Equações de diferenças e aplicações

Sistemas dinâmicos são todos os sistemas que evoluem no tempo, qualquer que seja a sua natureza, isto é, sistemas fisícos, biológicos, químicos, sociais, económicos, etc.. Esta evoluçãoo pode ser descrita (modelada) por equaçõess de diferenças, uma vez que esse tempo é muitas vezes medido em intervalos discretos. As equações de diferenças aparecem também quando se estuda métodos para a discretização de equações diferenciais. Assim, este trabalho tem por principal objectivo estudar as soluções de alguns tipos de equações de diferenças. Para isso, começa-se por introduzir o conceito de diferença e a sua relação com as equações de diferenças. Em seguida, determina-se a solução geral das todas as equações lineares de primeira ordem, bem como o estudo do seu comportamento assimptótico. Prossegue-se, desenvolvendo as principais técnicas para determinar a soluçãoo de equações de diferenças lineares de qualquer ordem. Em particular, estudam-se as equações com coeficientes constantes. Depois de se desenvolver a teoria básica dos sistemas lineares de equações de diferenças, particulariza-se aos sistemas lineares autónomos,com apenas duas variáveis dependentes, fazendo assim o estudo do comportamento das soluções no plano de fases. Por fim, utiliza-se a transformada Z como uma ferramenta que permite resolver equações de diferenças, em especial as equações de tipo convolução.

Uma fundamentação matemática para processamento digital de sinais intervalares

This work deals with a mathematical fundament for digital signal processing under point view of interval mathematics. Intend treat the open problem of precision and repesention of data in digital systems, with a intertval version of signals representation. Signals processing is a rich and complex area, therefore, this work makes a cutting with focus in systems linear invariant in the time. A vast literature in the area exists, but, some concepts in interval mathematics need to be redefined or to be elaborated for the construction of a solid theory of interval signal processing. We will construct a basic fundaments for signal processing in the interval version, such as basic properties linearity, stability, causality, a version to intervalar of linear systems e its properties. They will be presented interval versions of the convolution and the Z-transform. Will be made analysis of convergences of systems using interval Z-transform , a essentially interval distance, interval complex numbers , application in a interval filter.

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Encyclopedia contributions : entries S-Z in Oxford Companion to Australian Gardens

Shelton, E.M. (p.548); Sherwood Arboretum (p.550); Soutter, William (pp.563-4); Styles (pp.575-6); Summer-House (579-580); Trapnell, W.G. (p.602); Tropical Gardens (pp.604-5);Verandah Gardening (p.614); Wickham Park (p.642); Wijaya, Made (p.642); Williams, George (p.644); Williams Keith A (p.644).

Book review: ‘Anterior Eye Disease and Therapeutics A-Z' [2nd ed.] Edition, by A. Bruce and M. Loughnan. Churchill Livingstone (Elsevier), Edinburgh 2011

With the ever-increasing emphasis on ocular disease recognition in the practice of optometry and especially anterior eye disease management and therapeutics, any book addressing such issues is bound to have a captive audience. This second edition of Anterior Eye Disease and Therapeutics A–Z provides a succinct yet comprehensive coverage of this topic.

Using pulse transit delay in Z-scan to discriminate between excited-state absorption and other nonlinear processes in ZnO nanocones

We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.

Five-level Z-source diode-clamped inverter

This study proposes a five-level Z-source diode-clamped inverter designed with two intermediate Z-source networks connected between the dc input sources and rear-end inverter circuitry. By partially shorting the Z-source networks, new operating states not previously reported for two-level Z-source inverter are introduced here for operating the proposed inverter with voltage buck-boost energy conversion ability and five-level phase voltage switching. These characteristic features are in fact always ensured at the inverter terminal output by simply adopting a properly designed carrier modulation scheme, which always inserts two partial shoot-through states per half carrier cycle for smooth balanced operation. Theoretical findings and practical issues identified are eventually verified by constructing a scaled down laboratory prototype for testing.

Z-source-inverter-based flexible distributed generation system solution for grid power quality improvement

Distributed generation (DG) systems are usually connected to the grid using power electronic converters. Power delivered from such DG sources depends on factors like energy availability and load demand. The converters used in power conversion do not operate with their full capacity all the time. The unused or remaining capacity of the converters could be used to provide some ancillary functions like harmonic and unbalance mitigation of the power distribution system. As some of these DG sources have wide operating ranges, they need special power converters for grid interfacing. Being a single-stage buck-boost inverter, recently proposed Z-source inverter (ZSI) is a good candidate for future DG systems. This paper presents a controller design for a ZSI-based DG system to improve power quality of distribution systems. The proposed control method is tested with simulation results obtained using Matlab/Simulink/PLECS and subsequently it is experimentally validated using a laboratory prototype.

