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

Robust Observer Design for Uncertain Lipschitz Nonlinear Systems Based on Differential Mean Value Theorem: Application to Induction Motors

“…Assumption 1 (Zeghib et al 2019;Ichalal et al (2011): (Sector nonlinearity approach) Assume that for each i, j 1,…, n, we have (8)…”

“…In order to test the robustness of the proposed approach, we set a variation of 50% in the value of stator resistance compared to its nominal value. Figures 5, 6, and 7 illustrate the behavior of the proposed observer compared to Hammoudi approach (Hammoudi et al 2014) and Zeghib approach (Zeghib et al 2019) with parameter variations by simulating the real and estimated speed, αβ-axis stator currents and rotor flux components of the IM. It is clear from Fig.…”

“…For instance, the observer proposed by Ichalal et al (2011) was used by Hammoudi et al (2014) to estimate the state variables of induction motor. In Zeghib et al (2019), the DMVT approach combined with sector nonlinearity has been applied to design a robust extended observer of an IM (the ordinary states, and the rotor position), by taking the H ∞ norm into account to minimize the effect of the external disturbance on the estimation error. However, the effectiveness of the proposed method has been verified without taking into account the sensitivity to parametric variations.…”

“…Despite the importance of sensitivity to parametric variations in stability studies, but the previous works (Hammoudi et al 2014;Zeghib et al 2019) did not incorporate them due to the additional complexity and its implication (Dinesh and Sharma 2019). The first discussions about the problem of robust observer design for a class of Lipschitz nonlinear systems in the presence of disturbance and model uncertainties go back to the works of de Souza et al (1993).…”

“…Motivated by the above discussions, here we aim to improve state estimation robustness for induction motor using an idea, adapted from (Nguyen et al (2018) (the extension of the H∞ filtering method) and combined with DMVT, in which the stability conditions are obtained through the Lyapunov theory via a new LMI formulation. Our objective consists in developing less conservative LMI synthesis conditions taking into account the impact of parametric uncertainties, which were ignored in the earlier works (Hammoudi et al 2014;Zeghib et al 2019), as well as external disturbances simultaneously. The basic idea is the application of differential mean value theorem (DMVT) combined with sector nonlinearity to reformulate the nonlinearity term in the estimation error dynamics into a convex combination of known matrices as q-LPV system.…”