchronous Rotating d-q Axis Axis (dqThe PMSM application ofinaa arotating rotating coordinate transformation The application of coordinate transformation (dqThe application of a rotating coordinate transformation (dqtransformation) subject to the the rotor rotor position derivatives (Kim (Kim The application of a rotating coordinate transformation (dqtransformation) subject to position derivatives The application of a rotating coordinate transformation (dqtransformation) subject to the rotor position derivatives (Kim et al., 2018) 2018) is is given given as follows: follows: transformation) subject to the rotor position derivatives (Kim et al., as transformation) subject to the rotor position derivatives (Kim et al., 2018) is given as follows: et given as et al., al., 2018) 2018) is is di given as follows: follows: d di L Ri u d did eL q iiq d L u d Rss id d d eL q iq dt Ld di R i L ud d s d e q q dt d R i L i ud di (1) L d dt Rss idd ee Lqq iqq u dd (1) Lddd di s d e q q d (1) dt q di dt q L L i R i u (1) di q e d d s q q e f q L dt ee L R u ee ff (1) Lqq di Ldd iidd Rss iiqq uq di dtqqq u qq L id R ee L d ss iiq ee ff d id q uq Lqqq dt L R e d d s q q e f dt dt i where and denote the d-q frame current. i q d iq denote the d-q frame current. where iid and denotes the the ee denotes where d and iq denote the d-q frame current. e denotes the i where and denote the d-q frame current. denotes the i electrical speed, with representing the number of pole p qq denote d e d and e i where the d-q frame current. denotes the i representing the number of pole electrical speed, with q d speed, e electrical with p of pole p representing the number electrical speed, with representing the number of pole p electrical speed, with p representing the number of pole
2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 responsibility IFAC 229Control. Peer review© of International Federation of Automatic Copyright ©under 2019 IFAC 229 Copyright © 2019 IFAC 229 10.1016/j.ifacol.2019.08.179 Copyright © 2019 IFAC 229 Copyright © 2019 IFAC 229
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pairs. The control inputs of ud and u q are the input voltages, and the generated torque Te is given as Te
3 p ( f iq ( Ld Lq )id iq ) 22
where K p , x Lx ,0 c and K i , x Rx ,0c are P- and I- gains of (2)
the PI controller and fˆx (t ) , x d , q , represent the estimated disturbances defined as
2.2 Design of the disturbance observer based controller
fˆx ,1 (t ) : x ,1 (t ) x ,1 x ,1 Lx ,0ix (t )
The PMSM model can be rewritten as Lx ,0
did Rs ,0ix v x u x f x , dt vd Lq ,0eiq
(7)
x ,1 (t ) x ,1 x ,1 (t ) x2,1 x ,1 Lx ,0ix (t ) x ,1 x ,1 Rx ,0ix (t ) u x , PI (t ) , x d , q
x d,q (3)
d fˆx ,2 (t ) : x ,2 fˆx ,1 (t ) d x ,2 x ,2 nx ,2
vd Ld ,0eid f e
d d x ,2 x ,2 1 x ,2 n x ,2
Where x d , q, t 0 with the nominal parameters of Rs ,0 , Ld ,0 , Lq ,0 , and PM ,0 . f x represents the uncertainties and
x ,2
disturbances caused by the unmodeled dynamics and parameter mismatch; vx , x d , q , denote the calculated cross-coupling terms and back-EMF; and e is the measurement of e .
d fˆx (t ) : x ,3 fˆx ,2 (t ) d x ,3 x ,3 nx ,3
x ,3
(8)
fˆx ,1 , x d , q
(9)
d d 3 x ,3 1 x ,3 fˆx ,2 , x d , q n x ,3
where x ,( ) , x ,( ) , n x , ( ) , and d x , ( ) are disturbance observer gains to make the transfer function of disturbance to disturbance estimate as x ,1 s / nx ,2 1 s / nx ,3 1 s x ,1 s / d x ,2 1 s / d x ,3 1 Fˆx ( s ) , x d,q Fx ( s ) x ,1 s / nx ,2 1 s / nx ,3 1 1 x ,1 s s / d 1 s / d 1 x ,1 x ,2 x ,3
x ,1
(10)
where Fx ( s ) and Fˆx ( s ) are Laplace transforms of f x (t ) and fˆ (t ) . The proposed controller can be designed considering x
following sensitivity functions M x s
Fig. 1. Proposed current control algorithm structure
output error Ex ( s) : Fx ( s ) input disturbance
The overall structure of the proposed current control scheme is illustrated in Fig. 1.
