2. M.Tech Research Reports

Permanent URI for this collectionhttps://idr.nitk.ac.in/handle/123456789/16917

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Iterative Methods and their Applications for Solving Non-Linear Ill-Posed Equations
(National Institute of Technology Karnataka, Surathkal., 2023) K., Muhammed Saeed; George, Santhosh; P., Jidesh
This thesis deals with iterative methods and their convergence for solving non-linear equations in Banach Spaces. As an application, it also deals with solving non-linear ill posed equations in a Hilbert space setting. Under various assumptions, local and semi local convergence analyses of some iterative schemes are studied. We have established the desired order of convergence using weaker assumptions than those available in the literature. We have also extended some of the methods efficiently. Computable radii of convergence and dynamics analysis using the basin of attractions are other highlights. The first contribution of the thesis is the convergence analysis of a fifth-order it erative method using conditions only on the first Fréchet derivative. This increased the applicability of the method. In our second work, we used the iterative method for solving the regularized equation corresponding to a non-linear ill-posed equation. We introduced a new source condition and parameter choice strategy for the desired results. Thirdly, using Lipschitz-type assumptions on first and second derivatives instead of Taylor series expansion, we established third-order convergence of an iterative Home ier method. We further extended this method to the fifth and sixth order. Lastly, we studied another iterative method introduced by Traub. We established third-order con vergence without using Taylor series expansion. We extended this method to the fifth and sixth order.
Broadcast Domination in Graphs and its Critical Aspects
(National Institute of Technology Karnataka, Surathkal., 2024) Sen, Jishnu; Kola, Srinivasa Rao
Adistance related domination parameter deals with the idea where a subset of vertices are at an acceptable distances from the rest of the vertices. In this context, a vertex can dominate other vertices beyond its neighbors. Broadcast domination is a distance related domination parameter of a graph which captures the true flavor of the idea of varying dominating ability of a vertex. A dominating broadcast of a graph G is a func tion f :V(G)→{0,1,2,...,diam(G)} such that f(v) is at most the eccentricity of v, for all v ∈V(G), and for every vertex u ∈V(G), there exists a vertex v with f(v) > 0 and d(u,v) ⩽ f(v). The cost σ(f) of f is ∑v∈V(G) f(v). The minimum of costs over all the dominating broadcasts of G is called the broadcast domination number γb(G) of G. A dominating broadcast f is referred as an optimal dominating broadcast if σ(f)=γb(G). In this thesis, we present a new tight upper bound involving the order and the minimum degree, and a new tight lower bound for the same concerning the order and the maxi mumdegreeofG. Weimprovedtheupper bound for the broadcast domination numbers of a subclass of regular graphs. Further, we study the broadcast domination number for the generalized Petersen graphs and a subclass of circulant graphs. After that, we study the broadcast domination number of a graph under some graph operations. We present upper bounds for the broadcast domination numbers of lexicographic and modular prod ucts of graphs, in term of the broadcast domination numbers of its factor graphs. An algorithm for finding a dominating broadcast for the lexicographic product of graphs is given, which also produces an optimal dominating broadcast for some graphs. Also, we determine the exact values of the broadcast domination numbers for those products of graphs concerning path, cycle and complete graphs. Next, we study the broadcast dom ination of line graphs. We prove that γb(G) 2 ⩽γb(L(G))⩽γb(G) and improve the upper bound of the same for the line graphs of trees. We present a necessary and sufficient condition for radial line graphs of central trees, and exhibit constructions of infinitely many central trees T for which L(T) is radial. We give a characterization for radial line graphs of trees, and discuss the broadcast domination numbers for line graphs of caterpillars and i-subdivision graph of K1,n. We instigate the study of critical aspects in broadcast domination with respect to edge deletion and edge addition. A graph G with i γb(G) = k is said to be k-γ+ b-edge-critical (k-γ− b-edge-critical) if γb(G −e) > γb(G), for every edge e ∈ E(G) (if γb(G+e) < γb(G), for every edge e ∈ E( G)). We give a necessary and sufficient condition for k-γ+ b-edge-critical graph. We characterize k-γ− b edge-critical graphs for k = 1,2, and give necessary conditions of the same for k ⩾ 3. Further, we introduce the concept of the broadcast bondage number and the broadcast reinforcement number of a graph, and give some sharp upper bounds for them.