Performance evaluation of three-level Z-source inverters under semiconductor-failure conditions

This paper evaluates and proposes various compensation methods for three-level Z-source inverters under semiconductor-failure conditions. Unlike the fault-tolerant techniques used in traditional three-level inverters, where either an extra phase-leg or collective switching states are used, the proposed methods for three-level Z-source inverters simply reconfigure their relevant gating signals so as to ride-through the failed semiconductor conditions smoothly without any significant decrease in their ac-output quality and amplitude. These features are partly attributed to the inherent boost characteristics of a Z-source inverter, in addition to its usual voltage-buck operation. By focusing on specific types of three-level Z-source inverters, it can also be shown that, for the dual Z-source inverters, a unique feature accompanying it is its extra ability to force common-mode voltage to zero even under semiconductor-failure conditions. For verifying these described performance features, PLECS simulation and experimental testing were performed with some results captured and shown in a later section for visual confirmation.

Modulation and control of three-phase paralleled Z-source inverters for distributed generation applications

This paper presents a modulation and controller design method for paralleled Z-source inverter systems applicable for alternative energy sources like solar cells, fuel cells, or variablespeed wind turbines with front-end diode rectifiers. A modulation scheme is designed based on simple shoot-through principle with interleaved carriers to give enhanced ripple reduction in the system. Subsequently, a control method is proposed to equalize the amount of power injected by the inverters in the grid-connected mode and also to provide reliable supply to sensitive loads onsite in the islanding mode. The modulation and controlling methods are proposed to have modular independence so that redundancy, maintainability, and improved reliability of supply can be achieved. The performance of the proposed paralleled Z-source inverter configuration is validated with simulations carried out using Matlab/Simulink/Powersim. Moreover, a prototype is built in the laboratory to obtain the experimental verifications.

Evaluation of resonant damping techniques for Z-source current-type inverter

For the renewable energy sources whose outputs vary continuously, a Z-source current-type inverter has been proposed as a possible buck-boost alternative for grid-interfacing. With a unique X-shaped LC network connected between its dc power source and inverter topology, Z-source current-type inverter is however expected to suffer from compounded resonant complications in addition to those associated with its second-order output filter. To improve its damping performance, this paper proposes the careful integration of Posicast or three-step compensators before the inverter pulse-width modulator for damping triggered resonant oscillations. In total, two compensators are needed for wave-shaping the inverter boost factor and modulation ratio, and they can conveniently be implemented using first-in first-out stacks and embedded timers of modern digital signal processors widely used in motion control applications. Both techniques are found to damp resonance of ac filter well, but for cases of transiting from current-buck to boost state, three-step technique is less effective due to the sudden intermediate discharging interval introduced by its non-monotonic stepping (unlike the monotonic stepping of Posicast damping). These findings have been confirmed both in simulations and experiments using an implemented laboratory prototype.

Dual Z-source inverter with three-level reduced common mode switching

This paper presents the design of a dual Z-source inverter that can be used with either a single dc source or two isolated dc sources. Unlike traditional inverters, the integration of a properly designed Z-source network and semiconductor switches to the proposed dual inverter allows buck-boost power conversion to be performed over a wide modulation range with three-level output waveforms generated. The connection of an additional transformer to the inverter ac output also allows all generic wye- or delta-connected loads with three-wire or four-wire configuration to be supplied by the inverter. Modulation-wise, the dual inverter can be controlled using a carefully designed carrier-based pulse-width modulation (PWM) scheme that always will ensure balanced voltage boosting of the Z-source network, while simultaneously achieving reduced common-mode switching. Because of the omission of dead-time delays in the dual inverter PWM scheme, its switched common-mode voltage can be completely eliminated, unlike in traditional inverters where narrow common-mode spikes are still generated. Under semiconductor failure conditions, the presented PWM schemes can easily be modified to allow the inverter to operate without interruption and for cases where two isolated sources are used, zero common-mode voltage can still be ensured. These theoretical findings together with the inverter practicality have been confirmed both in simulations using PSIM with Matlab/Simulink coupler and experimentally using a laboratory implemented inverter prototype.