Presence of nonlinearities may lead to limit cycle oscillations (LCOs) in aeroelastic systems. LCOs can result in fatigue in wings leading to catastrophic failures. Existence of LCOs for velocities less than the linear flutter velocity has been observed during flight and wind tunnel tests, making such subcritical behavior highly undesirable. The objective of this dissertation is to investigate the existence of subcritical LCOs in aeroelastic systems and develop state feedback controllers to suppress them. The research results are demonstrated on a two degree of freedom airfoil section model with stiffness nonlinearity. Three different approaches are developed and discussed. The first approach uses a feedback linearization controller employing the aeroelastic modal coordinates. The use of modal coordinates results in a system which is linearly decoupled making it possible to avoid cancellation of any linear terms when compared to existing feedback linearization controllers which use the physical coordinates. The state and control costs of the developed controller are compared to the costs of the traditional feedback linearization controllers. Second approach involves the use of nonlinear normal modes (NNMs) as a tool to predict LCO amplitudes of the aeroelastic system. NNM dynamics along with harmonic balance method are used to generate analytical estimates of LCO amplitude and its sensitivities with respect to the introduced control parameters. A multiobjective optimization problem is solved to generate optimal control parameters which minimize the LCO amplitude and the control cost. The third approach uses a nonlinear state feedback control input obtained as the solution of a multiobjective optimization problem which minimizes the difference between the LCO commencement velocity and the linear flutter velocity. The estimates of LCO commencement velocity and its sensitivities are obtained using numerical continuation methods and harmonic balance methods. It is shown that the developed optimal controller eliminates any existing subcritical LCOs by converting them to supercritical LCOs. / Ph. D.

Power systems are extremely non-linear systems which require substantial modeling and control efforts to run continuously. The movement of the power system in parameter and state space is often not well understood, thus making it difficult or impossible to determine whether the system is nearing instability. This dissertation demonstrates several ways in which the power system stability boundary can be calculated. The power system movements evaluated here address the effects of inter-area oscillations on the system which occur in the seconds to minutes time period. The first uses gain scheduling techniques through creation of a set of linear parameter varying (LPV) systems for many operating points of the non-linear system. In the case presented, load and line reactance are used as parameters. The scheduling variables are the power flows in tie lines of the system due to the useful information they provide about the power system state in addition to being available for measurement. A linear controller is developed for the LPV model using H₂/H∞ with pole placement objectives. When the control is applied to the non-linear system, the proposed algorithm predicts the response of the non-linear system to the control by determining if the current system state is located within the domain of attraction of the equilibrium. If the stability domain contains a convex combination of the two points, the control will aid the system in moving towards the equilibrium. The second contribution of this thesis is through the development and implementation of a pseudo non-linear evaluation of a power system as it moves through state space. A system linearization occurs first to compute a multi-objective state space controller. For each contingency definition, many variations of the power system example are created and assigned to the particular contingency class. The powerflow variations and contingency controls are combined to run sets of time series analysis in which the Lyapunov function is tracked over three time steps. This data is utilized for a classification analysis which identifies and classifies the data by the contingency type. The goal is that whenever a new event occurs on the system, real time data can be fed into the trained tree to provide a control for application to increase system damping. / Ph. D.