A Study on Ill-Posed Equations and Iterative Methods
(National Institute of Technology Karnataka, Surathkal., 2024) R, Krishnendu; George, Santhosh; P, Jidesh
Many problems that arise in various fields of study can be modeled into equations that are well-posed/ill-posed (linear or nonlinear). Especially in science and engineer ing, most of the inverse problems are ill-posed. The first half of the thesis focuses on f inite dimensional realization of regularization methods for ill-posed problems. The second half deals with iterative methods for solving well-posed nonlinear equations. It is proved in the literature that the Fractional Tikhonov regularization method (FTR) reduces the over smoothing of the solution compared to the usual Tikhonov reg ularization method for ill-posed problems. In Chapter 2 of the thesis, the FTR method in the finite dimensional setting is studied. The regularization parameter is chosen using Raus and Gfrerer type discrepancy principle in this Chapter. The choice of regularization parameter and suitable source condition plays an im portant role in a regularization method. In Chapter 3, an efficient new parameter choice strategy is introduced. The advantage is that this parameter choice strategy computes the regularization parameter before computing the approximate solution and is depen dent on the given data of the problem. This new parameter choice also provide the optimal order. The proposed parameter choice strategy is depending on a new source condition. Higher order iterative methods are used to solve nonlinear equations. The conver gence order of these methods uses Taylor’s expansion and assumptions on the higher order Fréchet derivative of the operator. In Chapter 4 and Chapter 5, we have elimi nated the use of Taylor’s expansion and hence assumptions on the higher order Fréchet derivatives of the operator in the problem. Moreover, the desired convergence order of the iterative method is obtained without using assumptions on the higher order Fréchet derivatives and hence the applicability of these iterative methods are extended to prob lem which were not posible using earlier studies. These iterative methods are also applied to solve nonlinear ill-posed problems.
Investigations Into Control Strategies and Integrated Charging Solutions for Switched Reluctance Motor-Driven Electric Vehicles
(National Institute of Technology Karnataka, Surathkal, 2024) T. Faheemali; Dominic,Arun D.; Prajof, Prabhakaran
Electric vehicles (EVs) are increasingly recognized as a vital solution to mitigate greenhouse gas emissions and air pollution in the transportation sector. However, challenges such as limited driving range, higher upfront costs, and dependence on rare earth minerals hinder their widespread adoption. One promising solution lies in the Switched Reluctance Motor (SRM), distinguished by its simple structure devoid of permanent magnets or rotor conductors. This design offers inherent advantages such as efficient operation in high temperatures, robust fault tolerance, and minimal rotor losses, rendering SRMs a compelling choice for EV propulsion. Furthermore, the integration of integrated on-board chargers (IOBCs) adds another layer of efficiency and functionality to EV systems. By seamlessly combining motor driving and charging functions, IOBCs not only promise cost savings and reduced complexity but also offer increased power density. Notably, with bidirectional capability, IOBCs enable EVs to both charge from external sources and supply power back to the grid. This bidirectional functionality holds immense significance for diverse operating scenarios such as grid-to-vehicle (G2V), vehicle-to-grid (V2G), vehicle-to-load (V2L), and vehicle-to-home (V2H). This thesis explores the promising prospects of utilizing SRM drives in EVs and investigates the integration of IOBC systems. Acknowledging challenges such as higher torque ripple and lower power density associated with SRM motors for EVs, the research emphasizes the need for further research and enhancement in this domain. With a primary focus on enhancing efficiency, reducing costs, and increasing the overall power density of EV systems, the study aims to address key obstacles hindering the widespread adoption of EVs while advancing sustainable transportation solutions. This thesis also presents a precise simulation model of SRM for analyzing and conducting simulation studies on the proposed methods. This necessitates the characterization of the SRM, for which various methods are available in the literature, ranging from analytical approaches to electromagnetic Finite Element Analysis (FEA) tools. While FEA-based models offer high accuracy, this thesis initially details the procedure for developing a MATLAB Simulink model derived from the FEA-based characterization of the SRM prototype which is used in further studies. Additionally, obtaining a linearized SRM model is crucial for controller design. This thesis details the procedure for obtaining the linearized SRM model. Subsequently in the thesis, a novel SRM drive utilizing a Miller converterfed SRM motor for medium-power applications with a single current sensor is proposed to reduce cost and improve performance. The literature offers a variety of control strategies for SRM drives, yet for medium-power applications, those equipped with a dedicated position sensor and employing a fixed control strategy based on a linearized transfer function hold particular relevance. Also, there is a notable absence of a comprehensive control development procedure in the existing literature. Moreover, there lies an opportunity to reduce costs by minimizing the number of current sensors necessary for controlling the