Skip to main content

Advertisement

SpringerLink
Log in

Design and analysis of linear parameter varying control for IPMSM using new European driving cycle

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Electric traction motors are the most integral part of fully electric vehicles. Among all traction motors, based on high efficiency, power density, reliability, high torque-to-inertia ratio and control maturity, interior permanent magnet synchronous machine (IPMSM) has proved to be one of the most suitable choices. This paper compares and discusses the various state-of-the-art IPMSM control strategies based on key criteria such as robustness, performance, degree of complexity, and hardware implementation. In this paper, a robust gain scheduling LPV controller is designed for a nonlinear IPMSM in d–q reference frame taking into account the thermal effects. Linear Matrix Inequalities are used for synthesis conditions. The robust gain scheduling LPV adopts induced \(L_{2}\)/\(L_{\infty }\)-norm performance specifications in LPV framework using stator resistance as scheduling time varying parameter. The LPV controller results are validated by comparing them to proportional integral derivative and linear quadratic integrator control techniques using the new European driving cycle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

EV:

Electric vehicles

FEV:

Fully electric vehicles

PHEV:

Plugin hybrid electric vehicle

PMSM:

Permanent magnet synchronous machine

SRM:

Switched reluctance machine

IPMSM:

Interior permanent magnet synchronous motor

FOC:

Field-oriented control

LPV:

Linear parameter varying

EMF:

Electromotive force

LFT:

Linear fractional transformation

LMI:

Linear matrix inequality

MPC:

Model predictive control

MTPA:

Maximum torque per ampere

CCM:

Classical control methods

BM:

Bilinear matrix

DOC:

Degree of complexity

LQI:

Linear quadratic integrator

ICE:

Internal combustion engine

HEV:

Hybrid electric vehicle

IM:

Induction machine

SMPM:

Surface-mounted permanent magnet

VC:

Vector control

DTC:

Direct torque control

EM:

Electric machine

LSDP:

Loop shaping design procedure

PI, PID:

Proportional integral, proportional integral derivative

SMC:

Sliding mode control

EKF:

Extended Kalman filtering

IMC:

Internal mode control

FL:

Feedback linearization

TCA:

Traction challenges addressed

HWI:

Hardware implementation

NEDC:

New European driving cycle

RSME:

Root mean square error

\(V_{\textrm{s}d}\), \(V_{\textrm{s}q}\) :

Stator voltage in d- and q-axis

\(L_{\textrm{s}d}\), \(L_{\textrm{s}q}\) :

Inductance of stator in d- and q-axis

p :

Number of poles

\(\omega _{\textrm{m}}\) :

Rotor mechanical speed

B :

Viscous damping constant

\(K_{\textrm{p}}\), \(K_{\textrm{p}}\) :

coefficients for Proportional, Integral

Q :

Symmetric positive definite weighting matrix for states of system

\(i_{\textrm{s}d}\), \(i_{\textrm{s}q}\) :

Stator current in d- and q-axis

\(\psi _{\textrm{s}d}\), \(\psi _{\textrm{s}q}\) :

Flux of stator in d- and q-axis

\(\lambda\) :

Pole flux

J :

Moment of inertia

\(\tau _{\textrm{e}}\) :

Electromechanical torque

\(K_{\textrm{d}}\) :

Coefficients of derivative values

R :

Symmetric positive definite weighting matrix for input of system

References

  1. Asumendi J (2022) Driving into 2025: The future of electric vehicles. Retrieved from https://www.jpmorgan.com/global/research/electric-vehicles

  2. Ehsani M, Gao Y, Longo S, Ebrahimi K (2018) Modern electric, hybrid electric, and fuel cell vehicles. CRC Press, Boca Raton

    Google Scholar 

  3. Zeraoulia M, Benbouzid MEH, Diallo D (2006) Electric motor drive selection issues for HEV propulsion systems: a comparative study. IEEE Trans Veh Technol 55(6):1756–1764

    Article  Google Scholar 

  4. De Santiago J, Bernhoff H, Ekergård B, Eriksson S, Ferhatovic S, Waters R et al (2011) Electrical motor drivelines in commercial all-electric vehicles: a review. IEEE Trans Veh Technol 61(2):475–484

    Article  Google Scholar 

  5. Nanda G, Kar NC (2006) A survey and comparison of characteristics of motor drives used in electric vehicles. In: 2006 Canadian conference on electrical and computer engineering. IEEE, pp 811–814

