Stability analysis of nonlinear power electronics systems utilizing periodicity and introducing auxiliary state vector

Variable-structure piecewise-linear nonlinear dynamic feedback systems emerge frequently in power electronics. This paper is concerned with the stability analysis of these systems. Although it applies the usual well-known and widely used approach, namely, the eigenvalues of the Jacobian matrix of the Poincare/spl acute/ map function belonging to a fixed point of the system to ascertain the stability, this paper offers two contributions for simplification as well that utilize the periodicity of the structure or configuration sequence and apply an alternative simpler and faster method for the determination of the Jacobian matrix. The new method works with differences of state variables rather than derivatives of the Poincare/spl acute/ map function (PMF) and offers geometric interpretations for each step. The determination of the derivates of PMF is not needed. A key element is the introduction of the so-called auxiliary state vector for preserving the switching instant belonging to the periodic steady-state unchanged even after the small deviations of the system orbit around the fixed point. In addition, the application of the method is illustrated on a resonant dc-dc buck converter

Dynamics and stability issues of a single-inductor dual-switching DC-DC converter

A single-inductor two-input two-output power electronic dc–dc converter can be used to regulate two generally nonsymmetric positive and negative outputs by means of a pulsewidth modulation with a double voltage feedback. This paper studies the dynamic behavior of this system. First, the operation modes and the steady-state properties of the converter are addressed, and, then, a stability analysis that includes both the power stage and control parameters is carried out. Different bifurcations are determined from the averaged model and from the discrete-time model. The Routh–Hurwitz criterion is used to obtain the stability regions of the averaged (slow-scale) dynamics in the design parameter space, and a discrete-time approach is used to obtain more accurate results and to detect possible (fast-scale) subharmonic oscillations. Experimental measurements were taken from a system prototype to confirm the analytical results and numerical simulations. Some possible nonsmooth bifurcations due to the change in the switching patterns are also illustrated.Postprint (published version

Motor Drive Stabilization in its Chaotic Region

The paper is concerned with the stability analysisand the control of chaos in a permanent magnet dc drivesystem. The stability analysis is based on the eigenvalues ofthe Jacobian matrix of the Poincare Map Function (PMF).Using the auxiliary state vector, the Jacobian matrix can bedetermined without the derivation of the PMF. Acompensating ramp signal is used to avoid bifurcation. Theslope of the ramp signal is also determined by the auxiliarystate vector. The results are verified by computersimulations in the time domain

A Quantum Electrodynamical Foundation for Molecular Photonics

In this review the authors describe some of the advances in the quantum electrodynamical formulation of theory for molecular photonics. Earlier work has been extended and reformulated for application to real dispersive media—as reflected in the new treatment of refractive, dissipative, and resonance properties. Applications of the new theory have revealed new quantum optical features in two quite different aspects of the familiar process of second harmonic generation, one operating through local coherence within small particles and the other, a coherence between the quantum amplitudes for fundamental and harmonic excitation. Where the salient experiments have been performed, they exactly match the theoretical predictions

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Resonant Integrated Nonlinear Photonics for the Development of Compact and Stable Soliton Microcombs

Nonlinear nanophotonic devices are crucial building blocks of a fully integrated photonic system. They enable high-speed, high-throughput and customizable transfer of information, with applications ranging from biology to cutting edge quantum information technologies. A particularly important nanophotonics component is the micro-resonator. Not only do micro-resonators confine light and allow an effective increased length of interaction with a desired material platform, they are also highly compact. Through the amplification of light-matter interaction, nonlinear phenomena such as soliton comb generation, record breaking second and third harmonic generation as well as electro-optic frequency conversion have been observed on an integrated on-chip platform. The work presented here investigates the methods of integration and optimization of many such nonlinear micro-resonators with the ultimate goal of developing the first fully integrated and stabilized soliton microcomb

PERTURBATION METHODS IN NON-LINEAR SYSTEMS: Part I

This volume is an on-line reprint of the original book published 1972 by Springer-Verlag which was intended to provide a comprehensive treatment of contemporary developments in methods of perturbation for nonlinear systems of ordinary differential equations. In this respect, it appeared to be a unique work, with hundreds of citations. Even today is a basic reference in the approximate solution of non-linear differential equations, specially appearing in problems of Celestial Mechanics. The original goal was to describe perturbation techniques, discuss their advantages and limitations and give some examples. The approach was founded on analytical and numerical methods of nonlinear mechanics. Attention had been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique were outlined, but they only provided a foundation and were not the objective of the original book. Each chapter concluded with a detailed survey of the contemporary literature, supplemental information and more examples to complement the text, when necessary, for better comprehension

Design, Analysis and Fabrication of Silicon-Based Optical Materials and Photonic Crystal Devices

