Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index

Very recently (Banerjee et al. in Astrophys. Space, doi:1007/s10509-011-0836-1, 2011) the statistics of geomagnetic Disturbance storm (Dst) index have been addressed, and the conclusion from this analysis suggests that the underlying dynamical process can be modeled as a fractional Brownian motion with persistent long-range correlations. In this comment we expose several misconceptions and flaws in the statistical analysis of that work. On the basis of these arguments, the former conclusion should be revisited.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Robust control of underactuated wheeled mobile manipulators using GPI disturbance observers

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

Contribución al diseño de lazos de realimentación electrónica para microsistemas electromecánicos (MEMS) resonantes: ruido de fase generado en lazos osciladores por sus realimentaciones

En 1966, D. B. Leeson publicó el artículo titulado “A simple model of feedback oscillator noise spectrum” en el que, mediante una ecuación obtenida de forma heurística y basada en parámetros conocidos de los osciladores, proponía un modelo para estimar el espectro de potencia que cuantifica el Ruido de Fase de estos osciladores. Este Ruido de Fase pone de manifiesto las fluctuaciones aleatorias que se producen en la fase de la señal de salida de cualquier oscilador de frecuencia f_0. Desde entonces, los adelantos tecnológicos han permitido grandes progresos en cuanto a la medida del Ruido de Fase, llegando a encontrar una estrecha “zona plana”, alrededor de f_0, conocida con el nombre de Ensanchamiento de Línea (EL) que Leeson no llegó a observar y que su modelo empírico no recogía. Paralelamente han ido surgiendo teorías que han tratado de explicar el Ruido de Fase con mayor o menor éxito. En esta Tesis se propone una nueva teoría para explicar el espectro de potencia del Ruido de Fase de un oscilador realimentado y basado en resonador L-C (Inductancia-Capacidad). Al igual que otras teorías, la nuestra también relaciona el Ruido de Fase del oscilador con el ruido térmico del circuito que lo implementa pero, a diferencia de aquellas, nuestra teoría se basa en un Modelo Complejo de ruido eléctrico que considera tanto las Fluctuaciones de energía eléctrica asociadas a la susceptancia capacitiva del resonador como las Disipaciones de energía eléctrica asociadas a su inevitable conductancia G=1⁄R, que dan cuenta del contacto térmico entre el resonador y el entorno térmico que le rodea. En concreto, la nueva teoría que proponemos explica tanto la parte del espectro del Ruido de Fase centrada alrededor de la frecuencia portadora f_0 que hemos llamado EL y su posterior caída proporcional a 〖∆f〗^(-2) al alejarnos de f_0, como la zona plana o pedestal que aparece en el espectro de Ruido de Fase lejos de esa f_0. Además, al saber cuantificar el EL y su origen, podemos explicar con facilidad la aparición de zonas del espectro de Ruido de Fase con caída 〖∆f〗^(-3) cercanas a la portadora y que provienen del denominado “exceso de ruido 1⁄f” de dispositivos de Estado Sólido y del ruido “flicker” de espectro 1⁄f^β (0,8≤β≤1,2) que aparece en dispositivos de vacío como las válvulas termoiónicas. Habiendo mostrado que una parte del Ruido de Fase de osciladores L-C realimentados que hemos denominado Ruido de Fase Térmico, se debe al ruido eléctrico de origen térmico de la electrónica que forma ese oscilador, proponemos en esta Tesis una nueva fuente de Ruido de Fase que hemos llamado Ruido de Fase Técnico, que se añadirá al Térmico y que aparecerá cuando el desfase del lazo a la frecuencia de resonancia f_0 del resonador no sea 0° o múltiplo entero de 360° (Condición Barkhausen de Fase, CBF). En estos casos, la modulación aleatoria de ganancia de lazo que realiza el Control Automático de Amplitud en su lucha contra ruidos que traten de variar la amplitud de la señal oscilante del lazo, producirá a su vez una modulación aleatoria de la frecuencia de tal señal que se observará como más Ruido de Fase añadido al Térmico. Para dar una prueba empírica sobre la existencia de esta nueva fuente de Ruido de Fase, se diseñó y construyó un oscilador en torno a un resonador mecánico “grande” para tener un Ruido de Fase Térmico despreciable a efectos prácticos. En este oscilador se midió su Ruido de Fase Técnico tanto en función del valor del desfase añadido al lazo de realimentación para apartarlo de su CBF, como en función de la perturbación de amplitud inyectada para mostrar sin ambigüedad la aparición de este Ruido de Fase Técnico cuando el lazo tiene este fallo técnico: que no cumple la Condición Barkhausen de Fase a la frecuencia de resonancia f_0 del resonador, por lo que oscila a otra frecuencia. ABSTRACT In 1966, D. B. Leeson published the article titled “A simple