scholarly journals Modeling and simulation aspects of AC machines

2016 ◽  
Vol 65 (2) ◽  
pp. 315-326 ◽  
Author(s):  
Michael Popp ◽  
Patrick Laza ◽  
Wolfgang Mathis
Keyword(s):  
Complex System ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Space Representation ◽  
Ac Machines ◽  
State Space Representation ◽  
Drive Systems ◽  
Algebraic Constraints

Abstract In the field of power and drive systems, electrical AC machines are mostly modeled using a set of explicit ordinary differential equations in a state space representation. It is shown, that by using other equation types for simulation, algebraic constraints arising from aggregating several machines to a more complex system can directly be considered. The effects of different model variants on numerical ODE/DAE solvers are investigated in the focus of this work in order perform efficient simulations of larger systems possessing electrical AC machines.

scholarly journals Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

2019 ◽  
Vol 29 (6) ◽  
pp. 1297-1315 ◽  
Author(s):  
Filip Tronarp ◽  
Hans Kersting ◽  
Simo Särkkä ◽  
Philipp Hennig
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Gradient Field ◽  
Space Representation ◽  
Bayesian Filtering ◽  
State Space Representation ◽  
The Difference ◽  
New Perspective ◽  
Non Gaussian ◽  
Filtering Problem

Abstract We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP—which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a nonlinear Bayesian filtering problem and all widely used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers that are formulated in terms of generating synthetic measurements of the gradient field come out as specific approximations. Based on the nonlinear Bayesian filtering problem posed in this paper, we develop novel Gaussian solvers for which we establish favourable stability properties. Additionally, non-Gaussian approximations to the filtering problem are derived by the particle filter approach. The resulting solvers are compared with other probabilistic solvers in illustrative experiments.

scholarly journals State-space representation of a bucket-type rainfall-runoff model: a case study with State-Space GR4 (version 1.0)

2017 ◽  
Author(s):  
Léonard Santos ◽  
Guillaume Thirel ◽  
Charles Perrin
Keyword(s):  
Water Balance ◽  
Differential Equations ◽  
State Space ◽  
Operator Splitting ◽  
Space Representation ◽  
Rainfall Runoff ◽  
State Space Representation ◽  
Rainfall Runoff Model ◽  
Unit Hydrographs ◽  
Runoff Model

Abstract. In many conceptual rainfall-runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called "operator splitting". As a result, only the resolutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall-runoff model explicit. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which complexifies the structural analysis of the model, is removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in this type of model and make the resolution of the representation difficult, are replaced by a so-called "Nash cascade". This substitution also improves the lag parameter consistency across time steps. To illustrate this methodology, the GR4J model is taken as an example. The flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The state-space representation provides a more time-consistent model with time-independent parameters.

scholarly journals Simulation of several flying situations of paragliders

2021 ◽  
Vol 15 (1) ◽  
pp. 79-89
Author(s):  
Thanh Xuan Nguyen ◽  
Phuong Thi-Thu Phan ◽  
Tien Van Pham
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Simulation Modeling ◽  
Time Varying ◽  
Gravity Forces

Paragliding is an adventure and fascinating sport of flying paragliders. Paragliders can be launched by running from a slope or by a winch force from towing vehicles, using gravity forces as the motor for the motion of flying. This motion is governed by the gravity forces as well as time-varying aerodynamic ones which depend on the states of the motion of paraglider at each instant of time. There are few published articles considering mechanical problems of paragliders in their various flying situations. This article represents the mathematical modeling and simulation of several common flying situations of a paraglider through establishing and solving the governing differential equations in state-space. Those flying situations include the ones with constant headwind/tailwind with or without constant upwind; the ones with different scenario for the variations of headwind and tailwind combined with the upwind; the ones with varying pilot mass; and the ones whose several parameters are in the form of interval quantities. The simulations were conducted using a powerful Julia toolkit called DifferentialEquations.jl. The obtained results in each situation are discussed, and some recommendations are presented. Keywords: paraglider; simulation; modeling; state-space; ordinary differential equations; Julia; DifferentialEquations.jl

Construction of Differential Equations from Experimental Data

1987 ◽  
Vol 42 (8) ◽  
pp. 797-802 ◽  
Author(s):  
J. Cremers ◽  
A. Hübler
Keyword(s):  
Experimental Data ◽  
Differential Equations ◽  
State Space ◽  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Time Sequence ◽  
Space Representation ◽  
State Space Representation ◽  
Concise Description

A new algorithm to determine the number of degrees of freedom of dynamic systems is presented. To obtain a concise description of an observed chaotic time sequence, an approximation of the flow in a state space representation by series is shown to be useful.

Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Tom T. Hartley ◽  
Carl F. Lorenzo ◽  
Jean-Claude Trigeassou ◽  
Nezha Maamri
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
State Space ◽  
Fractional Order ◽  
Laplace Transforms ◽  
Space Representation ◽  
Infinite Dimensional ◽  
State Space Representation ◽  
Fractional Order Differential Equations ◽  
Dimensional State Space

Proper initialization of fractional-order operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a history-function-based initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinite-dimensional state-space representation along with its corresponding Laplace transform has also been presented. The purpose of this paper is to demonstrate that these two approaches to the initialization problem for fractional-order operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractional-order differential equations.

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