Identifiability of generalised Randles circuit models

The Randles circuit (including a parallel resistor and capacitor in series with another resistor) and its generalised topology have widely been employed in electrochemical energy storage systems such as batteries, fuel cells and supercapacitors, also in biomedical engineering, for example, to model the electrode-tissue interface in electroencephalography and baroreceptor dynamics. This paper studies identifiability of generalised Randles circuit models, that is, whether the model parameters can be estimated uniquely from the input-output data. It is shown that generalised Randles circuit models are structurally locally identifiable. The condition that makes the model structure globally identifiable is then discussed. Finally, the estimation accuracy is evaluated through extensive simulations

Structural Identifiability of Impedance Spectroscopy Fractional-Order Equivalent Circuit Models With Two Constant Phase Elements

Structural identifiability analysis of fractional-order equivalent circuit models (FO-ECMs), obtained through electrochemical impedance spectroscopy (EIS) is still a challenging problem. No peer-reviewed analytical or numerical proof does exist showing that whether impedance spectroscopy FO-ECMs are structurally identifiable or not, regardless of practical issues such as measurement noises and the selection of excitation signals. By using the coefficient mapping technique, this paper proposes novel computationally-efficient algebraic equations for the numerical structural identifiability analysis of a widely used FO-ECM with Gr\"{u}nwald-Letnikov fractional derivative approximation and two constant phase elements (CPEs) including the Warburg term. The proposed numerical structural identifiability analysis method is applied to an example from batteries, and the results are discussed. Matlab codes are available on github

Modeling, Parameter Identification, and Degradation-Conscious Control of Polymer Electrolyte Membrane (PEM) Fuel Cells

Polymer electrolyte membrane (PEM) fuel cells are touted as zero-emission alternatives to internal combustion engines for automotive applications. However, high cost and durability issues have hindered their commercialization. Therefore, significant research efforts are underway to better understand the scientific aspects of PEM fuel cell operation and engineer its components for improved lifetime and reduced cost. Most of the research in this area has been focused on material development. However, as demonstrated by Toyota's fuel cell vehicle, intelligent control strategies may lead to significantly improved durability of the fuel cell stack even with existing materials. Therefore, it seems that the outstanding issues can be better resolved through a combination of improved materials and effective control strategies. Accordingly, this dissertation aims to develop a model-based control strategy to improve performance and durability of PEM fuel cell systems for automotive applications. To this end, the dissertation first develops a physics-based and computationally efficient model for online estimation purposes. The need for such a model arises from the fact that detailed information about the internal states of the cell is required to develop effective control strategies for improved performance and durability, and such information is rarely available from direct measurements. Therefore, a software sensor must be developed to provide the required signals for a control system. To this end, this work utilizes spatio-temporal decoupling of the underlying problem to develop a model that can estimate water and temperature distributions throughout an operating fuel cell in a computationally efficient manner. The model is shown to capture a variety of complex physical phenomena, while running at least an order of magnitude faster than real time for dynamically changing conditions. The model is also validated with extensive experimental measurements under different operating conditions that are of interest for automotive applications. Furthermore, the dissertation extensively explores the sensitivity of the model predictions to a variety of parameters. The sensitivity results are used to study the parameter identifiability problem in detail. The challenges associated with parameter identification in such a large-scale physics-based model are highlighted and a model parameterization framework is proposed to address them. The proposed framework consists of three main components: (1) selecting a subset of model parameters for identification, (2) optimally designing experiments that are maximally informative for parameter identification, and (3) designing a multi-step identification algorithm that ensures sufficient regularization of the inverse problem. These considerations are shown to lead to effective model parameterization with limited experimental measurements. Finally, the dissertation uses a version of the proposed model to develop a degradation-conscious model-predictive control (MPC) framework to enhance the performance and durability of PEM fuel cell systems. In particular, a reduced-order model is developed for control design, which is then successively linearized about the current operating point to enable use of linear control design techniques that offer significant computational advantages. A variety of constraints on system safety and durability are considered and simulation case studies are conducted to evaluate the framework's utility in maximizing performance while respecting the durability constraints. It is also shown that the linear MPC framework employed here can generate the optimal control commands faster than real time. Therefore, the proposed framework is expected to be implementable in practical applications and contribute to extending the lifetime of fuel cell systems.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155288/1/goshtasb_1.pd