Hybrid nonlinear observer for battery state-of-charge estimation using nonmonotonic force measurements

Hamidreza Movahedi, Miriam A. Figueroa-Santos, Jason B. Siegel, Anna G. Stefanopoulou, Rajesh Rajamani

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This article focuses on state-of-charge (SOC) estimation in a lithium-ion battery, using measurements of terminal voltage and bulk force. A nonlinear observer designed using Lyapunov analysis relying on lower and upper bounds of the Jacobian of the nonlinear output function is utilized. Rigorous analysis shows that the proposed observer has feasible design solutions only in each piecewise monotonic region of the output functions and has no constant stabilizing observer gain when the entire SOC range is considered. The nonmonotonicity challenge is then addressed by designing a hybrid nonlinear observer that switches between several constant observer gains. The global stability of the switched system is guaranteed by ensuring overlap between regions and an adequate dwell time between switches. The performance of the observer is evaluated first through simulations using a high-fidelity battery model and then through experiments. The performance of the nonlinear observer is compared with that of an extended Kalman Filter. Simulation results show that with no model uncertainty the nonlinear observer provides estimates with an RMS error of 1.1%, while the EKF performs better, providing an RMS error less than 1%. However, when model error is introduced into this nonmonotonic system, the EKF becomes unstable for even very small model errors in the output curves. The nonlinear observer, on the other hand, continues to perform very well, providing accurate estimates and never becoming unstable. The experimental results verify the observations from the simulation and the experimental EKF is found to become unstable due to model errors, while the hybrid nonlinear observer continues to work reliably.

Original languageEnglish (US)
Article numbere38
JournalAdvanced Control for Applications: Engineering and Industrial Systems
Issue number3
StatePublished - Sep 2020

Bibliographical note

Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.


  • SOC estimation
  • force sensor
  • hybrid observer
  • lithium-ion batteries
  • nonlinear observer


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