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Electric vertical-take-off-and-landing multirotor aircraft has been emerging as a revolutionary transportation mode for both manned and unmanned applications, but this technology is limited by flight time and range restrictions. In this work, an energy-efficient model-based trajectory planning and feedback control framework is developed to improve the energy performance of a multirotor unmanned aerial vehicle. Target vehicle trajectories are planned by solving a formulated energy consumption optimization problem based on a system-level model, which accommodates the integrated dynamics of key vehicle subsystems. In order to implement the generated target trajectories, the framework also includes a PID feedback control architecture for real-time trajectory following. The framework is first verified under simulation, and shows an average reduction of 10.7% in energy consumption over a range of typical hover-to-hover operations, compared to the commonly used baseline flight control architecture. Through model-based analysis, key relationships that contribute to the improvements are identified and analyzed. These results demonstrate the importance of considering and coordinating all relevant system dynamics for efficient and holistic trajectory planning and control, which is absent in existing literature. The framework also demonstrates similar performance improvement under experimental validation, with an average energy reduction of 10.2% over the baseline controller despite the presence of significant real-world disturbances including wind effect.

Multirotor airplanes are widely used in many outdoor applications, e.g., agriculture, transportation, and public safety, where winds might be strong and prevalent. However, the effects of wind on multirotor aircraft are still not fully understood yet. The objective of this paper is to investigate and model wind effects on a real hovering octocopter. The wind is directly measured and considered as one of the inputs to the bare-airframe model. Then a series of models, each corresponding to a different wind condition, are identified from real flight data through a system identification approach. The time-domain validation results show that an average of 15% error reduction can be achieved by considering wind effects, captured by a wind correction term. The identified models will play an important role for the future development of model-based controllers for outdoor multirotor aircraft.

External short circuit (ESC) of lithium-ion batteries is one of the common and severe electrical failures in electric vehicles. In this study, a novel thermal model is developed to capture the temperature behavior of batteries under ESC conditions. Experiments were systematically performed under different battery initial state of charge and ambient temperatures. Based on the experimental results, we employed an extreme learning machine (ELM)-based thermal (ELMT) model to depict battery temperature behavior under ESC, where a lumped-state thermal model was used to replace the activation function of conventional ELMs. To demonstrate the effectiveness of the proposed model, we compared the ELMT model with a multi-lumped-state thermal (MLT) model parameterized by the genetic algorithm using the experimental data from various sets of battery cells. It is shown that the ELMT model can achieve higher computational efficiency than the MLT model and better fitting and prediction accuracy, where the average root mean squared error (RMSE) of the fitting is 0.65 °C for the ELMT model and 3.95 °C for the MLT model, and the RMES of the prediction under new data set is 3.97 °C for the ELMT model and 6.11 °C for the MLT model.

Emerging lithium-ion battery systems require high-fidelity electrochemical models for advanced control, diagnostics, and design. Accordingly, battery parameter estimation is an active research domain where novel algorithms are being developed to calibrate complex models from input-output data. Amidst these efforts, little focus has been placed on the fundamental mechanisms governing estimation accuracy, spurring the question, why is an estimate accurate or inaccurate? In response, we derive a generalized estimation error equation under the commonly adopted least-squares objective function, which reveals that the error can be represented as a combination of system uncertainties (i.e., in model, measurement, and parameter) and uncertainty-propagating sensitivity structures in the data. We then relate the error equation to conventional error analysis criteria, such as the Fisher information matrix, Cramér-Rao bound, and parameter sensitivity, to assess the benefits and limitations of each. The error equation is validated through several uni- and bivariate estimations of lithium-ion battery electrochemical parameters using experimental data. These results are also analyzed with the error equation to study the error compositions and parameter identifiability under different data. Finally, we show that adding target parameters to the estimation without increasing the amount of data intrinsically reduces the robustness of the results to system uncertainties.

Battery management for plug-in electric vehicles (PEVs) has attracted extensive research attention, with most existing studies focusing on PEV operating conditions. However, battery maintenance during idling remains largely unexplored, under which electrochemical side reactions can cause battery degradation. The degradation rate depends on battery states, e.g., state of charge (SOC) and temperature. Considering that PEV idling accounts for the majority of the time, the accumulated degradation could have a major impact on battery and vehicle lifetime. In this article, battery maintenance during extended idling periods is investigated by utilizing a commonly available infrastructure, i.e., the charging unit. An optimal charging profile is designed to maintain the battery states under desirable conditions to minimize degradation over the idling period while still satisfying the charging energy requirement. Optimal charging profiles are obtained under different ambient temperatures and stages of battery life, showing different features due to respective dominating degradation mechanisms. Compared with the optimal charging profile, constant-current (CC) charging could result in up to 51.6% higher capacity loss, and that of (fast) CC-constant-voltage charging could be up to 12.3 times higher under circumstances over a 12-h overnight idling period. Integration/accommodation of user and grid demand is also addressed by augmenting the optimization framework.