  6. Zhu Z, Chan C (2008) Electrical machine topologies and technologies for electric, hybrid, and fuel cell vehicles. In: 2008 IEEE vehicle power and propulsion conference. IEEE, pp 1–6

  7. Zhu ZQ, Howe D (2007) Electrical machines and drives for electric, hybrid, and fuel cell vehicles. Proc IEEE 95(4):746–765

    Article  Google Scholar 

  8. Zhang X, Zhang L, Zhang Y (2018) Model predictive current control for PMSM drives with parameter robustness improvement. IEEE Trans Power Electron 34(2):1645–1657

    Article  Google Scholar 

  9. Do TD, Choi HH, Jung JW (2015) Nonlinear optimal DTC design and stability analysis for interior permanent magnet synchronous motor drives. IEEE/ASME Trans Mechatron 20(6):2716–2725

    Article  Google Scholar 

  10. Korkmaz F, Topaloğlu İ, Çakir MF, Gürbüz R (2013) Comparative performance evaluation of FOC and DTC controlled PMSM drives. In: 4th international conference on power engineering, energy and electrical drives. IEEE, pp 705–708

  11. Bida VM, Samokhvalov DV, Al-Mahturi FS (2018) PMSM, vector control techniques—a survey. In: 2018 IEEE conference of Russian young researchers in electrical and electronic engineering (EIConRus). IEEE, pp 577–581

  12. Depenbrock M (1987) Direct self-control (DSC) of inverter fed induktion machine. In: 1987 IEEE power electronics specialists conference, pp 632–641

  13. Takahashi I, Noguchi T (1986) A new quick-response and high-efficiency control strategy of an induction motor. IEEE Trans Ind Appl IA–22(5):820–827

    Article  Google Scholar 

  14. Pellegrino G, Boazzo B, Jahns TM (2014) Direct flux control of PM synchronous motor drives for traction applications. In: 2014 IEEE transportation electrification conference and expo (ITEC). IEEE, pp 1–6

  15. Garcia XT, Zigmund B, Terlizzi AA, Pavlanin R, Salvatore L (2011) Comparison between FOC and DTC strategies for permanent magnet synchronous motors. Adv Electr Electron Eng 5(1):76–81

    Google Scholar 

  16. Rehman H, Xu L (2011) Alternative energy vehicles drive system: control, flux and torque estimation, and efficiency optimization. IEEE Trans Veh Technol 60(8):3625–3634

    Article  Google Scholar 

  17. Hajji Youssef MR, Malika Z (2016) Modeling and robust H control of a synchronous machine with a salient rotor. Int J Adv Res Sci Eng Technol 3(1):1332–1340

    Google Scholar 

  18. Khedri J, Monovariable H (2015) Robust controller for a permanent magnet synchronous machine (PMSM). Int J Eng Technol: IJET 7(2):553–561

    Google Scholar 

  19. Lin L, Tang HW, Tang J (2011) Robust control with input-output decoupling technique for an interior permanent magnet synchronous motor in electrical vehicle system. In: Advanced materials research, vol 317. Trans Tech Publications Ltd, pp 2461–2465

  20. Njeh M, Cauet S, Coirault P, Martin P (2011) control strategy of motor torque ripple in hybrid electric vehicles: an experimental study. IET Control Theory Appl 5(1):131–144

    Article  Google Scholar 

  21. Azaiz A, Ramdani Y, Meroufel A (2007) Design of robust control system for the PMSM motor. J Electr Eng Bratislava 58(6):326

    Google Scholar 

  22. Ban N, Ogawa H, Ono M, Ishida Y (2009) A servo control system using the loop shaping design procedure. Engineering and technology. World Academy of Science, London, p 60

    Google Scholar 

  23. Acevedo SS, Giraldo E, Giraldo D (2008) Speed control of induction motor using robust control with lsdp. In: 2008 electronics, robotics and automotive mechanics conference (CERMA’08). IEEE, pp 350–353

  24. Wallscheid O, Böcker J (2017) Derating of automotive drive systems using model predictive control. In: 2017 IEEE international symposium on predictive control of electrical drives and power electronics (PRECEDE). IEEE, pp 31–36

  25. Preindl M, Bolognani S (2012) Model predictive direct speed control with finite control set of PMSM drive systems. IEEE Trans Power Electron 28(2):1007–1015

    Article  Google Scholar 

  26. Ahmed AA (2015) Fast-speed drives for permanent magnet synchronous motor based on model predictive control. In: 2015 IEEE vehicle power and propulsion conference (VPPC). IEEE, pp 1–6

