Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.

Desenvolvimento de um estimador de estado para sistemas de distribuição de energia elétrica desbalanceados

Pós-graduação em Engenharia Elétrica - FEIS

Desenvolvimento de um sistema de gerenciamento de energia (EMS - Energy Management System) para a rede elétrica inteligente (Smart Grid)

Pós-graduação em Engenharia Elétrica - FEIS

Study of the effect of biodiesel fuel on passive oxidation in a catalyzed particulate filter

A 2007 Cummins ISL 8.9L direct-injection common rail diesel engine rated at 272 kW (365 hp) and 317 kW (425 hp) was used to load the filter to 2.2 g/L and passively oxidize particulate matter (PM) within an aftertreatment system consisting of a diesel oxidation catalyst (DOC) and catalyzed particulate filter (CPF). The tests conducted with the engine rated at 365 hp used a 2007 DOC and CPF. The tests conducted with the engine rated at 425 hp used a 2010 DOC and 2007 CPF. Understanding the passive NO2 oxidation kinetics of PM within the CPF allows for reducing the frequency of active regenerations (hydrocarbon injection) and the associated fuel penalties. Modeling the passive oxidation of accumulated PM in the CPF will lead to creating accurate state estimation strategies. The MTU 1-D CPF model will be used to simulate data collected from this study to examine differences in the PM oxidation kinetics when soy methyl ester (SME) biodiesel is used as the source of fuel for the engine, and when the engine is operated at a higher power rating. A test procedure developed by Hutton et al. [1, 2] was modified to improve the ability to model the experimental data and provide additional insight into passively oxidized PM in a partially regenerated CPF. A test procedure was developed to allow PM oxidation rates by NO2 to be determined from engine test cell data. An experimental matrix consisting of CPF inlet temperatures from 250 to 450 °C with varying NOX/PM from 25 to 583and NO2/PM ratios from 5 to 240 was used. SME biodiesel was volumetrically blended with ULSD in 10% (B10) and 20% (B20) portions. This blended fuel was then used to evaluate the effect of biodiesel on passive oxidation rates. Four tests were performed with B10 and four tests with B20. Gathering data to determine the effect of fuel type (ULSD and biodiesel blends) on PM oxidation is the primary goal. The engine used for this testing was then configured to a higher power rating and one of the tests planned was performed. Additional testing is scheduled to take place with ULSD fuel to determine the affect the engine rating has on the PM oxidation. The experimental reaction rates during passive oxidation varied based upon the average CPF temperature, NO2 concentrations, and the NOX/PM ratios for each engine rating and with all fuels. The data analysis requires a high fidelity model that includes NO2 and thermal oxidation mechanisms and back diffusion to determine the details of the PM oxidation process.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Range-based Weighted-likelihood Particle Filter for RSS-based Indoor Tracking

Attractive business cases in various application fields contribute to the sustained long-term interest in indoor localization and tracking by the research community. Location tracking is generally treated as a dynamic state estimation problem, consisting of two steps: (i) location estimation through measurement, and (ii) location prediction. For the estimation step, one of the most efficient and low-cost solutions is Received Signal Strength (RSS)-based ranging. However, various challenges - unrealistic propagation model, non-line of sight (NLOS), and multipath propagation - are yet to be addressed. Particle filters are a popular choice for dealing with the inherent non-linearities in both location measurements and motion dynamics. While such filters have been successfully applied to accurate, time-based ranging measurements, dealing with the more error-prone RSS based ranging is still challenging. In this work, we address the above issues with a novel, weighted likelihood, bootstrap particle filter for tracking via RSS-based ranging. Our filter weights the individual likelihoods from different anchor nodes exponentially, according to the ranging estimation. We also employ an improved propagation model for more accurate RSS-based ranging, which we suggested in recent work. We implemented and tested our algorithm in a passive localization system with IEEE 802.15.4 signals, showing that our proposed solution largely outperforms a traditional bootstrap particle filter.

