# Browsing by Subject "Stability"

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Item Open Access Data-Driven Parameter Estimation of Time Delay Dynamical Systems for Stability Prediction(2021) Turner, James D.Subtractive machining operations such as milling, turning, and drilling are an essential part of many manufacturing processes. Unfortunately, under certain combinations of machine settings, the motion of the cutting tool can become unstable, due to feedback between consecutive passes of the tool. This phenomenon is known as chatter. Mathematical models, specifically delay differential equations (DDEs), can describe the motion of the cutting tool and predict this instability. While these models are useful, estimates of the models' parameters are necessary in order to apply them to real systems. Unfortunately, estimating the parameters directly can be time-consuming, expensive, and difficult. The objective of this research is to develop automated methods to estimate these parameters indirectly, from time series measurements of the tool's motion which can be collected in a few minutes with sensors attached to the machine. The estimated parameters can then be used to predict when chatter will occur so that the machine operator can select appropriate settings.

One way to estimate the parameters of a dynamics model is to match the characteristic multipliers (CMs) predicted by the model to CMs estimated from time series data. CMs describe the behavior, such as stability, of a dynamical system near a limit cycle. While existing CM estimation methods are available, practical challenges such as measurement noise, limited time series length, and repeated CMs can substantially reduce their accuracy. The first part of this dissertation presents improved methods for estimating CMs from time series. Numerical validation studies demonstrate that the improved methods consistently provide more accurate CM estimates than existing methods in a variety of scenarios.

The second part of this dissertation introduces improvements to CM matching and trajectory matching methods for estimating the parameters of DDEs from noisy time series data. For CM matching, it incorporates the empirical CM estimation improvements from the previous part, and it introduces a way to match multiple CM estimates for each time series. For trajectory matching, it describes how to handle multivariate observations and prior knowledge in a principled way; it uses the spectral element method to provide a convenient representation of the initial interval and reduce the computational cost of computing the objective function; and it fits multiple time series simultaneously. Simulation results demonstrate that these improved methods work well in practice, although CM matching has some limitations which are not a problem for the trajectory matching method.

The final part of this dissertation introduces a new approach to estimate the parameters of a DDE model for milling from noisy time series data, based on the trajectory matching approach described in the previous part. It extends models from the literature to more closely fit the time series data, and it describes a procedure to estimate the unknown parameters in stages, without having to solve a global optimization algorithm for all the parameters simultaneously. Additionally, it adapts the spectral element method to make predictions for this model. Experimental results using time series data collected on an instrumented milling machine demonstrate that the model and fitting procedure successfully estimate parameters for which the predicted stability boundaries approximate the true stability boundaries.

Item Open Access Feasibility and Stability Results for Systems with Externally Triggered Switching(2023) Hall, Richard ArlenWhen designing controllers, it is important to consider their stability and safety. However, this can become difficult as the system's complexity increases. This work presents results on the persistent feasibility and stability of externally switching systems. This extends the previous results in the area, which were restricted to narrow classes of systems. The work begins with centralized systems and evolves to explore distributed classes of systems. As with other areas of control system design, distributed methods provide solutions to overcome scaling problems. There are several different tools used in this work to extend the class of systems for which safety and stability assurances can be made. Polytopic sets and their evolution under linear dynamics are used extensively. The parallelization of complex algorithms is another important tool used in these results. Parallelization is a key benefit of distributed systems and prevents the results from falling into the curse of dimensionality. Finally, novel methods of approximating and bounding values are developed, which further reduces the results' numerical complexity. While these approximations do introduce some conservatism, it is often less than the redundancy required in place of formal analysis. The full results of this work advance the study of externally switched systems to applications that, in the past, would not have been possible to study. While fully maturing the field is far too large a goal for any single doctoral dissertation, my contributions include several important advancements that have utility as stand-alone results and provide rich opportunities for future advancements in the field.

