Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Automotive Engineering

Committee Chair/Advisor

Robert Prucka

Committee Member

Qilun Zhu

Committee Member

Ardalan Vahidi

Committee Member

Chris S. Edrington


Lithium-ion batteries (LIBs) have been regarded as a crucial technology for electrifying a variety of applications, ranging from powering computers, phones, and hybrid electric vehicles (HEVs) to being a critical part of the modern centralized and distributed power grids. Battery systems performance is governed by embedded battery management systems (BMSs). The BMS includes battery state estimation algorithms and control rules, and it acts as the brain of battery-powered systems. The purpose of this research is to address unresolved difficulties associated with control algorithms in BMSs at all levels, from single battery cells to battery packs in hybrid electric vehicles (HEVs).\\

When using model-based estimation and control strategies, accurate LIB models are essential for improving the accuracy and performance of BMSs. We develop two types of LIBs models herein, including equivalent circuit models (ECMs) and electrochimical models. The ECMs consist of integer- and fractional-order circuit elements, and we develop them based on the cell measured impedance via Electrochemical impedance spectroscopy (EIS) tests. The nonlinear least square technique is utilized to estimate ECMs parameters using EIS data. The derived ECMs can accurately predict battery voltage dynamics in a variety of temperatures and states of charge (SOC) across a large frequency range.\\

ECMs have a simple structure that makes them suitable for online applications, but they lack information regarding electrochemical reactions at the microscopic level inside the battery. Electrochemical models, on the other hand, provide a comprehensive understanding of battery dynamics. However, they are computationally expensive for existing BMS microcontrollers. We propose a control-oriented version of electrochemical models, namely the single particle model with electrolyte dynamics (SPMe), which is computationally efficient while explaining the internal electrochemistry of the battery. The SPMe is developed based on a single particle assumption and Pad\'{e} approximation, and its parameters are estimated based on the measured cell's open circuit voltage (OCV) and driving cycle data. By developing SPMe, we want to establish the foundation for future research on estimating battery state of charge (SOC) and state of health (known as aging study), as well as developing optimal control algorithms for LIBs.\\

Next, we utilize the developed battery models to formulate three optimal control problems at the cell level and one at the system level in a HEV.

1-At the cell level, we will find the optimal current profile that: (i) maximizes accuracy of ECMs parameter identification in the Fisher information framework; (ii) maximizes SPMe parameter identification accuracy in the Fisher information framework; and (iii) minimizes charging time while reducing charging energy losses. To identify the global optimum solutions, we utilize optimal control theories, inducing Dynamic Programming (DP) and the Pontryagin method. For cases (i) and (iii), we apply the Pontryagin analysis to find closed-form solutions while constraints on battery SOC and current are imposed, and then DP and Quadratic Programming to provide the complete proof of optimality by solutions. In case (ii), we derive the parametric closed-form solutions of SPMe and its derivatives to parameters under a generic current input, and we utilize DP to assure the global optimal trajectories while taking nonlinearities and constraints into account. This optimization problem has ten states and one control input variable. It is verified that the forward DP with one discretized state variable can find the optimal solution.

2-At the system level, we address the minimum fuel problem for a tracked HEV used in military services by joint energy and thermal management of the vehicle powertrain. We will apply DP to determine the optimal battery SOC and temperature trajectories for optimal energy allocation between the battery pack and the internal combustion engine while satisfying propulsion and thermal loads. Next, the optimal solutions are abstracted to generate rule-based energy and thermal management strategy, which is applicable for real-time deriving missions.

This document is organized with five chapters. The first chapter covers the whole process of battery modeling. In chapter 2 and 3, increasing identifiability of ECMs and SPMe model is addressed based on Fisher information theory and design of experiments. In chapter 4, the optimal current profile for efficient charging of an LIB is investigated, and chapter 5 focuses on integrated optimal power and thermal management of a hybrid electric vehicle.

Available for download on Thursday, August 31, 2023