Cette thèse propose une nouvelle stratégie d'amortissement des oscillations de fréquence critiques par la modulation de l'injection rapide de puissances actives, qui ouvre la voie à l'utilisation d'actionneurs géographiquement dispersés, par exemple des ressources énergétiques distribuées (DERs), dans le contrôle des basses fréquences dynamique de l'angle du rotor du réseau électrique, qui comprend les oscillations interzones et les oscillations de fréquence transitoire. La méthode proposée intègre ces deux dynamiques différentes dans un cadre basé sur un système linéaire invariant dans le temps, dans lequel le contrôle de l'oscillation de fréquence transitoire est traduit en contrôle de la dynamique de mode commun du système. A cet effet, un examen attentif de la relation entre la variation transitoire de fréquence et la dynamique du mode commun est effectué; Les simulations montrent que le mode commun définit la forme d'un changement transitoire de faible signal de fréquence. La méthode de contrôle proposée vise à utiliser efficacement la réserve de marche limitée des DERs existants pour atténuer ces oscillations. Ceci est réalisé en découplant les actions de commande d'amortissement à différents endroits en utilisant les signaux d'oscillation du mode concerné comme commandes de puissance. Une base théorique pour cette commande de modulation découplée est fournie. Techniquement, les signaux d'oscillation modale souhaités sont filtrés en combinant linéairement les fréquences de l'ensemble du système, ce qui est déterminé par la technique (LQRSP). Avec la stratégie proposée, la modulation de chaque injection de puissance active peut être conçue efficacement en tenant compte de la limite de réponse et de la capacité de sortie en régime permanent du dispositif de support. Dans le cadre proposé, le signal de commande pour la commande de fréquence primaire est automatiquement déterminé dans une direction de commande (presque) optimale; des expériences montrent que ce signal a tendance à être la vitesse du système vue par le point d'injection de puissance. La commande modulante découplée a tendance à isoler les actions de commande pour les oscillations interzones et les oscillations de fréquence transitoire, ce qui atténue grandement les préoccupations concernant l'interaction entre la commande de ces deux types de dynamiques / This dissertation provides a novel wide-area control strategy for damping of critical frequency oscillations via modulation of fast active power injections, which paves the way for the utilization of large-scale geographically dispersed actuators, e.g., distributed energy resources (DERs), in the control of power system low-frequency rotor angle dynamics, this includes the inter-area oscillations and the transient frequency swing. The proposed method incorporates these two different dynamics into a linear time invariant (LTI) system based control framework, in which the control of the transient frequency swing is translated into the control of the system common mode dynamics. For this purpose, a careful examination of the relationship between the transient frequency swing and the common mode dynamics is carried out; extensive simulations show that the common mode defines the shape of a small-signal transient frequency swing. The proposed control method pursues an efficient utilization of the limited power reserve of existing DERs to mitigate these oscillations. This is accomplished by decoupling the damping control actions at different sites using the oscillation signals of the concerned mode as the power commands. A theoretical basis for this decoupled modulating control is provided. Technically, the desired sole modal oscillation signals are filtered out by linearly combining the system-wide frequencies, which is determined by the linear quadratic regulator based sparsity-promoting (LQRSP) technique. With the proposed strategy, the modulation of each active power injection can be effectively engineered considering the response limit and steady-state output capability of the supporting device. In the proposed control framework, the power command signal for the primary frequency control is determined in a (near) optimal control sense; experiments show that this signal tends to be the system speed seen by the power injection point. Importantly, the decoupled modulating control tends to isolate the control actions for the inter-area oscillations and the transient frequency swing, thereby greatly relieving the concern about the interaction between the control of these two types of dynamics.

A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ_s + λ_t <u>~</u>2Ï _q, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w_r<u>~</u>3w_q on the resonance λ_s + λ_t <u>~</u>2Ï _q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ_s + λ_t. / Master of Science

An electronic-hardware-based oscillogenic controller previously developed by P. K. Mercure was used as a model for translation into a software-based control algoritnm. The oscillogenic instrument, invented by P. R. Rony and P. K. Mercure, uses a feedback element (the oscillogenic controller) and a sensor component to produces a periodic signal yielding information about the instrument's sensor component. A control program that utilized the oscillogenic control algorithm was written in the Turbo Pascal programming language. An IBM PC with 640 kilobytes of read/write memory and with analog-to-digital and digital-to-analog converter boards running the control program performed as the controller component of an oscillogenic instrument. A sample time of 0.5 seconds was used for this study. The instrument's sensor component consisted of a forced air thermal system with air flow rates ranging from 8.4 to 3l kg/hr. The oscillogenic instrument's frequency was, over the limited range tested (0.032 to 0.062 hz), a linear indication of the thermal system's convective heat transfer coefficient, which varied from 230 to 400 W/m²-°C. / Master of Science

