MATLAB Applications: Numerical Simulations of Differential Equations and Introduction to Dynamic Systems

2004 ◽  
pp. 133-171
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Dynamic Systems

Multifidelity Recursive Cokriging for Dynamic Systems' Response Modification

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Luigi Bregant ◽  
Lucia Parussini ◽  
Valentino Pediroda
Keyword(s):  
Numerical Model ◽  
Numerical Simulations ◽  
Dynamic Systems ◽  
System Optimization ◽  
The Other ◽  
Experimental Measurements ◽  
Reciprocal Influence ◽  
Tests And Measurements ◽  
Invaluable Tool ◽  
Mixed Approach

In order to perform the accurate tuning of a machine and improve its performance to the requested tasks, the knowledge of the reciprocal influence among the system's parameters is of paramount importance to achieve the sought result with minimum effort and time. Numerical simulations are an invaluable tool to carry out the system optimization, but modeling limitations restrict the capabilities of this approach. On the other side, real tests and measurements are lengthy, expensive, and not always feasible. This is the reason why a mixed approach is presented in this work. The combination, through recursive cokriging, of low-fidelity, yet extensive, numerical model results, together with a limited number of highly accurate experimental measurements, allows to understand the dynamics of the machine in an extended and accurate way. The results of a controllable experiment are presented and the advantages and drawbacks of the proposed approach are also discussed.

Numerical Simulation of Distributed Dynamic Systems using Hybrid Tools of Intelligent Computing

2013 ◽  
pp. 360-383
Author(s):  
Fethi H. Bellamine ◽  
Aymen Gdouda
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Dynamic Systems ◽  
Mixed Boundary ◽  
Simulation Models ◽  
Control Synthesis ◽  
Scaling Analysis ◽  
Intelligent Computing ◽  
Boundary Constraints ◽  
Reduction Techniques

Developing fast and accurate numerical simulation models for predicting, controlling, designing, and optimizing the behavior of distributed dynamic systems is of interest to many researchers in various fields of science and engineering. These systems are described by a set of differential equations with homogenous or mixed boundary constraints. Examples of such systems are found, for example, in many networked industrial systems. The purpose of the present work is to review techniques of hybrid soft computing along with generalized scaling analysis for the solution of a set of differential equations characterizing distributed dynamic systems. The authors also review reduction techniques. This paves the way to control synthesis of real-time robust realizable controllers.

Artificial neural networks and adaptive neuro-fuzzy inference systems for parameter identification of dynamic systems

2020 ◽  
Vol 39 (5) ◽  
pp. 6145-6155
Author(s):  
Ramin Vatankhah ◽  
Mohammad Ghanatian
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Fuzzy Inference ◽  
Dynamic Equations ◽  
Control Analysis ◽  
Unknown Parameters ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Artificial Neural ◽  
Inference Systems

There would always be some unknown geometric, inertial or any other kinds of parameters in governing differential equations of dynamic systems. These parameters are needed to be numerically specified in order to make these dynamic equations usable for dynamic and control analysis. In this study, two powerful techniques in the field of Artificial Intelligence (AI), namely Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are utilized to explain how unknown parameters in differential equations of dynamic systems can be identified. The data required for training and testing the ANN and the ANFIS are obtained by solving the direct problem i.e. solving the dynamic equations with different known parameters and input stimulations. The governing ordinary differential equations of the system is numerically solved and the output values in different time steps are obtained. The output values of the system and their derivatives, the time and the inputs are given to the ANN and the ANFIS as their inputs and the unknown parameters in the dynamic equations are estimated as the outputs. Finally, the performances of the ANN and the ANFIS for identifying parameters of the system are compared based on the test data Percent Root Mean Square Error (% RMSE) values.

Propagation of bursting oscillations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4863-4875 ◽  
Author(s):  
Benjamin Ambrosio ◽  
Jean-Pierre Françoise
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Evolution ◽  
Global Attractor ◽  
Reaction Diffusion ◽  
Functional Space ◽  
Excitable Cells ◽  
Diffusion Type ◽  
Bursting Oscillations

We investigate a system of partial differential equations of reaction–diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional space. Numerical simulations show the existence in this attractor of recurrent solutions which are waves propagating from the central source. The propagation seems possible if the excitability of the neighbouring cells is above some threshold.

scholarly journals Note on the Sensitivity of Simulated Solutions of the Nonlinear Singularly Perturbed Dynamical System on the Used Different Rewriting into a System of First Order Differential Equations

2016 ◽  
Vol 24 (39) ◽  
pp. 51-55
Author(s):  
Vladimír Liška ◽  
Zuzana Šútova ◽  
Dušan Pavliak
Keyword(s):  
Dynamical System ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
First Order ◽  
First Order Differential Equations

Abstract In this paper we analyze the sensitivity of solutions to a nonlinear singularly perturbed dynamical system based on different rewriting into a System of the First Order Differential Equations to a numerical scheme. Numerical simulations of the solutions use numerical methods implemented in MATLAB.

Numerical vs. Experimental Predictions of Yaw Motion of Single Point Moored Vessel

2005 ◽  
Author(s):  
Mathieu Brotons ◽  
Philippe Jean
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Domain ◽  
Model Tests ◽  
Linear Differential Equations ◽  
Integration Scheme ◽  
Engineering Model ◽  
Non Linear ◽  
Linear Differential

The accurate prediction of SPM vessel yaw motion is important to its mooring system design. Inconsistencies have been observed between the numerical and model test predictions of offloading responses. In some cases, the numerical simulation predicted unstable yaw behavior of the vessel (fishtailing) while the model tests did not show such instability. This discrepancy between experiment and theory casts doubt as to whether the numerical simulation predicts correctly the vessel yaw motion. The work presented in this paper investigates the following two hypotheses to possibly explain the non-expected fishtailing in the numerical simulations: The mooring software may not accurately integrate non-linear differential equations that describe the yaw motion of the SPM vessel. Some damping terms may be under-estimated in the software (user input issue). To validate the integration scheme of the system of non-linear differential equations as implemented in the mooring software, a stability analysis has been conducted on a shuttle tanker moored to a West Africa deep water buoy. Variations of parameters like the hawser length, its axial stiffness and the vessel’s drag coefficients have been studied to explore their impacts on the vessel yaw stability. The approach is to identify without performing any time domain simulations, the domains of stability by linearizing the differential equations of SPM vessel’s yaw motion around its equilibrium point. The validity of the developed approach is then confirmed by performing time domain simulations of the same case. The second conjecture which may explain the non-expected fishtailing in numerical simulations was that some damping terms may be under-estimated. A semi empirical formula for the drag moment can be derived from rotation tests and comparisons were performed with the engineering model implemented in the mooring analysis software. The results show that by calibrating this damping term with the one derived from the experiments, the numerical simulations would match the stable yaw motion behavior as predicted during model tests. Following the above findings, a tool has been developed to fit the yaw drag moment engineering model based on experimental measurements, for any case of mooring analysis.

scholarly journals Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Tung Lam Nguyen ◽  
Trong Hieu Do ◽  
Hong Quang Nguyen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Vibration Suppression ◽  
Direct Method ◽  
Equations Of Motion ◽  
Gantry Crane ◽  
Partial Differential ◽  
Control Approach ◽  
Lyapunov’S Direct Method

The paper presents a control approach to a flexible gantry crane system. From Hamilton’s extended principle the equations of motion that characterized coupled transverse-transverse motions with varying rope length of the gantry is obtained. The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. The designed control is verified through extensive numerical simulations.

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