Adaptive Dead-Zone Dual Sliding Mode Observer for Reliable Electrochemical Model-Based SOC Estimation

arXiv:2508.21610 · eess.SY, cs.SY, math.OC · Submitted 2025-08-29 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Adaptive Dead-Zone Dual Sliding Mode Observer for Reliable Electrochemical Model-Based SOC Estimation".

Dev: The gist: The proposed method proposes an adaptive dead-zone dual sliding mode observer for reliable electrochemical model-based SOC estimation using an improved single-particle model.

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: So let's talk about the title and who wrote this. "Adaptive Dead-Zone Dual Sliding Mode Observer for Reliable Electrochemical Model-Based SOC Estimation." It sounds a bit technical, but it’s pointing directly at what they did: making an adaptive system that uses a dual observer with a dead zone to estimate battery charge accurately using an electrochemical model.

Dev: The authors are Guangdi Hua, Keyi Liao, Jian Ye, Feng Guo. They are from the School of Vehicles and Intelligent Transportation at Fuyao University of Science and Technology in China, Southwest Jiaotong University in Chengdu, VITO in Belgium, and EnergyVille in Genk.

Taro: So this isn't just theoretical work; these folks are applying it to real battery systems, which is important because the paper claims robustness under battery aging was confirmed using a cycle-aging model.

Rosa: That’s right. They aren't just sitting in a lab; they’re testing how this estimation method holds up when the battery itself starts changing over time, which is something we see constantly in EVs.

Dev: The paper suggests that this approach offers a reliable, accurate, and computationally efficient solution for SOC estimation because it limits unnecessary parameter updates when the system is stable.

Taro: So the implication here for us is that if we can get better estimates while the battery ages, we can make Battery Management Systems much smarter and safer in long-term applications.

The paper's summary: Rosa: To summarize what this paper is about, they are using an improved electrochemical single-particle model to describe battery behavior. This model is simpler than older ones because it reduces the order of partial differential equations while still capturing important concentration gradients and internal dynamics.

Dev: They then design a dual sliding mode observer, which has one part specifically for estimating the SOC and another part for estimating the online parameters of the battery model itself.

Taro: The paper’s core contribution seems to be introducing this adaptive dead-zone mechanism derived from Lyapunov theory. This is what lets them ensure stability by only activating parameter updates when a specific error bound is met, otherwise, they keep things running smoothly.

Rosa: That way they prevent error accumulation in the parameter estimation part, which used to be a big problem in these dual estimation setups. They showed that this method achieves superior accuracy compared to the conventional dual sliding mode observer and even some equivalent circuit model-based EKF methods.

Dev: The results show that under constant current and UDDS dynamic conditions, they keep SOC estimation errors within zero point two percent when the battery is initialized correctly, which is very tight for a real-time system.

The paper's improvements: Rosa: The main improvement they highlight is the adaptive dead-zone strategy itself. Instead of always updating parameters, they suspend those updates if the terminal voltage error stays within a certain range defined by that inequality involving x hat k and B i k, which keeps things stable.

Dev: That mechanism directly addresses the issue where parameter errors can propagate into state estimation errors; when the error is outside that bound, adaptation stops, and only the SOC observer keeps going.

Taro: And one of the really strong improvements they show is how it handles initial errors during convergence. They found that even starting with a thirty percent initial SOC error, it takes only about thirty seconds to eliminate that error and end up with final estimation errors below one percent.

Rosa: That rapid convergence is something that really matters for practical deployment because you don't want a system taking too long to settle after a power fluctuation or a change in conditions.

Dev: Plus, they confirmed robustness under battery aging using a cycle-aging model, where the adaptive dead-zone dual SMO maintained stable SOC estimation even when the parameters were drifting over four hundred cycles.

Conclusion: Rosa: So to wrap up, the paper on "Adaptive Dead-Zone Dual Sliding Mode Observer for Reliable Electrochemical Model-Based SOC Estimation" shows that combining an improved single-particle model with a dual observer and this adaptive dead zone makes SOC estimation highly accurate.