Sx s
(11) control input U x (s) : N x ( s ) measurement noise
Because the current ripple is the consequence of the disturbances f x , the controller should be designed to reject the disturbance. The control input is designed:
Lx ( s )
output I x (s) : E x ( s ) output error
u x (t ) u x , pi (t ) vx (t ) fˆx (t ),
Fig. 2 illustrates the effect of adopting the proposed controller (4) – (9). The control tracking error caused from disturbance M x ( s ) is 3 ~ 5 dB reduced on high speed ripple
x d , q (4)
frequency region. This implies additional design through adopting n x , ( ) , and d x , ( ) gives additional disturbance
where PI-control inputs u x , pi (t ) , x d , q are defined as u x , PI K p , x ex K i , x ex dt ex
rejection performance especially on torque ripple frequency region. The values of the machine parameters are arranged in Table. 1. The selected control gains are also arranged in Table. 2.
, x d , q (6)
i ix * x
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Fig. 2. Load disturbance sensitivity M q ( s ) : The frequency response of tracking error caused from disturbance
Fig. 4. Loop transfer function Lx ( s )
Fig. 3 shows the noise effect on control input S q ( s ) . High frequency above 1kHz are not amplified by additional frequency shapers n x , ( ) , and d x , ( ) in (8) and (9).
Therefore, the proposed control is designed to reduce the torque ripple additionally from the basic disturbance observer based control approach (7) by applying additional frequency shaper (8) and (9) considering the significant torque ripple is centred on specific frequency range.
Robust stability of the control system must be checked. By securing sufficient robust margins, the control system can be designed safely. Fig. 4 displays the loop transfer function Lq ( s ) and phase margin. The designed control loop is stable
Table 1. Machine parameters Ld [H]
value
because the phase margin is secured to 68.7deg.
Lq [H]
Rs []
f [Wb/m2 ]
1.26e-4 1.346e-4 3.15e-2
1.09e-2
Table 2. Control gains
value
value
c
1,x
1,x
1.26e-4
62.8
20.0
d 2, x
n2,x
d 3, x
n3, x
3.77e2
1.27e2
6.28e2
1.88e3
3. EXPERIMENT RESULTS In this section, the experiment results are illustrated in order to show the additional performance by adding (8) and (9) compared to (7). Fig. 3. Noise disturbance sensitivity S x ( s ) : The frequency
Fig. 5. illustrate the FFT of the 0A tracking control output when motor is rotating at speed of 1500RPM (poles = 6). The significant cogging ripples are centred around 75Hz. However, the peak value at 75Hz are decreased when applying the proposed controller. Fig. 6 shows the timedomain current output of Fig. 5. It can be seen that the proposed method gives lower standard deviation current outputs.
response of noise amplification effect on control input. Note that, the proposed control system has better disturbance attenuation, while the sensitivity and robustness are well maintained compare to the base disturbance observer which only applying (7) but not (8) and (9).
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Property for Electric Power Steering Applications. Energies, 11(5), p.1224. Jezernik, K., Korelič, J., and Horvat, R. (2013). PMSM sliding mode FPGA-based control for torque ripple reduction. IEEE Transactions on Power Electronics, 28(7), 3549-3556. Mattavelli, P., Tubiana, L. and Zigliotto, M. (2005). TorqueRipple Reduction in PM Synchronous Motor Drives Using Repetitive Current Control. IEEE Transactions on Power Electronics, 20(6), pp.1423-1431. Mohamed, Y. and El-Saadany, E. (2008). A Current Control Scheme With an Adaptive Internal Model for Torque Ripple Minimization and Robust Current Regulation in PMSM Drive Systems. IEEE Transactions on Energy Conversion, 23(1), pp.92-100. Rodriguez, C. and Amaratunga, G. (2008). Long-Lifetime Power Inverter for Photovoltaic AC Modules. IEEE Transactions on Industrial Electronics, 55(7), pp.25932601. Wang, H. and Blaabjerg, F. (2014). Reliability of Capacitors for DC-Link Applications in Power Electronic Converters—An Overview. IEEE Transactions on Industry Applications, 50(5), pp.3569-3578. Yang, J., Chen, W., Li, S., Guo, L. and Yan, Y. (2017). Disturbance/Uncertainty Estimation and Attenuation Techniques in PMSM Drives—A Survey. IEEE Transactions on Industrial Electronics, 64(4), pp.32733285.
Fig. 5. FFT of the output q-axis current signal.
ACKNOWLEDGEMENT This research was supported by a grant (17TLRP-C13544601, Development of Hybrid Electric Vehicle Conversion Kit for Diesel Delivery Trucks and its Commercialization for Parcel Services) from Transportation & Logistics Research Program (TLRP) funded byMinistry of Land, Infrastructure and Transport of Korean government.
Fig. 6. The output q-axis current signal of Fig. 5.
4. CONCLUSIONS In this study, by applying additional modification to the existing disturbance observer based feedback controller, the torque ripple of the PMSM control system is reduced. Although this software approach cannot make a significant improvement, it is meaningful that the approach does not require additional costs. The standard deviation of the current output is reduced to 62% level and, the cogging current ripple is decreased -5dB in the experiment.
REFERENCES Kim, Y., Seo, H., Kim, S. and Kim, K. (2018). A Robust Current Controller for Uncertain Permanent Magnet Synchronous Motors with a Performance Recovery 232