  27. Ahmed AA, Kim JS, Lee YI (2016) Model predictive torque control of PMSM for EV drives: a comparative study of finite control set and predictive dead-beat control schemes. In: 2016 eighteenth international middle east power systems conference (MEPCON). IEEE, pp 156–163

  28. Song Q, Jia C (2016) Robust speed controller design for permanent magnet synchronous motor drives based on sliding mode control. Energy Procedia 88:867–873

    Article  Google Scholar 

  29. Zhou Z, Zhang B, Mao D (2018) Robust sliding mode control of PMSM based on rapid nonlinear tracking differentiator and disturbance observer. Sensors 18(4):1031

    Article  Google Scholar 

  30. Qiao Z, Shi T, Wang Y, Yan Y, Xia C, He X (2012) New sliding-mode observer for position sensorless control of permanent-magnet synchronous motor. IEEE Trans Ind Electron 60(2):710–719

    Article  Google Scholar 

  31. Zaihidee FM, Mekhilef S, Mubin M (2019) Application of fractional order sliding mode control for speed control of permanent magnet synchronous motor. IEEE Access 7:101765–101774

    Article  Google Scholar 

  32. Vyncke TJ, Boel RK, Melkebeek JAA (2010) On the stator flux linkage estimation of an PMSM with extended Kalman filters. In: IET international conference on power electronics, machines and drives, pp 434–434

  33. Chaoui H, Sicard P (2011) Adaptive fuzzy logic control of permanent magnet synchronous machines with nonlinear friction. IEEE Trans Ind Electron 59(2):1123–1133

    Article  Google Scholar 

  34. Kim W, Shin D, Chung CC (2012) Microstepping using a disturbance observer and a variable structure controller for permanent-magnet stepper motors. IEEE Trans Ind Electron 60(7):2689–2699

    Article  Google Scholar 

  35. Lee Y, Shin D, Kim W, Chung CC (2017) Nonlinear \(H_{2}\) Control for a nonlinear system with bounded varying parameters, application to PM stepper motors. IEEE ASME Trans Mechatron 22(3):1349–1359

    Article  Google Scholar 

  36. Zhou K, Ai M, Sun D, Jin N, Wu X (2019) Field weakening operation control strategies of PMSM based on feedback linearization. Energies 12(23):4526

    Article  Google Scholar 

  37. Rahmat MS, Ahmad F, Yamin AKM, Aparow VR, Tamaldin N (2013) Modelling and torque tracking control of permanent magnet synchronous motor for hybrid electric vehicles. Int J Autom Mech Eng 7:955

    Article  Google Scholar 

  38. Deng Z, Nian X (2015) Robust control of permanent magnet synchronous motors. IEEE/CAA J Autom Sin 2(2):143–150

    Article  MathSciNet  Google Scholar 

  39. Patki RJ. Standard and modified internal model control schemes for PMSM drive

  40. Alfehaid AA, Strangas EG, Khalil HK (2016) Speed control of permanent magnet synchronous motor using extended high-gain observer. In: 2016 American control conference (ACC). IEEE, pp 2205–2210

  41. Liu Y, Zhang Z (2015) PMSM control system research based on vector control. In: First international conference on information sciences, machinery, materials and energy. Atlantis Press

  42. Mukti EW, Wijanarko S, Muqorobin A, Rozaqi L (2017) Field oriented control design of inset rotor PMSM drive. In: AIP conference proceedings, vol 1855. AIP Publishing LLC, p 020010

  43. Shao X, Zhang J, Zhao Z, Wen X (2005) Adaptive internal model control of permanent magnet synchronous motor drive system. In: 2005 international conference on electrical machines and systems, vol 3, pp 1843–1846

  44. Khiabani AG, Heydari A (2019) Optimal torque control of permanent magnet synchronous motors using adaptive dynamic programming. arXiv:1911.03534

  45. Cao Y, Wang X, Na R, Mao L (2011) Research on a improved PMSM vector control system. In: Proceedings of 2011 6th international forum on strategic technology, vol 2. IEEE, pp 678–683

  46. Wang Y, Fei J (2015) Adaptive fuzzy sliding mode control for PMSM position regulation system. Int J Innov Comput Inf Control 11(3):881–891

    Google Scholar 

  47. Ounnas D, Ramdani M, Chenikher S, Bouktir T (2015) A combined methodology of H∞ fuzzy tracking control and virtual reference model for a PMSM. Adv Electr Electron Eng 13(3):212–222