As the integration of electronic components grow so does the need for low power, low cost, and high-speed devices. These have resulted in an increased need for complementary metal-oxide semiconductor (CMOS) compatible materials and fabrication technique for novel structures as well as accurate models of the electromagnetic eld behavior in them. Recent advances in materials technology and fabrication techniques have made it feasible to consider silicon (Si)-based optical materials and photonic crystal (PhC) de- vices having physical dimensions of the order of the optical wavelength as the possible means to achieve these needs. Research has shown that light emission from Si is possible in low-dimensional state, i.e., Si-nanocrystals (Si-ncs). Furthermore, three-dimensional (3-D) control of light compatible with CMOS fabrication technology is required in order to fully integrate optical functionalities into the existing Si-technology. However, the di - culties in the fabrication of 3-D PhC waveguides have resulted in using two-dimensional (2-D) PhC structures. Finally, numerical simulations pro- vide a framework for quick low-cost feasibility studies and allow for design optimization before devices are fabricated. In this dissertation, we present our e orts along these directions. This dissertation addressed the method of obtaining high quantum e ciency from Si-ncs compatible with CMOS processing. Si ions were implanted into a fused-silica substrate (10 mm 10 mm 1 mmt) at room temperature in the Takasaki ion accelerators for advanced radiation application (TIARA) of the Japan Atomic Energy Agency. The implantation energy was 80 keV, and the implantation amount was 2 1017 ions/cm2. The Si-implanted sub- strate was cut into four pieces (5 mm 5 mm 1 mmt) using a diamond-wire saw, and the four pieces were annealed in ambient air at 1100, 1150, 1200, and 1250 oC for 25 min in a siliconit furnace. PL spectra were measured at room temperature with excitation using a He-Cd laser ( =325 nm). Ultra- violet (UV)-PL spectra having peaks around a wavelength of 370 nm were observed from all the samples. In our experiments, the UV-PL peak had a maximum intensity after annealing at 1250 oC, and the longer wavelength PL peak around 800 nm observed from the samples annealed at 1100 and 1150 oC disappeared by annealing above 1200 oC. The two PL peaks of the Si-ion-implanted samples may have originated from interface layers be- tween Si-ncs and SiO2 media. However, we successfully obtained only the UV-light emission peaks by selecting the proper annealing temperatures. UV-light-emitting materials are expected to be useful as light sources for next-generation optical-disk systems whose data densities are higher than Blu-ray Disk systems. Additionally, this dissertation addressed the numerical modeling of PhC de- vices. Accurate computations can provide a detailed understanding of the complex physical phenomena inherent in PhC devices. The nite-di erence time-domain (FDTD) method, which is widely used by many researchers around the Globe, is a powerful tool for modeling PhC devices. We devel- oped a modi ed and easy FDTD method based on a regular Cartesian Yee's lattice for calculating the dispersion diagram of triangular lattice PhCs. Our method uses the standard central-di erence equation, which is very easy to implement in any computing environment. The Bloch periodic boundary conditions are applied on the sides of the unit cell by translating the periodic boundary conditions to match with the directions of periodicity in the tri- angular lattice. Complete and accurate bandgap information is obtained by using this FDTD approach. Convergence, accuracy, and stability analysis were carried out, which ensures the reliability of this method. Numeri- cal results for 2-D transverse electric (TE) and transverse magnetic (TM) modes in triangular lattice PhCs are in good agreement with results from 2-D plane wave expansion method. The obtained results are in consistence with the reported ones. To ease the practical application of this method, clear explanations on the computer implementation are also provided. Finally, this dissertation addressed the use of CMOS-compatible fabrication method and 2-D periodic structures to realize the control of light in 3-D. In particular, we designed, analyzed and fabricated novel PhC waveguides utilizing Si-ion implantation and 2-D periodic structures. The transport of ions in matter (TRIM) prediction of implantation depth distribution pro le (1 1017 ions/cm2, 80 keV) shows the range of about 150 nm. Assuming the e ective refractive index of the Si-rich region to be 1.89 and by using FDTD method, the PhC design parameters based on the telecommunication wave- length ( =1.55 m) were obtained by varying the radius to lattice constant ratio (r=a) from 0.2 to 0.45. We analyzed both TE and TM mode prop- agation in triangular-lattice PhCs. The designed parameters were found to be a=664 nm and r=a=0.35. The PBG spanned from normalized fre- quency of 0.39 to 0.46 [2 c/a] in the TE-mode triangular lattice and the gap to midgap ratio was 0.16. The designed pattern was fabricated and the diameter, the period and the depth of air holes of the waveguide were estimated by atomic force microscopy (AFM) to be 464, 666 and 175 nm, respectively. Numerical results using FDTD characterization show that, straight line PhC waveguides can achieve 100% transmission, while the 60o bend showed 80% transmission owing to the dispersion mismatch at the two 60o bends. These results may serve as useful guides and components in future high- density photonic integrated circuits associated with optical communications, computing, and signal processing.学位記番号：工博甲40