Oscillators synchronization and its appilcations to engineering science

Abstract

Synchronization networks deal with the problem of synchronizing geographically dispersed oscillators or clocks, being part of countless Engineering applications, mainly in telecom systems. Specifically, synchronization networks have numerous applications in control systems, such as in servomotors angular speed control, in the Atomic Force Microscopy (AFM) problem and in active control of vibrating mechanical systems.In the AFM problem Phase-Locked Loops (PLLs) are used in order to generate the feedback signal to the AFM control system. In the Frequency-Modulated AFM (FM-AFM), the same feedback signal is used to generate topographical images of the sample.Similarly, in mechanical vibrating systems, the PLL can be used as a synthesizer by the control system, forcing the mechanical or electromechanical system to deliberately vibrate in pre-defined frequency. On the other hand, PLLs are also used for generating feedback signal for the control system, in order to build an Active Nonlinear Vibration Absorber.With the dynamically connected wireless networks grouth, such as the World-Wide-Web (WWW), complex networks topologies as the Mutually-Connected (MC) networks, regular networks, random connected networks, small-words, scale-free, and so on, are becoming an important research field. Seminal works from Watts and Strogatz - studing the USA electrical power distribution and the Caenorhabditis elegans neuronal network -, and from Barabási and Albert - investigating the WWW - had a huge impact, demonstrating the influence of the networks topology on diverse science areas, including Engineering. In the clock signal distribution problem, each node of the network is composed of a PLL that synchronizes a local oscillator to an incoming signal. The complex topology of the networks demand sophisticated control algorithms in order to assure the stability and performance. Besides, in most of the current applications, the PLLs are all digital or hybrid systems. According to the above, it is proposed as a research project : i) The development of the mathematical models of complex PLLs networks, considering digital and hybrid implementations; ii) The study of control designs in order to assure stability and performance. Similarly, as the PLLs have many applications in Control Systems, it is proposed iii) the Study of the PLLs networks to model problems such as the WWW, and biological systems, and iv) The study of applications in active nonlinear vibration control and in the AFM problem. (AU)