Disentangling mental imagery and perceptual expectation

Mental imagery and perception are thought to rely on similar neural circuits, and many recent behavioral studies have attempted to demonstrate interactions between actual physical stimulation and sensory imagery in the corresponding sensory modality. However, there has been a lack of theoretical understanding of the nature of these interactions, and both interferential and facilitatory effects have been found. Facilitatory effects appear strikingly similar to those that arise due to experimental manipulations of expectation. Using a self-motion discrimination task, we try to disentangle the effects of mental imagery from those of expectation by using a hierarchical drift diffusion model to investigate both choice data and response times. Manipulations of expectation are reasonably well understood in terms of their selective influence on parameters of the drift diffusion model, and in this study, we make the first attempt to similarly characterize the effects of mental imagery. We investigate mental imagery within the computational framework of control theory and state estimation. • Mental imagery and perception are thought to rely on similar neural circuits; however, on more theoretical grounds, imagery seems to be closely related to the output of forward models (sensory predictions). • We reanalyzed data from a study of imagined self-motion. • Bayesian modeling of response times may allow us to disentangle the effects of mental imagery on behavior from other cognitive (top-down) effects, such as expectation.

Water temperature and salinity data from southern elephant seals from Marion Island

Over the last decade, several hundred seals have been equipped with conductivity-temperature-depth sensors in the Southern Ocean for both biological and physical oceanographic studies. A calibrated collection of seal-derived hydrographic data is now available, consisting of more than 165,000 profiles. The value of these hydrographic data within the existing Southern Ocean observing system is demonstrated herein by conducting two state estimation experiments, differing only in the use or not of seal data to constrain the system. Including seal-derived data substantially modifies the estimated surface mixedlayer properties and circulation patterns within and south of the Antarctic Circumpolar Current. Agreement with independent satellite observations of sea ice concentration is improved, especially along the East Antarctic shelf. Instrumented animals efficiently reduce a critical observational gap, and their contribution to monitoring polar climate variability will continue to grow as data accuracy and spatial coverage increase.

Modelling and Control of Stepper Motors for High Accuracy Positioning Systems Used in Radioactive Environments

Hybrid Stepper Motors are widely used in open-loop position applications. They are the choice of actuation for the collimators in the Large Hadron Collider, the largest particle accelerator at CERN. In this case the positioning requirements and the highly radioactive operating environment are unique. The latter forces both the use of long cables to connect the motors to the drives which act as transmission lines and also prevents the use of standard position sensors. However, reliable and precise operation of the collimators is critical for the machine, requiring the prevention of step loss in the motors and maintenance to be foreseen in case of mechanical degradation. In order to make the above possible, an approach is proposed for the application of an Extended Kalman Filter to a sensorless stepper motor drive, when the motor is separated from its drive by long cables. When the long cables and high frequency pulse width modulated control voltage signals are used together, the electrical signals difer greatly between the motor and drive-side of the cable. Since in the considered case only drive-side data is available, it is therefore necessary to estimate the motor-side signals. Modelling the entire cable and motor system in an Extended Kalman Filter is too computationally intensive for standard embedded real-time platforms. It is, in consequence, proposed to divide the problem into an Extended Kalman Filter, based only on the motor model, and separated motor-side signal estimators, the combination of which is less demanding computationally. The efectiveness of this approach is shown in simulation. Then its validity is experimentally demonstrated via implementation in a DSP based drive. A testbench to test its performance when driving an axis of a Large Hadron Collider collimator is presented along with the results achieved. It is shown that the proposed method is capable of achieving position and load torque estimates which allow step loss to be detected and mechanical degradation to be evaluated without the need for physical sensors. These estimation algorithms often require a precise model of the motor, but the standard electrical model used for hybrid stepper motors is limited when currents, which are high enough to produce saturation of the magnetic circuit, are present. New model extensions are proposed in order to have a more precise model of the motor independently of the current level, whilst maintaining a low computational cost. It is shown that a significant improvement in the model It is achieved with these extensions, and their computational performance is compared to study the cost of model improvement versus computation cost. The applicability of the proposed model extensions is demonstrated via their use in an Extended Kalman Filter running in real-time for closed-loop current control and mechanical state estimation. An additional problem arises from the use of stepper motors. The mechanics of the collimators can wear due to the abrupt motion and torque profiles that are applied by them when used in the standard way, i.e. stepping in open-loop. Closed-loop position control, more specifically Field Oriented Control, would allow smoother profiles, more respectful to the mechanics, to be applied but requires position feedback. As mentioned already, the use of sensors in radioactive environments is very limited for reliability reasons. Sensorless control is a known option but when the speed is very low or zero, as is the case most of the time for the motors used in the LHC collimator, the loss of observability prevents its use. In order to allow the use of position sensors without reducing the long term reliability of the whole system, the possibility to switch from closed to open loop is proposed and validated, allowing the use of closed-loop control when the position sensors function correctly and open-loop when there is a sensor failure. A different approach to deal with the switched drive working with long cables is also presented. Switched mode stepper motor drives tend to have poor performance or even fail completely when the motor is fed through a long cable due to the high oscillations in the drive-side current. The design of a stepper motor output fillter which solves this problem is thus proposed. A two stage filter, one devoted to dealing with the diferential mode and the other with the common mode, is designed and validated experimentally. With this ?lter the drive performance is greatly improved, achieving a positioning repeatability even better than with the drive working without a long cable, the radiated emissions are reduced and the overvoltages at the motor terminals are eliminated.