Item Open Access Ferroelectric Thin Films for the Manipulation of Interfacial Forces in Aqueous Environments(2013) Ferris, Robert JosephFerroelectric thin films (FETFs) offer a promising new platform for advancing liquid-phase interfacial sensing devices. FETFs are capable of expressing surface charge densities that are an order of magnitude higher than those of traditional charged surfaces in liquid environments (e.g., common oxides, self-assembled monolayers, or electrets). Furthermore, the switchable polarization state of FETFs enables patterning of charge-heterogeneous surfaces whose charge patterns persist over a range of environmental conditions. Integration of FETFs into liquid-phase interfacial sensing devices, however, requires the fabrication of films with nanometer-scale surface roughness, high remnant polarization values, and interfacial stability during prolonged exposure. The objectives of my research were to i) fabricate ferroelectric ultra-smooth lead zirconium titanate (US-PZT) thin films with nanometer-scale surface roughness, ii) establish the interfacial stability of these films after prolonged exposure to aqueous environments, iii) measure the interfacial forces as a function of film polarization and ionic strength, iv) calculate the surface potential of the US-PZT surface using electric double layer (EDL) theory, and v) demonstrate the guided deposition of charged colloidal particles onto locally polarized US-PZT thin films from solution.

I demonstrate the use of ferroelectric US-PZT thin films to manipulate EDL interaction forces in aqueous environments. My work conclusively shows that the polarization state of US-PZT controls EDL formation and can be used to induce the guided deposition of charged colloidal particles in solution.

I present a robust fabrication scheme for making ferroelectric US-PZT thin films from a sol-gel precursor. By optimizing critical thermal processing steps I am able to minimize the in-plane stress of the film and reliably produce US-PZT thin films on the wafer-scale with mean surface roughness values of only 2.4 nm over a 25 μm2 area. I then establish US-PZT film stability in water by measuring changes in film topography, crystallinity, surface chemistry, and electrical properties as a function of exposure duration. My results show that fabrication of crack-free US-PZT thin film is critical for long-term film fidelity in aqueous environments. Furthermore, I found no change in film topography or bulk composition with increasing exposure duration. Prolonged exposure to aqueous environments, however, gradually oxidizes the surface of the US-PZT wich results in a decrease in film resistivity and polarization saturation. Next, I used colloidal probe force microscopy (CPFM) to measure the EDL interaction force as a function of separation distance between polarized US-PZT thin films and a clean borosilicate probe. CPFM measurements were performed on oppositely polarized US-PZT thin films, which expressed either a positive or negative surface charge, and over a range of ionic strengths. The inner-Helmholtz plane (IHP) potential of the US-PZT was determined by fitting the CPFM force-separation data to number of EDL models, including; an analytical EDL model using a constant potential boundary condition with a Stern layer, a charge regulation EDL model, and a numerical EDL model using the non-linear Poisson-Boltzmann equation. Each model provides good agreement with the experimentally measured and predict high IHP surface potential for the polarized US-PZT thin films in solution. Finally, I demonstrate the use of polarized US-PZT to induce the guided deposition of positively or negatively charged colloidal particles from aqueous environments. I explore the effects of ionic strength, particle size, surface roughness, and pH on particle deposition.

Overall, this work demonstrates, for the first time, that FETFs can be used as a platform to manipulate colloidal particles in aqueous environments. The experimental results demonstrate that the surface charge of the FETF is reduced by charge shielding and perform similarly to traditional, charged surfaces in aqueous environments.

Item Open Access Improving Stability and Selectivity in Electrochemical Reduction of Carbon Dioxide in an Aqueous Solution(2018) Ji, DongWith the rising level of CO2 in the atmosphere, methods capable of converting CO2 into useful fuels are urgently needed. The electrochemical CO2 reduction has gained significant interest recently due to its ability to use renewable energies. However, the poor stability of catalysts in electrochemical CO2 reduction limit its application in industry. Here we have developed a light-involving method to remove the surface carbonaceous species which are believed to poison the catalysts. By taking advantage of plasmonic properties of the copper catalyst, the stability of the catalysts has apparently improved.

Another problem in electrochemical CO2 reduction is the poor selectivity. One of the main reasons is the existence of the side reaction, hydrogen evolution reaction. Here we have developed a catalyst by dispersing atomic nickel on nitrogen-doped winged carbon nanotubes with the ability to suppress hydrogen evolution during CO2 reduction. The Faradaic Efficiency of CO reached 90% at -1.6 V vs. AgCl/Ag reference electrode while the efficiency of HER had been suppressed to less than 10% in the optimal reaction condition. By comparing with Ni NPs, the suppression of HER can be directly observed in LSV curve. It is suggested that this suppression may result from the lack of adjacent active sites for the Tafel mechanism in HER.