Dev: The key is that this mechanism controls the parameter updates by only activating them when the system error is within a provable bound, which keeps the entire estimator stable during operation.

Taro: For me, what stands out is how they showed rapid convergence from a bad starting point, eliminating an initial thirty percent SOC error in just thirty seconds and getting final errors under one percent.

Rosa: And we saw it hold up well even when the battery parameters were drifting due to aging over four hundred cycles. This suggests this method is a very reliable candidate for practical implementation in advanced battery management systems.

Dev: It’s a step forward because it balances high accuracy with lower computational cost compared to the conventional dual SMO, which is what real-time loops need.

Taro: Yeah, it seems like they’ve built something that doesn't just work on paper but has been shown to be robust in those kinds of dynamic, long-term scenarios.

School of Vehicles and Intelligent Transportation, Fuyao University of Science and Technology · School of Mechanical Engineering, Southwest Jiaotong University

eess.SY, cs.SY, math.OC

Submitted: 2025-08-29

Updated: 2026-10-14

Comments: 45 pages, 8 figures, https://www.sciencedirect.com/science/article/pii/S0306261926016995

Journal ref: Applied Energy, Volume 427, Part D, Article 129043 (2027)

DOI: 10.1016/j.apenergy.2026.129043

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 83/100

The gist: The gist: The proposed method proposes an adaptive dead-zone dual sliding mode observer for reliable electrochemical model-based SOC estimation using an improved single-particle model.

Key concepts

Electrochemical Model-Based SOC Estimation: This involves using mathematical models of how a battery works (like the IESP model) combined with observers or filters. The goal is to accurately determine the State of Charge (SOC)—how much energy is stored in the battery—by observing its voltage and current, rather than just using simple empirical formulas.
Sliding Mode Observer (SMO): A type of observer used to estimate the internal states of a system, such as SOC. It works by designing an observer that forces the system's error dynamics onto a predefined 'sliding surface.' This ensures that the estimated state converges quickly and reliably to its true value, even when facing nonlinearities.
Adaptive Dead-Zone Mechanism: This is a control strategy based on Lyapunov theory. It acts as a switch: if the estimation error is small (within a defined bound), both state and parameter estimators run normally. If the error becomes too large, it suspends parameter updates to prevent errors from accumulating, ensuring stability during adaptation.
Improved Extended Single-Particle Model (IESP): This is the physical model used to describe battery behavior. It builds upon a standard single-particle model by refining how factors like ohmic resistance and capacitance are treated. This improved physical representation provides a more accurate foundation for estimating the battery's SOC dynamics.

Terminology

Accuracy — 39× in this paper · explained in 1 episode
Robustness — 16× in this paper · explained in 5 episodes
State of Charge — 14× in this paper
Adaptation — 8× in this paper · explained in 1 episode
Fidelity — 6× in this paper · explained in 2 episodes
Adaptive Dead-Zone Mechanism — 3× in this paper · explained in 1 episode
Core — 3× in this paper · explained in 2 episodes
Adaptive Mechanism — 2× in this paper · explained in 1 episode
Computational overhead — 2× in this paper · explained in 2 episodes
Urban Dynamometer Driving Schedule — 2× in this paper
Adaptive Gating — 1× in this paper · explained in 1 episode
Adaptive Strategy — 1× in this paper · explained in 1 episode
Consistency — 1× in this paper · explained in 3 episodes
Generalizability — 1× in this paper · explained in 6 episodes
Interpretability — 1× in this paper · explained in 15 episodes
Lyapunov function — 1× in this paper · explained in 2 episodes
Online Adaptation — 1× in this paper · explained in 3 episodes

Summary

The gist: The proposed method proposes an adaptive dead-zone dual sliding mode observer for reliable electrochemical model-based SOC estimation using an improved single-particle model.

