Study of numeric Saturation Effects in Linear Digital Compensators

Saturation arithmetic is often used in finite precision digital compensators to circumvent instability due to radix overflow. The saturation limits in the digital structure lead to nonlinear behavior during large state transients. It is shown that if all recursive loops in a compensator are interrupted by at least one saturation limit, then there exists a bounded external scaling rule which assures against overflow at all nodes in the structure. Design methods are proposed based on the generalized second method of Lyapunov, which take the internal saturation limits into account to implement a robust dual-mode suboptimal control for bounded input plants. The saturating digital compensator provides linear regulation for small disturbances, and near-time-optimal control for large disturbances or changes in the operating point. Computer aided design tools are developed to facilitate the analysis and design of this class of digital compensators

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems

Hydrologic modeling using triangulated irregular networks : terrain representation, flood forecasting and catchment response

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2003.Includes bibliographical references.Numerical models are modern tools for capturing the spatial and temporal variability in the land-surface hydrologic response to rainfall and understanding the physical relations between internal watershed processes and observed streamflow. This thesis presents the development and application of a distributed hydrologic model distinguished by its representation of topography through a triangulated irregular network (TIN) and its coupling of the surface and subsurface processes leading to the catchment response. As a research tool for hydrologic forecasting and experimentation, the TIN-based Real-time Integrated Basin Simulator (tRIBS) fully incorporates spatial heterogeneities in basin topography, surface descriptors and hydrometeorological forcing to produce dynamic maps of hydrologic states and fluxes. These capabilities allow investigation of theoretical questions and practical problems in hydrologic science and water resources engineering. Three related themes are developed in this thesis. First, a set of methods are developed for constructing TIN topographic models from raster digital elevation models (DEM) for hydrologic and geomorphic applications. A new approach for representing a steady-state estimate of a particular watershed process within the physical mesh is introduced. Hydrologic comparisons utilizing different terrain models are made to investigate the suitable level of detail required for capturing process dynamics accurately. Second, the TIN-based model is utilized in conjunction with a rainfall forecasting algorithm to assess the space-time flood predictability. For two hydrometeorological case studies, the forecast skill is assessed as a function of rainfall forecast lead time, catchment scale and the spatial variability in the quantitative precipitation forecasts (QPF). Third, the surface and subsurface runoff response in a complex basin is investigated with respect to changes in storm properties and the initial water table position.The partitioning of rainfall into runoff production mechanisms is found to be a causative factor in the nonlinearity and scale-dependence observed in the basin hydrograph response. The model applications presented in this thesis highlight the advantages of TIN- based modeling for hydrologic forecasting and process-oriented studies over complex terrain. In particular, the multi-resolution and multi-scale capabilities are encouraging for a range of applied and scientific problems in catchment hydrology.by Enrique R. Vivoni.Ph.D

Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page

Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for modeling the evolution of dynamical systems. The DR-RNN architecture is inspired by iterative update techniques of line search methods where a fixed number of layers are stacked together to minimize the residual (or reduced residual) of the physical model under consideration. In this manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity numerical simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the full-order model size. We demonstrate the proposed reduced model on two uncertainty quantification test cases using Monte-Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable reduced model with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A two-fold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.Comment: 32 pages, 8 figures, accepted to JP

The Role of Non-Linearities in Visual Perception studied with a Computational Model of the Vertebrate Retina

Processing of visual stimuli in the vertebrate retina is complex and diverse. The retinal output to the higher centres of the nervous system, mediated by ganglion cells, consists of several different channels. Neurons in these channels can have very distinct response properties, which originate in different retinal pathways. In this work, the retinal origins and possible functional implications of the segregation of visual pathways will be investigated with a detailed, biologically realistic computational model of the retina. This investigation will focus on the two main retino-cortical pathways in the mammalian retina, the parvocellular and magnocellular systems, which are crucial for conscious visual perception. These pathways differ in two important aspects. The parvocellular system has a high spatial, but low temporal resolution. Conversely, the magnocellular system has a high temporal fidelity, spatial sampling however is less dense than for parvocellular cells. Additionally, the responses of magnocellular ganglion cells can show pronounced nonlinearities, while the parvocellular system is essentially linear. The origin of magnocellular nonlinearities is unknown and will be investigated in the first part of this work. As their main source, the results suggest specific properties of the photoreceptor response and a specialised amacrine cell circuit in the inner retina. The results further show that their effect combines in a multiplicative way. The model is then used to examine the influence of nonlinearities on the responses of ganglion cells in the presence of involuntary fixational eye movements. Two different stimulus conditions will be considered: visual hyperacuity and motion induced illusions. In both cases, it is possible to directly compare properties of the ganglion cell population response with psychophysical data, which allows for an analysis of the influence of different components of the retinal circuitry. The simulation results suggest an important role for nonlinearities in the magnocellular stream for visual perception in both cases. First, it will be shown how nonlinearities, triggered by fixational eye movements, can strongly enhance the spatial precision of magnocellular ganglion cells. As a result, their performance in a hyperacuity task can be equal to or even surpass that of the parvocellular system. Second, the simulations imply that the origin of some of the illusory percepts elicited by fixational eye movements could be traced back to the nonlinear properties of magnocellular ganglion cells. As these activity patterns strongly differ from those in the parvocellular system, it appears that the magnocellular system can strongly dominate visual perception in certain conditions. Taken together, the results of this theoretical study suggest that retinal nonlinearities may be important for and strongly influence visual perception. The model makes several experimentally verifiable predictions to further test and quantify these findings. Furthermore, models investigating higher visual processing stages may benefit from this work, which could provide the basis to produce realistic afferent input