Thermal management is a critical task of battery control to ensure the safe, efficient, and enduring performance of the battery system, which can be considered as an interconnected thermal network of cells. The basis of thermal management is the estimation of temperature and its gradient across the battery system, which has received extensive attention in the literature. However, existing works neglect two important constraints in practical battery systems: 1) limited number of available sensors and 2) presence of system uncertainty such as parameter error. This paper is the first to investigate robust battery system temperature estimation under sparse sensing and system uncertainty. We first propose a framework consisting of optimization problems at three different levels: 1) evaluation of the worst case estimation performance (error) under uncertainty; 2) robust observer design to minimize the worst case error; and 3) optimization of sensor locations. Two robust estimation methods are then used to solve the problem. The system uncertainty considered in this paper is the unknown resistance variability among battery cells, but the methodology can be applied to address other types of uncertainty. It is shown that the designed observers could guarantee and improve the robustness and reliability of estimation by significantly reducing the worst case estimation errors induced by uncertainty.

For the practice of system identification/parameter estimation, the quality of data has significant impact on the accuracy of results. Therefore, data optimization, or optimal experiment design, plays a critical role. Traditionally, the common practice is to design input excitation by maximizing the Fisher information, which is related to the variance of the estimation error. However, this approach suffers from fundamental limitations, including the assumption of no estimation bias and negligence of system uncertainties in measurement, model, and parameter, which severely affect the effectiveness of the method. In this paper, we establish new criteria and a novel framework for data optimization and uncertainty quantification to overcome the fundamental limitations. First, we derive a formula for quantifying the estimation error induced by sensor, model, and parameter uncertainties for the commonly used least-squares algorithm. Based on the formula, we identify desirable data structures, which could minimize the errors caused by each uncertainty. These structures are then adopted as new criteria to formulate the novel data optimization framework. The proposed methodology is applied to parameter estimation of a lithium-ion battery electrochemical model, showing up to one order of magnitude improvement in accuracy compared with the traditional Fisher-information-based approach.

The commercialization of lithium-ion batteries enabled the widespread use of portable consumer electronics and serious efforts to electrify trans-portation. Managing the potent brew of lithium-ion batteries in the large quantities necessary for vehicle propulsion is still challenging. From space applications a billion miles from Earth to the daily commute of a hybrid electric automobile, these batteries require sophisticated battery management systems based on accurate estimation of battery internal states. This system is the brain of the battery and is responsible for estimating the state of charge, state of health, state of power, and temperature. The state estimation relies on accurate prediction of complex electrochemical, thermal, and mechanical phenomena, which increases the importance of model and parameter accuracy. Moreover, as the batteries age, how should the parameters of the model change to accurately represent the performance, and how can we leverage the limited sensor information from the measured terminal voltage and sparse surface temperatures available in a battery system? With a frugal sensor set, what is the optimal sensor placement? This article reviews estimation techniques and error bounds regarding sensor noise and modeling errors, and concludes with an outlook on the research that will be necessary to enable fast charging, repurposing of batteries for grid energy storage, degradation prediction, and fault detection.

This paper presents the analysis, design, and experimental validation of parameter identification of battery/supercapacitor (SC) hybrid energy storage system (HESS) for the purpose of condition monitoring and maximum power estimation. The analytic bounds on the error of battery and SC parameter identification, considering voltage measurement noise, are obtained based on the Fisher information matrix and Cramer–Rao bound analysis. The identification of different parameters requires different signal patterns to ensure high accuracy, rendering tradeoffs in the multiparameter identification process. With an appropriately designed current profile, HESS parameters are identified using recursive least squares with a forgetting factor. The identified parameters are then used to estimate the maximum power capability of the HESS. The maximum power capabilities of the battery and SC are estimated for both 1 and 30 s time horizons. The parameter identification algorithm can be applied to systems including either batteries or SCs when the optimal excitation current can be injected. Experimental validation is conducted on an HESS test-bed, which shows that the proposed algorithm is effective in estimating the HESS maximum power based on appropriate current excitation.

