On low-pass reconstruction and stochastic modeling of PWM signals

Mathematical modeling of pulse width modulation (PWM) is given. For a band-limited, finite energy input signal, a PWM generation mechanism is investigated in linear and non-linear blocks separately. Following the common practice, a comparator block with a periodic reference signal is offered as a PWM generator and different sampling methodologies are discussed. For natural sampling, where the input signal is compared to the reference signal directly, lossless sampling conditions are derived. For a sawtooth reference signal, the convergence characteristics between lossless natural sampling and uniform sampling, where a zero-order hold (ZOH) block precedes the comparator, are analyzed. For a given input model, the convergence characteristics are tested with simulations and signal to absolute deviation energy for the difference between natural and uniform sampling is observed for different oversampling levels. Motivated by the separation of linear and non-linear blocks in PWM generation, a similar method for the analysis at the reconstruction end is pursued. In this pursuit, continuous-time low-pass filtering, preceded by oversampling, is analyzed as a linear suboptimal reconstruction mechanism from a PWM signal. Observing the mapping between input samples and pulse widths, an infinite energy, input-independent, structural component of a PWM signal is revealed. Manipulating the linear nature of the low-pass filtering, and equivalent model is proposed to analyze the finite energy, input-dependent component of the PWM signal separately. Frequency domain analysis for fixed-edge and double-edge PWM orientations and their corresponding input-dependent components are given. Using the frequency domain representations, performance bounds for low-pass reconstruction of a band-limited, finite energy input signal are derived and fundamental trade-offs between generator complexity and distortion attenuation capacity are revealed. Stochastic modeling of PWM processes for independent identically distributed (i.i.d.) pulse widths is discussed. For a fixed starting model of a PWM process, the violation of wide sense stationarity (WSS) is observed. By introducing a randomized starting point, independent of the pulse widths and uniformly distributed over a symbol interval, a WSS PWM process is constructed and its stochastic characteristics are analyzed. For i.i.d. uniform pulse widths, second moments are simulated revealing a smoothing effect in the double-edge PWM construction, consistent to the frequency domain analysis

Measurements, Models, Systems and Design

531 s.

Regulatory motif discovery using a population clustering evolutionary algorithm

This paper describes a novel evolutionary algorithm for regulatory motif discovery in DNA promoter sequences. The algorithm uses data clustering to logically distribute the evolving population across the search space. Mating then takes place within local regions of the population, promoting overall solution diversity and encouraging discovery of multiple solutions. Experiments using synthetic data sets have demonstrated the algorithm's capacity to find position frequency matrix models of known regulatory motifs in relatively long promoter sequences. These experiments have also shown the algorithm's ability to maintain diversity during search and discover multiple motifs within a single population. The utility of the algorithm for discovering motifs in real biological data is demonstrated by its ability to find meaningful motifs within muscle-specific regulatory sequences

Parallel structure general repetitive controller for general grid-connected PWM converters

This study investigates parallel structure general repetitive control (PSGRC) and its error convergence rate by using exponential function properties. PSGRC offers a general repetitive control solution for power converters to mitigate power harmonics distortions. PSGRC with appropriate settings will lead to various RCs with various error convergence rates at interested harmonic frequencies, e.g. conventional RC, dual-model RC, and odd harmonics RC. As application examples, PSGRC was applied into general grid-connected pulse-width-modulation (PWM) converter systems. Experimental results show the effectiveness and advantages of PSGRC: three/single-phase grid-connected PWM converters can achieve zero-error current tracking and very fast current error convergence rate upon demand

Development of Hybrid PS-FW GMPPT Algorithm for improving PV System Performance Under Partial Shading Conditions

A global maximum power point tracking (MPPT) algorithm hybrid based on Particle Swarm Fireworks (PS-FW) algorithm is proposed which is formed with Particle Swarm Optimization and Fireworks Algorithm. The algorithm tracks the global maximum power point (MPP) when conventional MPPT methods fail due to occurrence of partial shading conditions. With the applied strategies and operators, PS-FW algorithm obtains superior performances verified under simulation and experimental setup with multiple cases of shading patterns

Contributions on spectral control for the asymmetrical full bridge multilevel inverter