Item Open Access On Lipschitz analysis and Lipschitz synthesis for the phase retrieval problem(Linear Algebra and Its Applications, 2016-05-01) Balan, R; Zou, D© 2016 Elsevier Inc. All rights reserved. We prove two results with regard to reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievable nonlinear maps are bi-Lipschitz with respect to appropriate metrics on the quotient space. Specifically, if nonlinear analysis maps α,β:H→→ℝm are injective, with α(x)=(||)km=1 and β(x)=(||2)km=1, where {f1,...,fm} is a frame for a Hilbert space H and H=H/T1, then α is bi-Lipschitz with respect to the class of "natural metrics" Dp(x,y)=minφ||x-eiφy||p, whereas β is bi-Lipschitz with respect to the class of matrix-norm induced metrics dp(x,y)=||xx∗-yy∗||p. Second we prove that reconstruction can be performed using Lipschitz continuous maps. That is, there exist left inverse maps (synthesis maps) ω,ψ:ℝm→H of α and β respectively, that are Lipschitz continuous with respect to appropriate metrics. Additionally, we obtain the Lipschitz constants of ω and ψ in terms of the lower Lipschitz constants of α and β, respectively. Surprisingly, the increase in both Lipschitz constants is a relatively small factor, independent of the space dimension or the frame redundancy.Item Open Access Post-Buckled Stability and Modal Behavior of Plates and Shells(2012) Lyman, Theodore ClarenceIn modern engineering there is a considerable interest in predicting the behavior of post-buckled structures. With current lightweight, aerospace, and high performance applications, structural elements frequently operate beyond their buckled load. This is especially true of plates, which are capable of maintaining stability at loads several times their critical buckling load. Additionally, even structures such as cylindrical shells may be pushed into a post-buckled range in these extreme applications.

Because of the nature of these problems, continuation methods are particularly well suited as a solution method. Continuation methods have been extensively applied to a range of problems in mathematics and physics but have been used to a lesser extent in engineering problems. In the present work, continuation methods are used to solve a variety of buckling and stability problems of discrete dynamical systems, plates and cylinders. The continuation methods, when applied to dynamic mechanical systems, also provide very useful information regarding the modal behavior of the structure, including linearized natural frequencies and mode shapes as a by-product of the solution method.

To verify the results of the continuation calculations, the commercial finite element code ANSYS is used as an independent check. To confirm previously unseen stable equilibrium shapes for square plates, a set of experiments on polycarbonate plates is also presented.

Item Open Access The Search for Stability and the Inevitability of Change in the Writings and Life of Hermann Hesse(2017-12-13) Desimoni, VictoriaHow can human beings, whose main characteristic is to change constantly, find stability or internal stillness? This is a question that concerned Hermann Hesse his whole life. His answer to this question of stability itself changed over time. Hesse started with the belief that stability was acquired by dwelling on a farm, and ended with the conviction that stability as “stillness” is something human beings can never achieve. Hesse’s final answer is that we are wanderers, constantly incomplete, always in process of more. In this project, I look closely at Hesse’s progress of thought from his first answer to his final answer. Hesse asks this question in his first novel Peter Camenzind (1904) and provides a final answer in one of his last novels, Narcissus and Goldmund (1930). I conduct my analysis through the close reading of these two novels, together with a study of Hesse’s historical background from his childhood to his mid-fifties. His historical background is necessary to understand the metamorphosis of his thought. As a way of elucidating Hesse’s ideas, I compare them to Martin Heidegger’s and Jean-Paul Sartre’s philosophical theories. Hesse’s first answer is surprisingly similar to Heidegger’s belief that the way in which we, human beings, are in the world is by “dwelling.” Dwelling is our essence. His second answer leaves Heidegger aside, and mirrors instead Sartre’s theory that a person is what she makes of herself through her actions; there is no one specific essence that corresponds to the human being, and we are, in Sartre’s words, condemned to invent ourselves constantly.