SRM drive. The thesis offers a comprehensive control development, dynamic simulation, analysis, and experimental validation of the same. Speed and current controllers are designed using the K-factor method, and the efficacy of the proposed drive is rigorously evaluated across various operating modes in MATLAB Simulink. Additionally, a hardware prototype is developed and the digital control algorithm is implemented on the DSP microcontroller TMS320F28379D based on the designed controllers to further assess drive performance. The results obtained validate the robustness and dynamic performance of the proposed cost-effective SRM drive with single current sensor across variable speed, variable torque, and constant power modes of operation. In the literature, the single-pulse control (SPC) of SRM is discussed for high-speed applications, operating at the fundamental switching frequency to reduce core and switching losses effectively. However, its suitability for wide speed control is limited due to significant torque ripple. To address this, extending the constant conduction period with v/f control can mitigate torque ripple by facilitating torque sharing during winding commutation. Nevertheless, this extended conduction angle may result in negative torque production and a lower torque-to-ampere ratio. This research conducts an analysis of conventional SPC, conventional v/f conii trol, and the impact of a wider conduction angle on torque ripple and efficiency through simulation studies. Moreover, it investigates the effect of accelerated demagnetization on torque ripple and efficiency in v/f controlled SRM drives with a wider conduction angle. This thesis introduces a novel bidirectional dual-port ´Cuk converter-fed SRM drive with accelerated demagnetization capability. In the proposed ´Cuk converter-fed SRM drive, the magnetization voltage controls the speed and provides a decoupled higher demagnetization voltage, thus accelerating demagnetization. This facilitates reduced switching losses and core losses similar to those in SPC, while ensuring reduced torque ripple with a wider conduction period and a higher torque ampere ratio due to accelerated demagnetization. Additionally, the proposed system incorporated IOBC capability. In G2V mode, the converter is reconfigured to adopt a two-stage, non-isolated charger topology, comprising a diode bridge followed by a ´Cuk converter in the reverse direction. Detailed control development and analysis are presented in the thesis. The proposed SRM drive with IOBC capability is validated through simulations and an experimental prototype. It demonstrates robust performance across various modes of operation and offers cost reduction and increased overall power density. Existing literature identifies two types of IOBCs for SRM-based electric vehicles: one leveraging machine windings as inductors and the other not. While utilizing machine windings offers advantages like higher power density, it also introduces risks such as instantaneous torque pulsation. To ensure reliable utilization of machine windings as filter inductors, maintaining zero instantaneous torque (ZIT) during charging modes is imperative. This thesis extensively investigates the utilization of machine windings as filter inductors, highlighting potential benefits in terms of power density and cost reduction. In the literature, the issue of common-mode voltage in non-isolated IOBCs for SRM based EVs have not received much attention. Additionally, the SRM based IOBCs proposed in the literature have no bidirectional capability limiting the operating modes. Bidirectional capabilities for IOBCs enable versatile operating modes by allowing EVs to feed power back to the grid or other electrical loads. Additionally, the literature lacks detailed qualitative analysis of IOBCs using machine windings as filter inductors, including the impact of even harmonics from unequal inductances in positive and negative cycles. This thesis introduces a IOBC system with bidirectional capability for a 4-phase SRM drive based EV. In the proposed drive outlined in the thesis, the converter is reconfigured as a two-phase interleaved totem pole PFC converter, utilizing machine windings as filter inductors. This configuration enables the suppression of common-mode voltage or current and higher efficiency compared to previously reported IOBCs, without the need for additional magnetic contactors. During charging, four stable ZIT positions are identified, ensuring reliable utilization of machine windings as filter inductors, thereby mitigating wear and tear induced by torque pulsations. The thesis provides a detailed analysis of instantaneous torque during charging modes, supported by FEA and MATLAB simulation results to validate ZIT. This versatile IOBC demonstrates bidirectional capability, accommodating various operational modes such as G2V, V2G, V2H, and V2L. The performance of the proposed system is further validated through an experimental prototype, affirming the advantages of the proposed IOBC, which utilizes SRM windings as filter inductors, promising versatile operating modes with bidirectional capability and reduced common-mode voltage. In conclusion, this thesis presents a comprehensive exploration of utilizing SRMs in EVs and the integration of IOBCs to enhance efficiency and functionality. Through simulation studies and experimental validation, novel solutions for SRM drives and IOBC systems for SRM based EVs are proposed, addressing challenges such as torque ripple, efficiency, and cost. The results demonstrate robust performance and validate the advantages of the proposed systems, paving the way for advancements in sustainable transportation solutions.