Las topologías de circuitos inversores multinivel pueden trabajar a tensiones y potencias mayores que las alcanzadas por convertidores convencionales de dos niveles. Además, la conversión multinivel reduce la distorsión armónica de las variables de salida y en algunos casos, a pesar del aumento de elementos de conmutación, también reduce las pérdidas de conversión al incrementarse el número de niveles. La reducción de distorsión alcanzada por el número de niveles puede aprovecharse para reducir las pérdidas de conmutación disminuyendo la frecuencia de las señales portadoras. Para reducir aún más esta frecuencia sin degradar el espectro, nosotros controlamos las pendientes de las portadoras triangulares. Primero se han desarrollado dos modelos analíticos para predecir el espectro del voltage de salida, dependiendo de: el índice de modulación MA, la razón de distribución de voltaje K de las fuentes de alimentación , y las cuatro pendientes de las portadoras{r1, r2, r3, r4}. El primer modelo considera el Muestreo Natural y se basa en Series Dobles de Fourier (SDF) mientras que el segundo modelo, utiliza la Serie Sencilla de Fourier (SSF) introduciendo el concepto de Muestreo Pseudo-Natural, una aproximación digital de la modulación natural. Ambos modelos son programados en Matlab, verificados con Pspice y validados con un prototipo experimental que contiene un modulador digital implementado con DSP.La concordancia entre las modulaciones natural y pseudo-natural, asi como entre sus respectivos modelos, es aprovechada por un algorítmo genético (AG) donde la THD es la función costo a reducir. Después de varios ensayos y de sintonizar el AG, se genera una matriz que contiene conjuntos de portadoras optimizadas dentro un rango específico de las variables {MA,K} y es probada con un segundo prototipo en lazo cerrado. Un lazo lento digital modifica las portadoras creadas por un dsPIC en modulaciones PWM; estas son demoduladas y sus amplitudes corregidas por un lazo de acción anticipada. Estas portadoras se comparan con una referencia sinusoidal que a su vez es modificada por variables de estado, generando finalmente la modulación multinivel en lazo cerrado. Los resultados finales demuestran la fiabilidad de la reducción de armónicos usando la programación de las pendientes de las portadoras. Palabras claves: inversor multinivel, PWM, distorsión armónica, modelo espectral, pendiente de portadora, conjunto de portadoras, distribución de niveles, Serie Doble de Fourier, Serie Simple de Fourier, muestreo natural, muestreo regular, muestreo pseudo-natural , Algoritmos Genéticos.Multilevel inverter (MI) topologies can work at higher voltage and higher power than conventional two-level converters. In addition, multilevel conversion reduces the output variables harmonic distortion and, sometimes, in spite of the devices-count increment, the conversion losses can also decrease by increasing the number of levels. The harmonic distortion reduction achieved by increasing the number of levels, can be used to further reducing the switching losses by decreasing the inverter carrier frequencies. To reduce even more the switching frequency without degrading output spectrum, we control the triangular carrier waveforms slopes. First, to achieve this target, two analytical models have been created in order to predict the inverter output voltage spectrum, depending on diverse parameters: the amplitude modulation index MA, the voltage distribution K of the inverter input sources, and the four carrier slopes {r1, r2, r3, r4}. The first model considers Natural Sampling and is based on Double Fourier Series (DFS) whereas the second model based on Simple Fourier Series (SFS), introduces the concept of Pseudo-Natural Sampling, as a digital approximation of the natural modulation. Both models are programmed in Matlab, verified with Pspice simulations and validated with a first experimental prototype with a DSP digital modulator.The good agreement between natural and pseudo-natural modulations, as well as their respective DFS and SFS models, is exploited by a Genetic Algorithm (GA) application where THD is the cost function to minimize. After testing and properly tuning the GA, a framework matrix containing the optimized carriers set for a specific range of variables {MA,K} is generated and then, tested with a second, closed-loop prototype. A slow digital loop modifies the carrier slopes created by dsPIC microcontroller as PWM modulations, whose amplitude, once demodulated, are affected by a feed-forward loop. These carriers, compared with a sinusoidal reference, state-feedback modified, generate finally the closed-loop multilevel modulation. The final results demonstrates the feasibility of harmonic reduction by means of carrier slopes programming. Keywords: multilevel inverter, PWM, harmonic distortion, spectral modeling, carrier slope, carriers set, level distribution, Double Fourier Series, Simple Fourier Series, natural sampling, regular sampling, pseudo-natural sampling, Genetic Algorithms

Error minimising gradients for improving cerebellar model articulation controller performance

In motion control applications where the desired trajectory velocity exceeds an actuator’s maximum velocity limitations, large position errors will occur between the desired and actual trajectory responses. In these situations standard control approaches cannot predict the output saturation of the actuator and thus the associated error summation cannot be minimised.An adaptive feedforward control solution such as the Cerebellar Model Articulation Controller (CMAC) is able to provide an inherent level of prediction for these situations, moving the system output in the direction of the excessive desired velocity before actuator saturation occurs. However the pre-empting level of a CMAC is not adaptive, and thus the optimal point in time to start moving the system output in the direction of the excessive desired velocity remains unsolved. While the CMAC can adaptively minimise an actuator’s position error, the minimisation of the summation of error over time created by the divergence of the desired and actual trajectory responses requires an additional adaptive level of control.This thesis presents an improved method of training CMACs to minimise the summation of error over time created when the desired trajectory velocity exceeds the actuator’s maximum velocity limitations. This improved method called the Error Minimising Gradient Controller (EMGC) is able to adaptively modify a CMAC’s training signal so that the CMAC will start to move the output of the system in the direction of the excessive desired velocity with an optimised pre-empting level.The EMGC was originally created to minimise the loss of linguistic information conveyed through an actuated series of concatenated hand sign gestures reproducing deafblind sign language. The EMGC concept however is able to be implemented on any system where the error summation associated with excessive desired velocities needs to be minimised, with the EMGC producing an improved output approximation over using a CMAC alone.In this thesis, the EMGC was tested and benchmarked against a feedforward / feedback combined controller using a CMAC and PID controller. The EMGC was tested on an air-muscle actuator for a variety of situations comprising of a position discontinuity in a continuous desired trajectory. Tested situations included various discontinuity magnitudes together with varying approach and departure gradient profiles.Testing demonstrated that the addition of an EMGC can reduce a situation’s error summation magnitude if the base CMAC controller has not already provided a prior enough pre-empting output in the direction of the situation. The addition of an EMGC to a CMAC produces an improved approximation of reproduced motion trajectories, not only minimising position error for a single sampling instance, but also over time for periodic signals