Nonlinear Model Predictive Control Strategies for Optimal Charging of a Lithium-Ion Battery
Authors: Aduru Sai Varun , Pathak Manan , Kolluri Suryanarayana , Braatz Richard D. , Subramanian Venkat R. 
Published: February 2020

Lithium-ion (Li-ion) batteries, due to their high energy/power density, good temperature range and long battery life, can be used in a wide range of applications from electric vehicles to smart phones and smart grids1
2. For an optimal and safe operation of a Li-ion battery, Battery Management Systems (BMS) are pivotal. BMS monitors voltage, current and temperature, predicts State of Charge (SOC), State of Health (SOH) and estimates time before complete charge/discharge3. BMS depends on the mathematical models of Li-ion batteries for managing and regulating their performance. Most of the current BMS deploy empirical or semi-empirical models which may lead to inaccurate predictions of internal states3. Comparatively, using first principles models based on electrochemical and thermodynamic principles help in accurately predicting the dynamic nature of the internal states3. Therefore, BMS based on physics-based models is imperative for an enhanced and efficient performance of a Li-ion battery.
Model Predictive Control (MPC) can be used in the design of BMS due its efficiency in handling constraints in an explicit manner and its ability for performing multivariable control.4–6 In MPC, the controller uses an explicit process model to generate a sequence of manipulated variable moves over a control horizon by optimizing an objective over a prediction horizon in a receding horizon approach.7–9 Classical MPC algorithms use linear process models to predict the outputs over the prediction horizon4,5. But, the main limitation in such classical MPC schemes is the usage of the linear prediction models restricting their application only to mildly nonlinear processes9. Though linear approximations of the first principles models have been used in the past for determining optimal charging profiles for Li-ion batteries,4–6 these versions might not be well placed to accurately capture the dynamics of the system. Traditionally, high computational cost of online calculations has been often cited as one of the main reasons for restricted use of nonlinear MPC formulations for battery models4–6. To the best of our knowledge, non-linear model predictive control (NMPC) has not yet been applied on physics-based battery models.
In the current work, we present a strategy to formulate an NMPC framework for the reformulated pseudo-2D model in real-time. Such a strategy will be extremely useful for BMS applications. The performance objective in NMPC is defined to minimize the error between the deviation of the desired controlled variable from its set point. Optimal current densities (manipulated variables), satisfying a set of different bounds for a defined performance criteria, are reported. The performance of the proposed strategy is illustrated by (i) servo and regulatory control problems with Voltage, SOC as output variables (ii) maximizing SOC, (iii)minimizing the capacity fade, while simultaneously having constraints on state variables such as temperature and anode over-potential to mitigate lithium plating.

Acknowledgements

The work presented herein was funded in part by the Advanced Research Projects Agency –Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275 along with the Clean Energy Institute (CEI) at the University of Washington (UW) and the Washington Research Foundation.

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