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A robust extended H observer based on the mean value theorem designed for induction motor drives

  • Okba ZeghibEmail author
  • Abdelkrim Allag
  • Meriem Allag
  • Bilal Hamidani
Original Article
  • 3 Downloads

Abstract

This paper focus on the synthesis of a robust extended H observer based on the combination of the mean value theorem and the sector non-linearity approach, which is applied to the estimation of all ordinary states of the Induction Motor (IM) and the rotor position under the Open Loop Field Oriented Control (OL-FOC). The main objective of this observer is to ensure a minimum disturbance attenuation level of the estimation error; at first, we introduce and formulate the problem of the robust extended observer that can be designed based on these approaches, secondly it will be applied to a class of Lipschitz nonlinear system of the IM. At this stage, it is possible to express the nonlinear error dynamics of the state observer error as a convex combination of known matrices with time varying coefficients as in linear parameter varying systems. Then, it is easy to use the Lyapunov theory such that the stability conditions are obtained and expressed in a form of Linear Matrix Inequalities (LMI’s), so, the extended observer gain is determined by solving the LMI’s through the YALMIP software. The effectiveness of the concept of the proposed approach is performed by measuring the two line currents and estimating all the IM drive states and the rotor position under the OL-FOC through an illustrative simulation to affirm the effectiveness of the proposed concept.

Keywords

Mean value theorem Induction motor Open loop field oriented control Robust extended H observer Disturbance attenuation level Lipschitz form Linear matrix inequalities 

List of symbols

x(t)

State vector

\(\hat{x}\left( t \right)\)

Estimated state vector

xr(t)

Reference state vector

e(t)

State estimation error

u(t)

Input vector

y(t)

Output vector

w(t)

Disturbance vector

wr, ws

Rotor and stator speed

wrr

Rotor speed reference

wsr

Electrical stator speed reference

\(\theta_{r}\)

Rotor position

\(\varPsi_{rd} , \varPsi_{rq}\)

The (d,q) Rotor flux

\(\varPsi_{r}\)

Rotor flux reference

isd, isq

The (d,q) stator currents

Uds, Uqs

The (d,q) stator voltages

Udsr, Uqsr

The (d,q) open loop controls

Lr, Ls

Rotor and stator inductances

Rr, Rs

Rotor and stator resistances

J

Moment of inertia

f

Friction coefficient

np

Pole pair number

TL

Load torque

M

Mutual inductance

L0

Observer gain

Notes

References

  1. Ahrens JH, Khalil HK (2009) High-gain observers in the presence of measurement noise: a switched-gain approach. Automatica 45:936–943MathSciNetCrossRefzbMATHGoogle Scholar
  2. Allag A, Benakcha A, Allag M, Zein I, Ayad MY (2015) Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of PMSM motor application. Front Energy 9:413CrossRefGoogle Scholar
  3. Alonge F, Cirrincione M, Pucci M, Sferlazza A (2017) A nonlinear observer for rotor flux estimation of induction motor considering the estimated magnetization characteristic. IEEE Trans Ind Appl 53:5952–5965CrossRefGoogle Scholar
  4. Asseu O, Kouacou MA, Ori TR, Yéo Z, Koffi M, Lin-Shi X (2010) Nonlinear control of an induction motor using a reduced-order extended sliding mode observer for rotor flux and speed sensorless estimation. Engineering 2:813CrossRefGoogle Scholar
  5. Gacho J, Zalman M (2010) IM based speed servodrive with luenberger observer. J Electr Eng 61:149Google Scholar
  6. Hammoudi MY, Allag A, Becherif M, Benbouzid M, Alloui H (2014) Observer design for induction motor: an approach based on the mean value theorem. Front Energy 8:426–433CrossRefGoogle Scholar
  7. Ichalal D, Marx B, Mammar S, Maquin D, Ragot J (2018) How to cope with unmeasurable premise variables in Takagi–Sugeno observer design: dynamic extension approach. Eng Appl Artif Intell 67:430–435CrossRefGoogle Scholar
  8. Kandoussi Z, Boulghasoul Z, Elbacha A, Tajer A (2017) Sensorless control of induction motor drives using an improved MRAS observer. J Electr Eng Technol 12:1456–1470Google Scholar
  9. Manohar M, Das S (2017) Current sensor fault-tolerant control for direct torque control of induction motor drive using flux-linkage observer. IEEE Trans Ind Inf 13:2824–2833CrossRefGoogle Scholar
  10. Meziane S, Toufouti R, Benalla H (2008) Nonlinear control of induction machines using an extended kalman filter. Acta Polytech Hung 5:41–58Google Scholar
  11. Park C-W, Lee S (2007) Nonlinear observer based control of induction motors. Electr Eng (Archiv fur Elektrotechnik) 90:107–113CrossRefGoogle Scholar
  12. Regaya CB, Farhani F, Zaafouri A, Chaari A (2017) An adaptive sliding-mode speed observer for induction motor under backstepping control. Int J Innov Comput I 11:763–771Google Scholar
  13. Tanaka K, Ohtake H, Wang HO (2007) A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions. IEEE Trans Fuzzy Syst 15:333–341CrossRefGoogle Scholar
  14. Yin Z, Li G, Zhang Y, Liu J, Sun X, Zhong Y (2017) A Speed and flux observer of induction motor based on extended Kalman filter and Markov chain. IEEE Trans Power Electron 32:7096–7117CrossRefGoogle Scholar
  15. Zaidi S, Naceri F, Abdssamed R (2014) Input–output linearization of an induction motor using MRAS observer. Int J Adv Sci Technol 68:49–56CrossRefGoogle Scholar
  16. Zhao L, Huang J, Liu H, Li B, Kong W (2014) Second-order sliding-mode observer with online parameter identification for sensorless induction motor drives. IEEE Trans Ind Electron 61:5280–5289CrossRefGoogle Scholar
  17. Zina HB, Allouche M, Souissi M, Chaabane M, Chrifi-Alaoui L, Bouattour M (2016) Descriptor observer based fault tolerant tracking control for induction motor drive. Automatika 57:703–713CrossRefGoogle Scholar
  18. Zina HB, Allouche M, Souissi M, Chaabane M, Chrifi-Alaoui L (2017) Robust sensor fault-tolerant control of induction motor drive. Int J Fuzzy Syst 19:155–166MathSciNetCrossRefGoogle Scholar
  19. Zina HB, Allouche M, Souissi M, Chaabane M, Chrifi-Alaoui L, Bouattour M (2018) A Takagi–Sugeno fuzzy control of induction motor drive: experimental results. Int J Autom Control 12:44–61CrossRefGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.LEVRES laboratory, Fac. TechnologyUniversity of El OuedEl OuedAlgeria
  2. 2.LMSE laboratory, Fac TechnologyUniversity of BiskraBiskraAlgeria

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