Abstract
This paper presents an alternative to solve the speed sensorless control of a surface-mounted synchronous motor based on localization of compact invariant sets (LCIS) and the Thau observer. Through the LCIS, the domain of attraction of the system dynamics is analyzed, allowing to obtain global knowledge about its operational bounds and its associated Lipschitz constant. Necessary and sufficient conditions for existence of a stable observer are fulfilled by two inequalities, providing two different sets of stability conditions and, as a consequence, two observers are proposed. The observer design is based on the availability of stator currents for measurement and stator voltages for feedback in a rotating reference frame. The designed observers are able to work in a wide speed range and also estimate rotor position accurately, even at low speed and zero-crossing speed. Simulations demonstrate that the observers can estimate both rotor speed and position. Additionally, the observers are experimentally validated with the Technosoft\(^{\textregistered }\) MCK28335 platform. Results show that the observers can solve sensorless problem in a real-world scenario.
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References
Krause PC, Wasynczuk O, Sudhoff SD (2002) Analysis of electric machinery and drive systems, 3rd edn. Institute of Electrical & Electronics Engineers (IEEE)
Chau KT, Chan CC, Liu C (2008) Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles. IEEE Trans Ind Electron 55(6):2246–2257
Verrelli CM (2012) Synchronization of permanentmagnet electric motors: new nonlinear advanced results. Nonlinear Anal Real World Appl 13(1):395–409
Accetta A, Cirrincione M, Pucci M (2012) TLS EXIN based neural sensorless control of a high dynamic PMSM. Control Eng Pract 20(7):725–732
Acarnley PP, Watson JF (2006) Review of position-sensorless operation of brushless permanent-magnet machines. IEEE Trans Ind Electron 53(2):352–362
Gümüş B, Özdemir M (2005) Sensorless vector control of a permanent magnet synchronous motor with fuzzy logic observer. Electr Eng 88(5):395–402
Chen SY, Luo Y, Pi YG (2015) Pmsm sensorless control with separate control strategies and smooth switch from low speed to high speed. ISA Trans 58:650–658
Yu J, Chen B, Yu H, Gao J (2011) Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping. Nonlinear Anal Real World Appl 12(1):671–681
Zaher AA (2008) A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system. Chaos Interdiscip J Nonlinear Sci 18(1):013111
Coria LN, Starkov KE (2009) Bounding a domain containing all compact invariant sets of the permanent-magnet motor system. Commun Nonlinear Sci Numer Simul 14(11):3879–3888
Zribi M, Oteafy A, Smaoui N (2009) Controlling chaos in the permanent magnet synchronous motor. Chaos Solitons Fractals 41(3):1266–1276
Ahmad M (2010) High performance AC drives: modelling, analysis and control. Springer, Berlin
Marino R, Tomei P, Verrelli CM (2010) Induction motor control design. Springer, London
Bifaretti S, Iacovone V, Rocchi A, Tomei P, Verrelli CM (2012) Nonlinear speed tracking control for sensorless pmsms with unknown load torque: from theory to practice. Control Eng Pract 20(7):714–724
Holtz J (2006) Sensorless control of induction machines: with or without signal injection. IEEE Trans Ind Electron 53(1):7–30
Chi W-C, Cheng M-Y (2014) Implementation of a sliding-mode-based position sensorless drive for highspeed micro permanent-magnet synchronous motors. ISA Trans 53(2):444–453
Karabacak M, Eskikurt HI (2011) Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control. Math Comput Modell 53(9–10):2015–2030
Karabacak M, Eskikurt HI (2012) Design, modelling and simulation of a new nonlinear and full adaptive backstepping speed tracking controller for uncertain PMSM. Appl Math Modell 36(11):5199–5213
Shi H (2011) A novel scheme for the design of backstepping control for a class of nonlinear systems. Appl Math Model 35(4):1893–1903
Li W, Lin W, Liu PX (2007) Speed tracking control based on backstepping of permanent magnet synchronous motor with uncertainty. In: International conference on mechatronics and automation. IEEE. doi:10.1109/icma.2007.4304154
Rebouh S, Kaddouri A, Abdessemed R, Haddoun A (2011) Adaptive backstepping speed control for a permanent magnet synchronous motor. In: International conference on management and service science. IEEE. doi:10.1109/icmss.2011.5999372
Oksuztepe E, Omac Z, Kurum H (2013) Sensorless vector control of PMSM with non-sinusoidal flux using observer based on FEM. Electr Eng 96(3):227–238
Alsofyani IM, Idris NRN (2013) A review on sensorless techniques for sustainable reliability and efficient variable frequency drives of induction motors. Renew Sustain Energy Rev 24:111–121
Tomei P, Verrelli CM (2011) Observer-based speed tracking control for sensorless permanent magnet synchronous motors with unknown load torque. IEEE Trans Autom Control 56(6):1484–1488
Shah D, Espinosa-Pérez G, Ortega R, Hilairet M (2012) An asymptotically stable sensorless speed controller for non-salient permanent magnet synchronous motors. Int J Robust Nonlinear Control 24(4):644–668
Alahakoon S, Fernando T, Trinh H, Sreeram V (2013) Unknown input sliding mode functional observers with application to sensorless control of permanent magnet synchronous machines. J Frankl Inst 350(1):107–128
Tomei P, Verrelli CM (2008) A nonlinear adaptive speed tracking control for sensorless permanent magnet step motors with unknown load torque. Int J Adapt Control Signal Process 22(3):266–288
Thau FE (1973) Observing the state of non-linear dynamic systems. Int J Control 17(3):471–479
Starkov KE, Coria LN, Aguilar LT (2012) On synchronization of chaotic systems based on the thau observer design. Commun Nonlinear Sci Numer Simul 17(1):17–25
Krishchenko AP, Starkov KE (2006) Localization of compact invariant sets of the Lorenz system. Phys Lett A 353(5):383–388
Starkov KE, Coria LN (2013) Global dynamics of the Kirschner–Panetta model for the tumor immunotherapy. Nonlinear Anal Real World Appl 14(3):1425–1433
Mahboobi SH, Shahrokhi M, Pishkenari HN (2006) Observer-based control design for three well-known chaotic systems. Chaos Solitons Fractals 29(2):381–392
Kim W, Shin D, Chung CC (2012) The Lyapunov-based controller with a passive nonlinear observer to improve position tracking performance of microstepping in permanent magnet stepper motors. Automatica 48(12):3064–3074
Acknowledgements
This work was supported by TecNM Project 5153.13-P, PRODEP Research Group ITTIJ-CA-6 and CONACYT Project 178323. We are pleased to acknowledge the helpful and insightful comments of the reviewers.
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Campos, P.J., Coria, L.N. & Trujillo, L. Nonlinear speed sensorless control of a surface-mounted PMSM based on a Thau observer. Electr Eng 100, 177–193 (2018). https://doi.org/10.1007/s00202-016-0491-1
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DOI: https://doi.org/10.1007/s00202-016-0491-1