Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Reduced-order modeling of power electronics components and systems

This dissertation addresses the seemingly inevitable compromise between modeling fidelity and simulation speed in power electronics. Higher-order effects are considered at the component and system levels. Order-reduction techniques are applied to provide insight into accurate, computationally efficient component-level (via reduced-order physics-based model) and system-level simulations (via multiresolution simulation). Proposed high-order models, verified with hardware measurements, are, in turn, used to verify the accuracy of final reduced-order models for both small- and large-signal excitations. At the component level, dynamic high-fidelity magnetic equivalent circuits are introduced for laminated and solid magnetic cores. Automated linear and nonlinear order-reduction techniques are introduced for linear magnetic systems, saturated systems, systems with relative motion, and multiple-winding systems, to extract the desired essential system dynamics. Finite-element models of magnetic components incorporating relative motion are set forth and then reduced. At the system level, a framework for multiresolution simulation of switching converters is developed. Multiresolution simulation provides an alternative method to analyze power converters by providing an appropriate amount of detail based on the time scale and phenomenon being considered. A detailed full-order converter model is built based upon high-order component models and accurate switching transitions. Efficient order-reduction techniques are used to extract several lower-order models for the desired resolution of the simulation. This simulation framework is extended to higher-order converters, converters with nonlinear elements, and closed-loop systems. The resulting rapid-to-integrate component models and flexible simulation frameworks could form the computational core of future virtual prototyping design and analysis environments for energy processing units

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Parametric reduced-order aeroelastic modelling for analysis, dynamic system interpolation and control of flexible aircraft

This work presents an integral framework to derive aeroelastic models for very flexible aircraft that can be used in design routines, operational envelope analysis and control applications. Aircraft are modelled using a nonlinear geometrically-exact beam model coupled with an Unsteady Vortex-Lattice Method aerodynamic solver, capable of capturing important nonlinear couplings and effects that significantly impact the flight characteristics of very flexible aircraft. Then, complete linearised expressions of the aircraft system about trim reference conditions at possibly large deformations are presented. The nature of the aerodynamic models results in a high-dimensional system that requires of model reduction methods for efficient analysis and manipulation. Krylov-subspace model reduction methods are implemented to reduce the dimensionality of the multi-input multi-output linearised aerodynamic model and achieve a very significant reduction in the size of the size of the system. The reduced aerodynamic model is then coupled with a modal expression of the linearised beam model, resulting in a compact aeroelastic state-space that can be efficiently used on desktop hardware for linear analysis or as part of internal control models. These have been used to explore the design space of a very flexible wing with complex aeroelastic properties to determine the flutter boundaries, for which experimental data has become available that validates the methods presented herein. Additionally, they have been integrated in a model predictive control framework, where the reduced linear aerodynamic model is part of the control model, and the simulation plant is the nonlinear flight dynamic/aeroelastic model connected as a hardware-in-the-loop platform. Finally, in order to accelerate the design space exploration of very flexible structures, state-space interpolation methods are sought to obtain, with a few linearised models sampled across the domain, interpolated state-spaces anywhere in the parameter-space in a fast and accurate manner. The performance of the interpolation schemes is heavily dependent on the location of the sampling points on the design space, therefore, a novel adaptive Bayesian sampling scheme is presented to choose these points in an optimal approach that minimises the interpolation error function.Open Acces

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces