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

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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.

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Abbreviations

x(t):

State vector

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

Estimated state vector

x r(t):

Reference state vector

e(t):

State estimation error

u(t):

Input vector

y(t):

Output vector

w(t):

Disturbance vector

w r, w s :

Rotor and stator speed

w rr :

Rotor speed reference

w sr :

Electrical stator speed reference

\(\theta_{r}\) :

Rotor position

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

The (d,q) Rotor flux

\(\varPsi_{r}\) :

Rotor flux reference

i sd, i sq :

The (d,q) stator currents

U ds, U qs :

The (d,q) stator voltages

U dsr, U qsr :

The (d,q) open loop controls

L r, L s :

Rotor and stator inductances

R r, R s :

Rotor and stator resistances

J :

Moment of inertia

f :

Friction coefficient

n p :

Pole pair number

T L :

Load torque

M :

Mutual inductance

L 0 :

Observer gain

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Authors and Affiliations

  1. LEVRES laboratory, Fac. Technology, University of El Oued, 39000, El Oued, Algeria

    Okba Zeghib, Abdelkrim Allag & Bilal Hamidani

  2. LMSE laboratory, Fac Technology, University of Biskra, 07000, Biskra, Algeria

    Meriem Allag

Authors
  1. Okba Zeghib
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  2. Abdelkrim Allag
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  3. Meriem Allag
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  4. Bilal Hamidani
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Correspondence to Okba Zeghib.

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Appendix

Appendix

In the part, a flow chart about the different steps in order to obtain the robust extended observer gain for the class of strong nonlinear system that the IM drive:

figure a

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Zeghib, O., Allag, A., Allag, M. et al. A robust extended H∞ observer based on the mean value theorem designed for induction motor drives. Int J Syst Assur Eng Manag 10, 533–542 (2019). https://doi.org/10.1007/s13198-019-00766-0

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  • DOI: https://doi.org/10.1007/s13198-019-00766-0

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