model of feedback oscillator noise spectrum” in which, by means of an equation obtained heuristically and based on known parameters of the oscillators, a model was proposed to estimate the power spectrum that quantifies the Phase Noise of these oscillators. This Phase Noise reveals the random fluctuations that are produced in the phase of the output signal from any oscillator of frequencyf_0. Since then, technological advances have allowed significant progress regarding the measurement of Phase Noise. This way, the narrow flat region that has been found around f_(0 ), is known as Line Widening (LW). This region that Leeson could not detect at that time does not appear in his empirical model. After Leeson’s work, different theories have appeared trying to explain the Phase Noise of oscillators. This Thesis proposes a new theory that explains the Phase Noise power spectrum of a feedback oscillator around a resonator L-C (Inductance-Capacity). Like other theories, ours also relates the oscillator Phase Noise to the thermal noise of the feedback circuitry, but departing from them, our theory uses a new, Complex Model for electrical noise that considers both Fluctuations of electrical energy associated with the capacitive susceptance of the resonator and Dissipations of electrical energy associated with its unavoidable conductance G=1/R, which accounts for the thermal contact between the resonator and its surrounding environment (thermal bath). More specifically, the new theory we propose explains both the Phase Noise region of the spectrum centered at the carrier frequency f_0 that we have called LW and shows a region falling as 〖∆f〗^(-2) as we depart from f_0, and the flat zone or pedestal that appears in the Phase Noise spectrum far from f_0. Being able to quantify the LW and its origin, we can easily explain the appearance of Phase Noise spectrum zones with 〖∆f〗^(-3) slope near the carrier that come from the so called “1/f excess noise” in Solid-State devices and “flicker noise” with 1⁄f^β (0,8≤β≤1,2) spectrum that appears in vacuum devices such as thermoionic valves. Having shown that the part of the Phase Noise of L-C oscillators that we have called Thermal Phase Noise is due to the electrical noise of the electronics used in the oscillator, this Thesis can propose a new source of Phase Noise that we have called Technical Phase Noise, which will appear when the loop phase shift to the resonance frequency f_0 is not 0° or an integer multiple of 360° (Barkhausen Phase Condition, BPC). This Phase Noise that will add to the Thermal one, comes from the random modulation of the loop gain carried out by the Amplitude Automatic Control fighting against noises trying to change the amplitude of the oscillating signal in the loop. In this case, the BPC failure gives rise to a random modulation of the frequency of the output signal that will be observed as more Phase Noise added to the Thermal one. To give an empirical proof on the existence of this new source of Phase Noise, an oscillator was designed and constructed around a “big” mechanical resonator whose Thermal Phase Noise is negligible for practical effects. The Technical Phase Noise of this oscillator has been measured with regard to the phase lag added to the feedback loop to separate it from its BPC, and with regard to the amplitude disturbance injected to show without ambiguity the appearance of this Technical Phase Noise that appears when the loop has this technical failure: that it does not fulfill the Barkhausen Phase Condition at f_0, the resonance frequency of the resonator and therefore it is oscillating at a frequency other than f_0.

A Wireless Charging System Applying Phase-Shift and Amplitude Control to Maximize Efficiency and Extractable Power

Wireless power transfer (WPT) is an emerging technology with an increasing number of potential applications to transfer power from a transmitter to a mobile receiver over a relatively large air gap. However, its widespread application is hampered due to the relatively low efficiency of current Wireless power transfer (WPT) systems. This study presents a concept to maximize the efficiency as well as to increase the amount of extractable power of a WPT system operating in nonresonant operation. The proposed method is based on actively modifying the equivalent secondary-side load impedance by controlling the phase-shift of the active rectifier and its output voltage level. The presented hardware prototype represents a complete wireless charging system, including a dc-dc converter which is used to charge a battery at the output of the system. Experimental results are shown for the proposed concept in comparison to a conventional synchronous rectification approach. The presented optimization method clearly outperforms state-of-the-art solutions in terms of efficiency and extractable power.