A robust adaptive battery state of charge estimation based on integrated Luenberger observer: An investigation for electric urban air mobility application

• Published in: Journal of energy storage Vol. 128; p. 117128
• Main Authors: Rezaei, Omid, Dinh, Quang Truong
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 30.08.2025
• Subjects: Accuracy; Estimation; eVTOL; Hꝏ integrated observer; Lithium-ion battery; Robustness; State of charge; Lithium-ion battery; Hꝏ integrated observer; Accuracy; Estimation; eVTOL; Robustness; State of charge
• ISSN: 2352-152X
• DOI: 10.1016/j.est.2025.117128

Since the development of electric vertical take-off and landing (eVTOL) aircraft plays an important role in the realization of zero-emission urban air transportation (UAT), it has become the subject of much recent research. In the development of eVTOLs' battery power source, accuracy of the state of charge (SoC) estimation is a key challenge that has a direct effect on their flight performance and safety. This accuracy is affected by destructive factors including system nonlinearities and uncertainties, measurement noises and disturbances or even faults. This paper tackles these issues by introducing an innovative integrated Luenberger observer (ILO) which gathers the benefits of robust and adaptive observers to effectively estimate the SoC based on the prediction and rejection of the above-mentioned factors' effects. First, the uncertainties and nonlinearities together with the measurement faults are treated as an additional unwanted term to the battery model. As the battery has a low inertia, this term is considered to satisfy the Lipschitz condition, and the rate of their variation is considered limited. Then, to estimate the unwanted term and eliminate its effect on the SoC estimation, a mediating variable is designed to function as an augmented variable to the state space model of the battery. Based on the augmented model of the battery, a distinguished structure for the observer is introduced, and its gain is defined in such a way that the coupling term in the obtained estimation error dynamics is eliminated. In this way, the conservatism of the stability proof is reduced. After that, based on Lyapunov theory, the stability problem of the proposed observer is transformed into a linear matrix inequality (LMI) problem to be solved for the derivation of the control parameters. The effectiveness of the proposed observer is verified through real-time experiments of fresh and aged 2.4 Ah Li-ion battery cells under two test scenarios including hybrid pulse power characterization (HPPC) and an eVTOL flight demanded power profile. The results confirm the superiority of the proposed observer compared to a state-of-the-art robust and adaptive observer. •Integrated Luenberger observer for accurate battery state-of-charge estimation•A mediating variable is designed to deal with model uncertainties, unwanted terms•The elimination of conservatism is guaranteed by a novel observer gain design•Experiments under different cases have been done to validate the proposed algorithm