Investigations of Different Approaches for Controlling the Speed of an Electric Motor with Nonlinear Dynamics Powered by a Li-ion Battery – Case Study

*Roxana-Elena Tudoroiu, Mohammed Zaheeruddin, Nicolae Tudoroiu, Sorin Mihai Radu and Hana Chammas*

### **Abstract**

This research investigated different nonlinear models, state estimation techniques and control strategies applied to rechargeable Li-ion batteries and electric motors powered and adapted to these batteries. The finality of these investigations was achieved by finding the most suitable design approach for the real-time implementation of the most advanced state estimators based on intelligent neural networks and neural control strategies. For performance comparison purposes, was chosen as case study an accurate and robust EKF state of charge (SOC) estimator built on a simple second-order RC equivalent circuit model (2RC ECM) accurate enough to accomplish the main goal. An intelligent nonlinear autoregressive with exogenous input (NARX) Shallow Neural Network (SSN) estimator was developed to estimate the battery SOC, predict the terminal voltage, and map the nonlinear open circuit voltage (OCV) battery characteristic curve as a function of SOC. Focusing on nonlinear modeling and linearization techniques, such as partial state feedback linearization, for "proof concept" and simulations purposes in the case study, a third order nonlinear model for a DC motor (DCM) drive was selected. It is a valuable research support suitable to analyze the performance of state feedback linearization, system singularities, internal and zero dynamics, and solving reference tracking problems.

**Keywords:** Li-ion battery, SOC, Simscape generic model, PID control, state feedback linearization, NARX shallow neural network, NARMA-L2 neuro controller

### **1. Introduction**

Clean and efficient transportation across the planet is only possible if governments and scientists focus on stimulating and sustaining the automotive industry of electric vehicles (EVs) by developing and deploying the most advanced battery technologies. Nowadays, Li-ion battery technologies have made significant progress and have

undoubtedly proven to have a promising future and great potential for development. These are recommended for their excellent features, such as lightweight, high-energy density, low memory effect and relatively low self-discharge, outperforming almost all other competing batteries of different chemistries on the market [1, 2]. Thanks to several improvements in Li-ion battery technologies recently, they have become safer, eliminating explosion hazards as much as possible and their chemistry is less toxic, both to nature and to humans. Battery state of charge (SOC) is an essential internal parameter that plays a vital role in utilizing battery energy efficiency, operating safely under various realistic conditions and environments, and extending battery life [3, 4]. The SOC is a piece of valuable information on the remaining capacity available during the operation of EV car. As the central internal state of the battery, the SOC is continuously supervised by a battery management system (BMS), which is integrated into the EV energy storage system (ESS) structure to power the traction powertrain [1–6]. The SOC can be calculated directly by a simple open-loop integration operation, known as the coulomb counting method or the ampere method since it accumulates the charge transferred between the battery and the environment over time. However, this measurement method is prone to the initial value of SOC and accuracy of the current profile data set measurement. The ampere method accumulates significant errors caused by the integration operation that accumulates errors over time [7]. The battery SOC estimation is one of the main tasks of a BMS. An extensive critical review of Lithium-ion battery SOC, and a smarter BMS description for EV applications are made in [8]. Being interpreted as a remaining capacity of the battery, the SOC is also an important support for energy management (EM) and control strategies. An interesting comprehensive review on Energy Management Strategies (EMS) for EVs taking into consideration the realistic conditions of Li-ion battery degradation based on aging models is found in HAL Open Science that includes the most representatives research papers from 2021 IEEE Access, with a new release version in 2023 [9]. The accuracy of Li-ion battery SOC estimation has a significant impact on the efficient operation and EMS of the battery. Many of studies are dedicated to advancing the BMS functions, such as intelligent cell balancing and charging control strategies for lithium-ion battery packs [10], SOC and state of health (SOH) monitoring [11–13], and thermal battery control temperature [14].

Nowadays, an impressive amount of work has been done in the research field to investigate and study large-scale new developments and implementations of SOC estimation algorithms to be applied to an extensive range of applications in the EV automotive industry. The main flaw of coulomb counting method is that it is not suitable in real time online SOC estimation. Also, it is noteworthy to know that the battery model accuracy significantly impacts SOC estimation. The well-known equivalent circuit model (ECM) is suitable for online estimation due to its simplicity and mastering well the relationship between parameters [1], [3–6]. The traditional methods include the most popular Kalman filter (KF) algorithms, among them linear KF and linearized extended KF (EKF) [5, 6, 15, 16], and nonlinear unscented KF (UKF) [7], ensemble KF (EnKF) [17], particles filter (PF) [18], which are commonly used as a nonlinear filter estimation methods. Only the linear KF is an optimal state estimator compared to the EKF, a suboptimal estimation algorithm. Still, it is an appropriate state estimator for complex working conditions with severe current fluctuations [7]. Compared to EKF, the UKF method uses an unscented transform to obtain the statistics of the process noise covariance and reaches a fast convergence speed and high estimation accuracy [7]. Also, its robustness is better when estimating

### *Investigations of Different Approaches for Controlling the Speed of an Electric Motor… DOI: http://dx.doi.org/10.5772/intechopen.112383*

the SOC of different chemistry batteries. To achieve higher accuracy of state estimation, various intelligent algorithms based on Machine Learning (ML) and Deep Learning (DL) Artificial Intelligence (AI) models are applied to the SOC estimation and terminal voltage prediction, as those developed in [7, 12, 13, 17, 19–38] easily to be adapted to all types of batteries and chemistries. The neural networks (NNs) learning techniques have a wide range of applications and are suitable for all types of batteries chemistry. Well, these learning techniques such as machine learning (ML) and deep learning (DL) models require large amounts of accurate training data [27–30]. The estimation accuracy and the convergence speed of the Li-ion battery SOC depend on the chosen training method, architecture structures, number of hidden layers and hidden neurons, learning rate, gradient value and on number of samples and epochs [29, 30]. The flow of this research paper is organized into four sections, as follows. For "proof concept" and simulation purposes, in Section 2 a generic Simulink Simscape model, simple and accurate is adopted to power a particular small EV car. The model parameters are extracted from a Simulink Simscape battery block set up for a preset model of the Li-ion battery. Additionally, the battery Simscape model is used for performance comparison with the adopted second-order ECM battery model (2RC ECM) used as support in Section 3 to build an accurate and robust EKF SOC estimator. In Section 3 is developed and implemented a NARX SNN intelligent SOC estimator. Section 4 is chosen as a case study of a DCM Drive nonlinear model of the high complexity of applying the state feedback linearization as a powerful tool for nonlinear control systems in a closed loop. Also, the model singularities, internal and zero dynamics stabilizability and reference tracking problems to solve represent some issues /challenges that merit being studied. Additionally, the traditional PID control strategy is a valuable tool used in this last section for performance comparison. At the end of Section 4, a learning NARMA-L2 controller intelligent strategy is applied to learn and linearize the DCM Drive nonlinear model. Therefore, this research work opens other directions of research to explore the application of clever neuro-control strategies on a large scale in future developments in the EV automotive industry.