This paper presents an experimental study on the parameter identification of a battery pack, which determines the relationship between identification accuracy and measurement data. Parameter identification of the lithium-ion battery is poor when the input-output data, i.e., the input current and output voltage, is not appropriate. In addition, selection/optimization of an appropriate data set for estimation needs to adapt to different applications. A first-order equivalent circuit model is adopted to model a battery pack, and the identification accuracy is analyzed for both the single-parameter and multi-parameter identification scenarios. It is found that the accuracy of different identification scenarios is influenced by the voltage noise, the current amplitude, and the current frequency. Three experiments using sine waves with different frequencies are then performed to characterize a lithium-ion battery pack. Experimental results show that the current profile with the optimal frequency content achieves the best identification performance. Therefore, it is validated that the identification accuracy can be improved when the current excitation satisfies certain criteria.

Li-ion battery systems have been widely used as an essential power source in many applications. To ensure the safety and longevity of the system, a battery pack thermal model is often used in combination with distributed temperature sensors for thermal management and monitoring purposes. Due to the limited number of sensors and sparse measurement, sensor deployment to maximize the observability of the system thermal dynamics has been a critical topic, which has attracted research attention but remains to be resolved. This paper is devoted to exploring the pattern of optimal sensor locations for scalable battery systems under different observability criteria. A battery pack thermal model is first developed based on a single cell thermal model and considering the thermal interconnection between cells in the pack. Sensor location optimization is then performed by maximizing two Gramian-based observability metrics, which quantify different aspects of system observability. Optimal sensor locations obtained under the two metrics are analyzed and compared for battery systems of different sizes. Based on the results, deployment patterns of optimal sensor locations are extracted and analyzed theoretically by correlating to the physics of the battery thermal dynamics. Moreover, the influences of critical parameters of battery packs on system observability are also analyzed and discussed.

Electric multirotor aircraft with vertical-take-off-and-landing capabilities are emerging as a revolutionary transportation mode. This paper studies optimal control of a multirotor unmanned aerial vehicle based on a system-level multiphysical model. The model considers aerodynamics of the rotor-propeller assembly, electro-mechanical dynamics of the motor and motor controller, and rigid-body dynamics of the vehicle, as control based on a system-level model incorporating all these dynamics and their coupling is missing in literature. A forward flight operation is considered for time-optimal and energy-optimal control, as well as battery voltages of 25 V and 21 V. Energy-optimal control is shown to reduce the energy required for the operation by 38.5% at 25 V, while reducing the battery voltage increases the minimum operation time by 19.8%. The energy-optimal cruise velocity is also examined, demonstrating that the optimal velocity predicted without considering rotor aerodynamics uses 35.2% more energy per meter travelled than is required at the true optimal velocity.

Plug-in electric vehicle (PEV) is emerging as one of the most viable choices for the transportation sector to reduce fossil fuel consumption and CO2 emission. As the most critical component of PEV, battery systems require intensive management and diagnostics to ensure safety, efficiency, and endurance. Most existing studies focus on battery management when PEVs are under operation while none has explored battery maintenance during overnight parking, which accounts for a majority of the time (> 12 hours per day). Battery states during this period significantly affect the lifetime due to the side reactions that occur even when the battery is not in use. The process occurs at an accelerated rate when the battery energy level or temperature is too high or too low. In this paper, we propose to utilize an existing infrastructure available to PEV owners, the home charging unit, for intelligent battery maintenance during overnight parking. We will design an optimal charging profile that would charge the battery to a specific level while maintaining its states at optimal conditions to minimize degradation due to side reactions over the whole overnight period. Optimal charging profiles are created for different ambient temperatures and at different stages of battery life to investigate various scenarios. To demonstrate the effectiveness of the designed optimal charging profiles, the total capacity loss overnight is compared with those of three standard charging profiles.

Data optimization, or optimal experiment design, is an effective way to improve and guarantee the accuracy of state and parameter estimation, as the quality of data has significant impact on the estimation accuracy. Such capability is especially critical for energy systems requiring high reliability. The common practice of data optimization is to design input excitation by maximizing the Fisher information, and hence minimizes the variance of the estimation error. However, such approach suffers from fundamental limitations, including negligence of estimation bias and system uncertainties in measurement, model, and parameter, which severely restrict the applicability and effectiveness of the method. This paper aims at establishing new criteria and a novel framework for data optimization and estimation error quantification to overcome the fundamental limitations. First, a generic formula is derived for quantifying the estimation error subject to sensor, model, and parameter uncertainties for the commonly used least-squares algorithm. Based on the formula, desirable data structures, which could minimize the errors caused by each uncertainty, are identified. These structures are then used as new criteria to formulate the novel data optimization framework. The proposed methodology is applied to the parameter estimation problem of a lithium-ion battery electrochemical model in simulation and experiments, showing up to two orders of magnitude improvement in estimation accuracy compared with the traditional Fisher-information-based approach and other baselines.