Sintonia automática do filtro de kalman unscented.

O filtro de Kalman estendido tem sido a mais popular ferramenta de filtragem não linear das últimas quatro décadas. É de fácil implementação e apresenta baixo custo computacional. Nos casos nos quais as não linearidades do sistema dinâmico são significativas, porém, o filtro de Kalman estendido pode apresentar resultados insatisfatórios. Nessas situações, o filtro de Kalman unscented substitui com vantagens o filtro de Kalman estendido, pois pode apresentar melhores estimativas de estado, embora ambos os filtros exibam complexidade computacional de mesma ordem. A qualidade das estimativas de estado do filtro unscented está intimamente ligada à sintonia dos parâmetros que controlam a transformada unscented. A versão escalada dessa transformada exibe três parâmetros escalares que determinam o posicionamento dos pontos sigma e, consequentemente, afetam diretamente a qualidade das estimativas produzidas pelo filtro. Apesar da importância do filtro de Kalman unscented, a sintonia ótima desses parâmetros é um problema para o qual ainda não há solução definitiva. Não há nem mesmo recomendações heurísticas que garantam o bom funcionamento do filtro unscented na maior parte dos problemas tratáveis por meio de filtros Gaussianos. Essa carência e a importância desse filtro para a área de filtragem não linear fazem da busca por mecanismos de sintonia automática do filtro unscented área de pesquisa ativa. Assim, este trabalho propõe técnicas para sintonia automática dos parâmetros da transformada unscented escalada. Além da sintonia desses parâmetros, também é abordado o problema de sintonizar as matrizes de covariância dos ruídos de processo e de medida demandadas pelo modelo do sistema dinâmico usado pelo filtro unscented. As técnicas propostas cobrem então a sintonia automática de todos os parâmetros do filtro.

Optimal cloning for finite distributions of coherent states

We derive optimal cloning limits for finite Gaussian distributions of coherent states and describe techniques for achieving them. We discuss the relation of these limits to state estimation and the no-cloning limit in teleportation. A qualitatively different cloning limit is derived for a single-quadrature Gaussian quantum cloner.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Development of hardware in the loop real-time control techniques for hybrid power systems involving distributed demands and sustainable energy sources

The future power grid will effectively utilize renewable energy resources and distributed generation to respond to energy demand while incorporating information technology and communication infrastructure for their optimum operation. This dissertation contributes to the development of real-time techniques, for wide-area monitoring and secure real-time control and operation of hybrid power systems. ^ To handle the increased level of real-time data exchange, this dissertation develops a supervisory control and data acquisition (SCADA) system that is equipped with a state estimation scheme from the real-time data. This system is verified on a specially developed laboratory-based test bed facility, as a hardware and software platform, to emulate the actual scenarios of a real hybrid power system with the highest level of similarities and capabilities to practical utility systems. It includes phasor measurements at hundreds of measurement points on the system. These measurements were obtained from especially developed laboratory based Phasor Measurement Unit (PMU) that is utilized in addition to existing commercially based PMU’s. The developed PMU was used in conjunction with the interconnected system along with the commercial PMU’s. The tested studies included a new technique for detecting the partially islanded micro grids in addition to several real-time techniques for synchronization and parameter identifications of hybrid systems. ^ Moreover, due to numerous integration of renewable energy resources through DC microgrids, this dissertation performs several practical cases for improvement of interoperability of such systems. Moreover, increased number of small and dispersed generating stations and their need to connect fast and properly into the AC grids, urged this work to explore the challenges that arise in synchronization of generators to the grid and through introduction of a Dynamic Brake system to improve the process of connecting distributed generators to the power grid.^ Real time operation and control requires data communication security. A research effort in this dissertation was developed based on Trusted Sensing Base (TSB) process for data communication security. The innovative TSB approach improves the security aspect of the power grid as a cyber-physical system. It is based on available GPS synchronization technology and provides protection against confidentiality attacks in critical power system infrastructures. ^