Motivation and Problem Statement

Accurate state of charge (SOC) estimation is critical for ensuring the safety, reliability, and efficiency of lithium-ion batteries in electric vehicles and energy storage systems. Electrochemical models provide high fidelity for SOC estimation but introduce challenges due to parameter variations, nonlinearities, and computational complexity. While electrochemical models capture internal mechanisms based on physical principles, their high computational burden hinders direct real-time applications. Model-based estimation methods have received significant attention because they combine battery models with observers or filters to achieve closed-loop estimation. However, simultaneous state and parameter estimation is prone to divergence because errors in the state observer can propagate into the parameter estimator.

Model Development

The study utilizes an improved extended single-particle model (IESP) to describe battery behavior. This model is developed based on the extended single particle model (ESP) by making reasonable modifications to the ohmic resistance and capacitance. The terminal voltage is obtained by subtracting concentration over-potential, reaction over-potential, and ohmic over-potential from the open-circuit voltage. The solid-phase lithium concentration evolves according to Fick’s second law. Spatial discretization or approximate methods are typically employed to solve this equation, with the parabolic approximation method being widely adopted for its simplicity and computational efficiency.

Algorithm Design

The proposed algorithm consists of two parts: a state SMO for SOC estimation and a parameter SMO for online model parameter estimation. The state SMO is designed to estimate the battery SOC, and it incorporates an output-injection term to improve tracking performance. The parameter SMO is formulated based on the terminal voltage equation, with the output equation being given by U(tk−1) = EOCV[xs,i,surf(tk−1)] − ηcon(tk−1) − ηact(tk−1) − ηohm(tk−1) + vθk−1.

Adaptive Dead-Zone Mechanism

To prevent error accumulation in parameter estimation, an adaptive dead-zone is introduced based on Lyapunov theory. The central idea is to derive a Lyapunov-based bound on the terminal-voltage error such that, when the error stays within this bound, the closed-loop observer is (practically) stable. The adaptive dead-zone range of the dual SMO can be expressed as ey/k < xˆk + A−1Bik + A−1BK sgn(xk − xˆk)∥L∥sλm∥I + P‖. If the terminal voltage error satisfies this inequality, i.e. the error is inside the bound, both state and parameter estimators are activated. If the error exceeds the bound, i.e. lies outside the bound, parameter adaptation is suspended while the state SMO continues to operate.

Validation and Results

The proposed method was validated under constant-current and UDDS dynamic conditions. Under correct SOC initialization, the adaptive dead-zone dual SMO achieves superior accuracy compared with conventional dual SMO and equivalent circuit modelbased EKF methods, maintaining SOC estimation errors within 0.2% under correct initialization. Even under a 30% initial SOC error, the algorithm exhibits rapid convergence, requiring only about 30 s to eliminate the initial error and achieving final SOC estimation errors below 1%. Furthermore, robustness under battery aging was confirmed using a cycle-aging model, where the adaptive dead-zone dual SMO maintained stable SOC estimation despite parameter drift. Computational efficiency analysis shows that the adaptive dead-zone dual sliding mode observer reduces execution time compared to the conventional dual SMO by limiting unnecessary parameter updates.

Conclusion

The adaptive dead–zone dual SMO achieves both higher estimation accuracy and lower computational cost compared to the conventional dual SMO. The algorithm also proved robust under aging conditions, maintaining stable accuracy around 0.2% even after 400 cycles. The proposed ADZ–DSMO combines accuracy, robustness, and efficiency, making it a promising candidate for practical implementation in advanced battery management systems.

Acknowledgments

This work was supported by the Chengdu Technological Innovation Research and Development Project [Grant No.2024-YF08–00031-GX]; the Sichuan Provincial Department of Science and Technology [Grant No.23YYJCYJ0096, Grant No.2024YFHZ0267]; and the Research Foundation – Flanders (FWO) [Grant No. 1252326N].

Conflict of Interest

The authors declare that they have no conflict of interest.

Author Contributions

Guangdi Hu: Conceptualization, Methodology, Writing – original draft.

Keyi Liao: Software, Visualization, Writing – original draft.