Intracranial electroencephalography (iEEG) provides superior diagnostic and research benefits over non-invasive EEG in terms of spatial resolution and the level of electrophysiological detail. Post-operative Computed Tomography (CT) scans provide the precision in electrode localization required for clinical purposes; however, to use this data for basic sleep research the challenge lies in identifying the precise locations of the implanted electrodes’ recording sites in terms of neuroanatomical regions as well as reliable scoring of their sleep data without the aid of facial electrodes. While existing methods can be combined to determine their exact locations in three-dimensional space, they fail to identify the functionally relevant gray matter areas that lie closest to them, especially if the points lie in the white matter. We introduce an iterative sphere inflation algorithm in conjunction with a unified pipeline to detect the exact as well as nearest regions of interest for these recording sites. Next, for sleep scoring purposes, we establish differences observed in alpha band activity between wakefulness and rapid eye movement (REM) sleep in frontal and temporal regions of iEEG patients. Lastly, we implement an automated sleep scoring method relying on the variations in alpha and delta bands power during sleep which can be applied to large sets of iEEG data recorded without accompanying electrooculogram (EOG) and electromyogram (EMG) electrodes available across labs for use in studies pertaining to neural dynamics during sleep. / M.S. / Patients with epilepsy (a neurological disorder characterized by seizures) who do not respond to medication often undergo invasive monitoring of their brains’ electrical activity using intracranial electroencephalography (iEEG). iEEG requires a surgery in which electrodes are inserted directly into the patient’s brain for better measurements. While they are monitored, these patients offer a unique opportunity for research studies that investigate the role of sleep in various learning, memory mechanisms and other health-related areas. This is because the direct contact of the electrodes with the brain tissue provides far superior quality and resolution of brain activity data in comparison to non-invasive cap-based EEG that healthy subjects wear over their scalp. However, in order to derive meaningful conclusions from these invasive recordings, we must first know the exact areas of the brain from which each site records the electrical data. We must then be able to identify which stage of sleep the patient is in at any given point in time, to be able to successfully correlate specific sleep stage-related activity with our research objectives; these patients often lack the facial electrodes used for standard sleep scoring procedures. To solve the first problem, we present an electrode localization method along with an algorithm to determine which neighboring regions contribute most to a given site’s recorded data. For the second problem, we first establish a difference in the behavior of alpha waves in the brain between wakefulness and rapid eye movement (REM) sleep. Lastly, we present an automated method to classify sleep data into different stages based on the variation in alpha waves and delta waves found during sleep.

An analytical and experimental investigation was conducted to determine the bond strength of liquid squeeze-films subjected to oscillating loads normal to the plane of the film. A mass with a flat circular bottom was placed on a rigid flat base covered with a thin layer of liquid. A sinusoidal vibration was then imparted to the base, and the acceleration level necessary to break the bond of the liquid film was measured under both atmospheric and vacuum ambient pressure conditions. The effects of a number of variables, in particular the mass, contact area, oscillatory frequency, fluid vapor pressure, viscosity, and surface tension, were considered. Results indicated that liquid squeeze-films can be used to support vibrating loads of considerable magnitude, even in a vacuum environment. The limiting factor on the bond strength was found to be the fluid cavitation pressure which can be negative. An analysis was developed based on Reynolds lubrication theory and predicted accurately the basic trends of the data. / Master of Science

