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This article discusses the options and challenges of dynamic models for the diagnosis and operation of Li-ion batteries. It provides a concise yet understandable overview on models and dynamics, and it discusses future developments needed to progress the field. The diagnosis and operation of batteries require an understanding of the main processes and their dynamics, parameters, and time constants. Processes with large time constants, such as thermal transport are equally important for safe high-performance operation as are processes with shorter time constants such as diffusion. Depending on the specific problem or operating condition, taking all of the scales into account is often unavoidable. Three separate, yet closely connected model classes are reviewed in terms of physical insight and their capabilities and limits: mechanistic models, equivalent circuit models, and data-driven models. We provide guidance for the selection of a suitable model for the particular diagnosis and operation problem of interest. The optimization of battery diagnosis and operation require versatile and simple models that span multiple time scales and allow physical insight and ease of parameterization. Fusing the existing modeling approaches may help to fully exploit their potential while integrating first-principles physical insight and measurement data.

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This paper describes a design and two-level tuning method for fuzzy proportional-integral derivative (FPID) controllers for a multivariable process where the fuzzy inference uses the inference of standard additive model. The proposed method can be used for any n x n multi-input-multi-output process and guarantees closed-loop stability. In the two-level tuning scheme, the tuning follows two steps: low-level tuning followed by high-level tuning. The low-level tuning adjusts apparent linear gains, whereas the high-level tuning changes the nonlinearity in the normalized fuzzy output. In this paper, two types of FPID configurations are considered, and their performances are evaluated by using a real-time multizone temperature control problem having a 3 x 3 process system.