Jian Ye: Supervision, Writing – review & editing.

Feng Guo: Conceptualization, Supervision, Writing – original draft, Writing – review & editing.

References

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[2] G. Harper, R. Sommerville, E. Kendrick, L. Driscoll, P. Slater, R. Stolkin, A Walton, P Christensen O Heidrich S Lambert et al., Recycling lithium-ion batteries from electric vehicles nature 575 (7781) (2019) 75–86.

[3] K. Haghverdi, D. L. Danilov, G. Mulder, L. D. Couto, F Guo R.-A Eichel Review of the safe operating area (soa) for batteries: Evolving concepts and structured frameworks Journal of Power Sources 652 (2025) 237483.

[4] V Vega-Garita, M Heydarzadeh, A H Dadash E Immonen The need for aging-aware control methods in lithium-ion batteries A review Journal of Energy Storage 132 (2025) 117653.

[5] F Guo L. D Couto G Mulder K Trad G Hu O Capron K Haghverdi A systematic review of electrochemical model-based lithium-ion battery state estimation in battery management systems Journal of Energy Storage 101 (2024) 113850.

[6] L Wu Z Lyu Z Huang C Zhang C Wei Physics-based battery soc estimation methods: Recent advances and future perspectives Journal of Energy Chemistry 89 (2024) 27–40.

[7] C Wang M Yang X Wang Z Xiong F Qian C Deng C Yu Z Zhang X Guo A review of battery soc estimation based on equivalent circuit models Journal of Energy Storage 110 (2025) 115346.

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Improvements for AI systems

Adaptive Dead-Zone Dual SMO for Robust State Estimation: The proposed adaptive dead-zone dual SMO guarantees stability by suspending parameter updates when the terminal–voltage error lies within a rigorously defined bound, thereby ensuring that parameter updates occur only when the system is provably stable. This mechanism prevents divergence and maintains accuracy under model uncertainties and parameter drift.
High-Fidelity SOC Estimation under Dynamic Conditions: The system can achieve higher accuracy than the conventional dual SMO and maintain SOC estimation errors within 0.2% under both constant current and dynamic conditions, as validated by simulations involving UDDS profiles.
Rapid Convergence Under Initial Error Conditions: The algorithm demonstrates rapid convergence, requiring only about 30 s to eliminate the initial error when starting with a 30% initial SOC error, significantly outperforming previous methods that required approximately 100 s for convergence.
Enhanced Robustness Against Model Parameter Drift During Aging: The proposed method is robust under battery aging, maintaining stable SOC estimation despite parameter drift, whereas the conventional dual SMO saw errors increase nearly fourfold after 400 cycles due to continuous parameter updating outside the stability boundary.

Abstract

Accurate state-of-charge (SOC) estimation is essential for safe and efficient lithium-ion battery operation. Electrochemical models provide physically grounded SOC estimates, but nonlinear voltage dynamics and coupled state-parameter errors can destabilize online adaptation. This paper proposes an adaptive dead-zone dual sliding-mode observer (ADZ-DSMO) based on an improved extended single-particle (IESP) model. A state SMO estimates SOC-related states, while a parameter SMO updates dominant model parameters. An online-computable, Lyapunov-guided adaptive boundary selectively gates parameter updates while the state observer remains active at every sampling step. Validation on a Panasonic NCR18650PF cell under 1C and 3C constant-current discharge and the Urban Dynamometer Driving Schedule (UDDS) and New European Driving Cycle (NEDC) profiles shows lower SOC estimation errors than conventional dual SMO and the IESP-based dual extended Kalman filter (DEKF). Compared with DEKF, the proposed observer provides faster recovery from a 30% initial SOC bias. Selective parameter updating reduces the average per-step computation time compared with the always-updating dual SMO. Temperature tests and capacity-based, model-generated aging cases further assess robustness. These results support adaptive gating as a means of reducing error propagation and computational overhead in electrochemical-model-based joint state-parameter estimation.