Le but poursuivi dans cette thèse est la mesure du déplacement de la fréquence hyperfine du Rubidium 87 plongé dans l'azote moléculaire (N₂) à différentes densités, autour d'une température T₀ de 60 °C. Les résultats sont représentés par un développement en série, jusqu’au second degré en (T-T₀).Nous donnons la valeur des coefficients de déplacement de fréquence, définis comme les coefficients de ce développement normalisés à la densité de N₂. Nous avons observé une non linéarité du déplacement de fréquence en fonction de la densité de N₂, que nous interprétons comme découlant d'une erreur systématique sur la densité. Cette interprétation s'appuie sur une évaluation théorique de la non linéarité, et nous conduit à donner au coefficient de pression la valeur de la pente à l'origine de la courbe du déplacement de fréquence en fonction de la densité… / Québec Université Laval, Bibliothèque 2019

In this Thesis the theoretical understanding of oscillations in coronal structures is developed. In particular, coronal loops are modelled as magnetic slabs of plasma. The effect of introducing inhomogeneities on the frequency of oscillation is studied. Current observations indicate the existence of magnetohydrodynamic (MHD) modes in the corona, so there is room for improved modelling of these modes to understand the physical processes more completely. One application of the oscillations, on which this Thesis concentrates, is coronal seismology. Here, the improved theoretical models are applied to observed instances of coronal MHD waves with the aim of determining information regarding the medium in which these waves propagate. In Chapter two, the effect of gravity on the frequency of the longitudinal slow MHD mode is considered. A thin, vertical coronal slab of magnetised plasma, with gravity acting along the longitudinal axis of the slab is studied, and the effect on the frequency of oscillation for the uniform, stratified and structured cases is addressed. In particular, an isothermal plasma, a two-layer plasma and a plasma with a linear temperature profile are studied. Here, a thin coronal loop, with its footpoints embedded in the chromosphere-photosphere is modelled, and the effects introduced by both gravity and the structuring of density at the footpoint layers are studied. In this case, gravity increases the frequency of oscillation and causes amplification of the eigenfunctions by stratification. Furthermore, density enhancements at the footpoints cause a decrease in the oscillating frequency, and can inhibit wave propagation, depending on the parameter regime. In Chapter three, the effects introduced to the transverse fast MHD mode when gravity acts across a thin coronal slab of magnetised plasma are considered. This study concentrates on the modification of the frequency due to the dynamical effect of gravity in the equation of motion, neglecting the effect of stratification. Here, gravity causes a reduction of the oscillating frequency of the fundamental fast mode, and increases the lower cutoff frequency. In effect, for this configuration, gravity allows the transition between body and surface modes, in a slab geometry. It is found, in these two studies, that each harmonic is affected in a unique manner due to structuring or stratification of density. With this knowledge, in Chapter four, a new parameter is derived; P1/2P2, the ratio of the period of the fundamental harmonic of oscillation to twice the period of its first harmonic. This parameter is shown to be a measure of the longitudinal structuring of density along a coronal loop, and the departure of this ratio from unity can yield information regarding the lengthscales of the structure. This process is highlighted using the known observations, indicating that P1/2P2 may prove to be a useful diagnostic tool for coronal seismology. Finally, in Chapter five, outwardly propagating coronal slow MHD modes are observed and are used to infer coronal parameters. The possibility of using these oscillations to infer near-resolution lengthscales in coronal loops -- fine-scale strands -- is also discussed. TRACE observations are used to determine the average period, phase speed, detection length, amplitude and energy flux for the propagating slow MHD mode. The indication is that the source of these oscillations appears very localised in space, and the driver only acts for a few periods, suggesting the perturbations are driven by leaky p-modes (solar surface modes).

This study considers the effect, on plasma ion oscillations, of various lengths of discharge tubes as well as various cross sections of discharge tubes. Four different gases were used in generating the plasma. Gas pressure and discharge voltage and current were varied to obtain a large number of signals. A historical survey is given to familiarize the reader with the field. The experimental equipment and procedure used in obtaining data is given. An analysis of the data obtained is presented along with possible explanations for the observed phenomena. Suggestions for future study are made.