The models for lithium-ion batteries vary in their computational complexity, accuracy and internal state predictions. While physics based models [2, 3] give key insights inside the battery, and could be used for estimating the internal states, these can’t easily be directly employed for online control because of their high computational requirements. To meet these requirements, various approaches are continuously attempted by different researchers.
Multivariable control techniques have already been shown for a variety of systems. Dynamic matrix control (DMC) [4], internal model control (IMC) [5] and model algorithmic control (MAC) [6] have already been illustrated in the past. These models rely on the linear approximations of the experimentally obtained step response data. Physics based battery models are highly non-linear in nature and controlling them efficiently would ideally require the battery models to be imbedded directly in the controller. This presents challenges in convergence and efficiency of the algorithms.
In our past work, we explored the use of simultaneous optimization [7, 10] and control vector parameterization (CVP) [8, 9, 10] optimization strategies to predict the optimal charging current profiles. Northrop et. al. and Subramanian et. al. [11, 12] did model reformulation to reduce the computation time.
In this work, we present an alternative approach to control batteries applying the concept of differential geometry. This approach is called as Generic Model Control [13], or Reference Control Synthesis [14]. This work enables robust stabilization and control of battery models to set point as an alternative approach. As compared to the generic model control approaches implemented by previous researchers, we implement the same using the direct DAE numerical solvers including iteration free solvers recently developed in our group [15].
The results are presented for single input single objective (maximizing charge stored with current input), single input multiple objective (maximizing charge stored with minimizing fade and temperature rise), constrained problems (controlling the temperature rise and fade while charging), along with models and plants with time delays. The proposed new approach is compared with simultaneous and direct optimization strategies. It is expected that the proposed approach will be more robust if not globally optimal.
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 and the Clean Energy Institute at the University of Washington, Seattle.
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