This paper presents the results and analysis of an exhaustive simulation study where switched fractional order model reference adaptive control (SFOMRAC) is used for first order plants, along with the analytical proof of boundedness and convergence of the scheme. The analysis is focused on the controlled system behavior through the integral of the time-weighted squared control error (ITSE) and on the control energy through the integral of the squared control signal (ISI). Controller parameters such as fractional order, adaptive gain, and switching time are varied along the simulation studies, as well as plant parameters and reference models. The results show that SFOMRAC controllers can be found for every plant and reference model used such that both system behavior and control energy can be improved, compared to equivalent nonswitched fractional order and integer order control strategies.

The well-balanced combination of high energy density and competitive cycle performance has established lithium-ion batteries as the technology of choice for Electric Vehicles (EVs) energy storage. Nevertheless, battery degradation continues to pose challenges to EV range, safety, and long-term reliability, making accurate estimation of their State of Health (SoH) crucial for efficient battery management, safety, and improved longevity. This paper addresses a compelling research question surrounding the possibility of developing a real-time, non-invasive, and efficient methodology for estimating lithium-ion battery SoH without battery removal, relying solely on voltage and current data. Our approach integrates the fitting abilities of Maximum Likelihood Estimation (MLE) with the dynamic uncertainty propagation of Bayesian Filtering to provide accurate and robust online SoH estimation. By reconstructing the open-circuit voltage curve from real-time data, the MLE estimates battery capacity during discharge cycles, while Bayesian Filtering refines these estimates, accounting for uncertainties and variations. The methodology is validated using an available dataset from Stanford University, demonstrating its effectiveness in tracking battery degradation under driving profiles. The results indicate that the approach can reliably estimate battery SoH with mean absolute errors below 1%, confirming its suitability for scalable EV applications.

Thermal effects exert a crucial influence on the electrical behavior of lithium-ion batteries, significantly impacting key parameters such as the open circuit voltage curve, internal impedance, and cell degradation rate. Furthermore, these effects may give rise to electrolyte loss, resulting in a reduction in capacity. The cycling of batteries inherently generates internal heat, establishing a direct relationship between cell temperature and power demand. This article aims to provide a methodology to model electrothermal relations and temperature influence on electrical behavior in lithium-ion cells, as well as a simulation of extended cell operation under arbitrary power loads, presenting a novel approach not previously explored. It does this by considering three models: the Bernardi model for heat generation within the cell, a thermal lumped model for the cell’s temperature, and the Vogel-Fulcher-Tammann model for the capacity change as a function of temperature. These models are then connected to a state-of-the-art open circuit voltage model of a cell, providing a connection from the thermal world back into the electrical world. Experiments with different power demands occur on the simulation, including estimation of thermal parameters with relative errors under 1%, visualizing the effects of the integrated models and potential for real-cell applications.