    Google Scholar 

  48. Shamma JS, Athans M (1990) Analysis of gain scheduled control for nonlinear plants. IEEE Trans Autom Control 35(8):898–907

    Article  MathSciNet  MATH  Google Scholar 

  49. Pohl L, Vesely I, Graf M (2013) Real-time implementation of LPV controller for PMSM drive. In: IECON 2013-39th annual conference of the IEEE industrial electronics society. IEEE, pp 3072–3077

  50. Pohl L, Vesely L (2011) Robustness analysis of PMSM LPV controller. In: Proceedings of DAAAM conference, vol 2011

  51. Pohl L, Buchta L (2016) H\(\infty\) tuning technique for PMSM cascade PI control structure. In: 2016 6th IEEE international conference on control system, computing and engineering (ICCSCE). IEEE, pp 119–124

  52. Altun Y, Gulez K (2012) Linear parameter varying control of permanent magnet synchronous motor via parameter-dependent Lyapunov function for electrical vehicles. In: 2012 IEEE international conference on vehicular electronics and safety (ICVES 2012). IEEE, pp 340–345

  53. Machmoum S, Chervel P, Darengosse C, Machmoum M (2005) A linear parameter variant H\(\infty\) controller design for a permanent magnet synchronous machine. In: 2005 European conference on power electronics and applications. IEEE, p 11

  54. Pohl L, Buchta L (2015) Cascade H linear parameter varying control of PMSM. In: 2015 17th European conference on power electronics and applications (EPE’15 ECCE-Europe). IEEE, pp 1–8

  55. Lee Y, Lee SH, Chung CC (2017) LPV H\(\infty\) control with disturbance estimation for permanent magnet synchronous motors. IEEE Trans Ind Electron 65(1):488–497

    Article  Google Scholar 

  56. Lee J, Tasoujian S, Grigoriadis K, Franchek M (2020) Output-feedback linear parameter varying control of permanent magnet synchronous motors. In: Dynamic systems and control conference, vol 84270. American Society of Mechanical Engineers, p V001T03A006

  57. Parvathy Thampi M, Chitra Kiran N (2023) A review on controlling techniques for permanent magnet synchronous motor (PMSM) and current state of the art in the research area. Communications 7:8–17

    Google Scholar 

  58. Singh S, Tiwari A (2017) Various techniques of sensorless speed control of PMSM: a review. In: 2017 second international conference on electrical, computer and communication technologies (ICECCT). IEEE, pp 1–6

  59. Deo HV, Shekokar R (2014) A review of speed control techniques using PMSM. Int J Innov Res Technol 1(11):2349–6002

    Google Scholar 

  60. Cheng M, Chan CC (2014) General requirement of traction motor drives. In: Encyclopedia of automotive engineering, pp 1–18

  61. Li J, Yu JJ, Chen Z (2013) A review of control strategies for permanent magnet synchronous motor used in electric vehicles. Appl Mech Mater 321:1679–1685

  62. Yang Z, Shang F, Brown IP, Krishnamurthy M (2015) Comparative study of interior permanent magnet, induction, and switched reluctance motor drives for EV and HEV applications. IEEE Trans Transp Electr 1(3):245–254

    Article  Google Scholar 

  63. Jeong N, Yang S, Kim K, Wang M, Kim H, Suh M (2016) Urban driving cycle for performance evaluation of electric vehicles. Int J Autom Technol 17(1):145–151

    Article  Google Scholar 

  64. Altun Y, Gulez K, Mumcu TV, Kizilkaya MÖ (2013) A novel feed-forward controller for PMSMs. In: 2013 3rd international conference on electric power and energy conversion systems. IEEE, pp 1–5

  65. Alizadeh Pahlavani MR, Damroodi H (2016) LPV control for speed of permanent magnet synchronous motor (PMSM) with PWM Inverter. J Electr Comput Eng Innov 4(2):185–193

    Google Scholar 

  66. Lee H, Lee Y, Shin D, Chung CC (2015) H control based on LPV for load torque compensation of PMSM. In: 2015 15th international conference on control, automation and systems (ICCAS). IEEE, pp 1013–1018

  67. Hwang H, Lee Y, Shin D, Chung CC (2014) \(H_{2}\) control based on LPV for speed control of permanent magnet synchronous motors. In: 2014 14th international conference on control, automation and systems (ICCAS 2014). IEEE, pp 922–927

