Identification of the dynamic characteristics of nonlinear structures

Imperial Users onl

Nonlinear dynamics and applications of MEMS and NEMS resonators.

Rich nonlinear behaviours have been observed in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) resonators. This dissertation has performed a systematic study of nonlinear dynamics in various MEMS and NEMS resonators that appear to be single, two coupled, arrayed, parametric driven and coupled with multiple-fields, with the aim of exploring novel applications. New study on dynamic performance of a single carbon nanotube resonator taking account of the surface induced initial stress has been performed. It is found that the initial stress causes the jumping points, the whirling and chaotic motions to appear at higher driving forces. Chaotic synchronization of two identical MEMS resonators has been theoretically achieved using Open-Plus-Closed-Loop (OPCL) method, and the coupled resonating system is designed as a mass detector that is believed to possess high resistance to noise. The idea of chaotic synchronization is then popularized into wireless sensor networks for the purpose of achieving secure communication. The arising of intrinsic localised mode has been studied in microelectromechanical resonators array that is designed intentionally for an energy harvester, which could potentially be used to achieve high/concentrated energy output. Duffing resonators with negative and positive spring constants can exhibit chaotic behaviour. Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos. Based on the principle of nanomechanical transistor and quantum shuttle mechanism, a high sensitive mass sensor that consists of two mechanically coupled NEMS resonators has been postulated, and the mass sensor which can be realized in large-scale has also been investigated and verified. Furthermore, an novel transistor that couples three physical fields at the same time, i.e. mechanical, optical and electrical, has been designed, and the coupled opto-electro-mechanical simulation has been performed. It is shown from the dynamic analysis that the stable working range of the transistor is much wider than that of the optical wave inside the cavity

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition

Dynamics of resonant tunneling diode optoelectronic oscillators

Tese de dout., Física, Faculdade de Ciências e Tecnologia, Univ. do Algarve, 2012The nonlinear dynamics of optoelectronic integrated circuit (OEIC) oscillators comprising semiconductor resonant tunneling diode (RTD) nanoelectronic quantum devices has been investigated. The RTD devices used in this study oscillate in the microwave band frequency due to the negative di erential conductance (NDC) of their nonlinear current voltage characteristics, which is preserved in the optoelectronic circuit. The aim was to study RTD circuits incorporating laser diodes and photo-detectors to obtain novel dynamical operation regimes in both electrical and optical domains taking advantage of RTD's NDC characteristic. Experimental implementation and characterization of RTD-OEICs was realized in parallel with the development of computational numerical models. The numerical models were based on ordinary and delay di erential equations consisting of a Li enard's RTD oscillator and laser diode single mode rate equations that allowed the analysis of the dynamics of RTD-OEICs. In this work, several regimes of operation are demonstrated, both experimentally and numerically, including generation of voltage controlled microwave oscillations and synchronization to optical and electrical external signals providing stable and low phase noise output signals, and generation of complex oscillations that are characteristic of high-dimensional chaos. Optoelectronic integrated circuits using RTD oscillators are interesting alternatives for more e cient synchronization, generation of stable and low phase noise microwave signals, electrical/optical conversion, and for new ways of optoelectronic chaos generation. This can lead to simpli cation of communication systems by boosting circuits speed while reducing the power and number of components. The applications of RTD-OEICs include operation as optoelectronic voltage controlled oscillators in clock recovery circuit systems, in wireless-photonics communication systems, or in secure communication systems using chaotic waveforms

Hilbert-Huang Transform: biosignal analysis and practical implementation

Any system, however trivial, is subjected to data analysis on the signals it produces. Over the last 50 years the influx of new techniques and expansions of older ones have allowed a number of new applications, in a variety of fields, to be analysed and to some degree understood. One of the industries that is benefiting from this growth is the medical field and has been further progressed with the growth of interdisciplinary collaboration. From a signal processing perspective, the challenge comes from the complex and sometimes chaotic nature of the signals that we measure from the body, such as those from the brain and to some degree the heart. In this work we will make a contribution to dealing with such systems, in the form of a recent time-frequency data analysis method, the Hilbert-Huang Transform (HHT), and extensions to it. This thesis presents an analysis of the state of the art in seizure and heart arrhythmia detection and prediction methods. We then present a novel real-time implementation of the algorithm both in software and hardware and the motivations for doing so. First, we present our software implementation, encompassing realtime capabilities and identifying elements that need to be considered for practical use. We then translated this software into hardware to aid real-time implementation and integration. With these implementations in place we apply the HHT method to the topic of epilepsy (seizures) and additionally make contributions to heart arrhythmias and neonate brain dynamics. We use the HHT and some additional algorithms to quantify features associated with each application for detection and prediction. We also quantify significance of activity in such a way as to merge prediction and detection into one framework. Finally, we assess the real-time capabilities of our methods for practical use as a biosignal analysis tool