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


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.


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


State vector

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

Estimated state vector


Reference state vector


State estimation error


Input vector


Output vector


Disturbance vector

wr, ws

Rotor and stator speed


Rotor speed reference


Electrical stator speed reference


Rotor position

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

The (d,q) Rotor flux


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


Moment of inertia


Friction coefficient


Pole pair number


Load torque


Mutual inductance


Observer gain



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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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