  68. Yang Z, Chai Y, Yin H, Tao S (2018) LPV model based sensor fault diagnosis and isolation for permanent magnet synchronous generator in wind energy conversion systems. Appl Sci 8(10):1816

    Article  Google Scholar 

  69. Zgorski A, Bayon B, Scorletti G, Lin-Shi X (2012) LPV observer for PMSM with systematic gain design via convex optimization, and its extension for standstill estimation of the position without saliency. In: 3rd IEEE international symposium on sensorless control for electrical drives (SLED 2012). IEEE, pp 1–6

  70. Quang NP, Dittrich JA et al (2008) Vector control of three-phase AC machines, vol 2. Springer, Berlin

    Google Scholar 

  71. Li S, Sarlioglu B, Jurkovic S, Patel NR, Savagian P (2017) Analysis of temperature effects on performance of interior permanent magnet machines for high variable temperature applications. IEEE Trans Ind Appl 53(5):4923–4933

    Article  Google Scholar 

  72. Ding X, Liu J, Mi C (2011) Online temperature estimation of IPMSM permanent magnets in hybrid electric vehicles. In: 2011 6th IEEE conference on industrial electronics and applications, pp 179–183

  73. Li S, Sarlioglu B, Jurkovic S, Patel NR, Savagian P (2017) Comparative analysis of torque compensation control algorithms of interior permanent magnet machines for automotive applications considering the effects of temperature variation. IEEE Trans Transp Electr 3(3):668–681

    Article  Google Scholar 

  74. Wilson SD, Stewart P, Taylor BP (2010) Methods of resistance estimation in permanent magnet synchronous motors for real-time thermal management. IEEE Trans Energy Convers 25(3):698–707

    Article  Google Scholar 

  75. Li S, Sarlioglu B, Jurkovic S, Patel N, Savagian P (2016) Evaluation of torque compensation control algorithm of IPM machines considering the effects of temperature variations. In: 2016 IEEE transportation electrification conference and expo (ITEC). IEEE, pp 1–7

  76. Bilgin O, Kazan FA (2016) The effect of magnet temperature on speed, current and torque in PMSMs. In: 2016 XXII international conference on electrical machines (ICEM). IEEE, pp 2080–2085

Download references

Acknowledgements

The authors would like to appreciate Control and Signal Processing Research Group (CASPR) of the Capital University of Science and Technology (CUST) Islamabad, Pakistan, Center for Automotive Research (CAR), The Ohio State University, Columbus, USA, and Dr Nadeem Ahmad for providing technical guidance.

Author information

Authors and Affiliations

  1. School of Electrical and Electronics Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang, Malaysia

    Hassam Muazzam & Mohamad Khairi Ishak

  2. Center for Automotive Research (CAR), The Ohio State University, Columbus, OH, 43212, USA

    Athar Hanif

  3. Electrical Engineering Department, Capital University of Science and Technology, Islamabad, 44000, Pakistan

    A. I. Bhatti

  4. Electrical Engineering Department, University of Engineering and Technology, Taxila, 47080, Pakistan

    Sadaqat Ali

Authors
  1. Hassam Muazzam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamad Khairi Ishak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Athar Hanif
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. I. Bhatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sadaqat Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamad Khairi Ishak.

Additional information

Technical Editor: Marcelo Areias Trindade.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

  1. 1.

    Robust stability with tracking error less than 1% and response time of 5 s

    $$\begin{aligned} W_{\textrm{s}}= \begin{bmatrix} \frac{100+0.1s}{s+0.5} &{} 0\\ 0 &{} \frac{100+0.1s}{s+0.5}\\ \end{bmatrix} \end{aligned}$$
  2. 2.

    Achieve overshoot of the system approximately 11%

    $$\begin{aligned} W_{\textrm{T}}= \begin{bmatrix} 0.9 &{} 0 \\ 0 &{} 0.9\\ \end{bmatrix} \end{aligned}$$
  3. 3.

    To limitize control action to 60 dB

    $$\begin{aligned} W_{\textrm{T}}= \begin{bmatrix} 0.001 &{} 0 \\ 0 &{} 0.001\\ \end{bmatrix} \end{aligned}$$

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Muazzam, H., Ishak, M.K., Hanif, A. et al. Design and analysis of linear parameter varying control for IPMSM using new European driving cycle. J Braz. Soc. Mech. Sci. Eng. 45, 368 (2023). https://doi.org/10.1007/s40430-023-04261-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-023-04261-3

Keywords

Search

Navigation