scholarly journals Software Tool for Acausal Physical Modelling and Simulation

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1199 ◽  
Author(s):  
Jimenez ◽  
Belmonte ◽  
Garrido ◽  
Ruz ◽  
Vazquez
Keyword(s):  
Discrete Event ◽  
Software Tool ◽  
Physical Modelling ◽  
Differential Algebraic Equations ◽  
Modelling And Simulation ◽  
Algebraic Equations ◽  
Discrete Events ◽  
Analysis And Design ◽  
Index Reduction ◽  
Model Equations

Modelling and simulation are key tools for analysis and design of systems and processes from almost any scientific or engineering discipline. Models of complex systems are typically built on acausal Differential-Algebraic Equations (DAE) and discrete events using Object-Oriented Modelling (OOM) languages, and some of their key concepts can be explained as symmetries. To obtain a computer executable version from the original model, several algorithms, based on bipartite symmetric graphs, must be applied for automatic equation generation, removing alias equations, computational causality assignment, equation sorting, discrete-event processing or index reduction. In this paper, an open source tool according to OOM paradigm and developed in MATLAB is introduced. It implements such algorithms adding an educational perspective about how they work, since the step by step results obtained after processing the model equations can be shown. The tool also allows to create models using its own OOM language and to simulate the final executable equation set. It was used by students in a modelling and simulation course of the Automatic Control and Industrial Electronics Engineering degree, showing a significant improvement in their understanding and learning of the abovementioned topics after their assessment.

Index reduction of differential algebraic equations by differential Dixon resultant

2018 ◽  
Vol 328 ◽  
pp. 189-202 ◽  
Author(s):  
Xiaolin Qin ◽  
Lu Yang ◽  
Yong Feng ◽  
Bernhard Bachmann ◽  
Peter Fritzson
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Index Reduction

Projection Method With Minimal Correction Procedure for Numerical Simulation of Constrained Dynamics

2017 ◽  
Author(s):  
Patrick S. Heaney ◽  
Gene Hou
Keyword(s):  
Projection Method ◽  
Numerical Technique ◽  
Correction Method ◽  
Differential Algebraic Equations ◽  
Constrained Systems ◽  
Correction Procedure ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Index Reduction ◽  
Algebraic Constraints

This paper describes a numerical technique for simulating the dynamics of constrained systems, which are described generally by differential-algebraic equations. The Projection Method for index reduction of a differential-algebraic equation and a minimal correction procedure are described. This procedure ensures algebraic constraints are satisfied during the numerical integration of the reduced index system of differential equations. Two examples illustrate how the method can be utilized to solve constrained multibody and rotational dynamics problems. The efficiency and accuracy of the proposed index-reduction and minimal correction method are then evaluated.

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

Modular Modeling Using Lagrangian DAEs

2000 ◽  
Author(s):  
Robert Piché ◽  
Mikko Palmroth
Keyword(s):  
Software Design ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Simulation Software ◽  
Algebraic Equations ◽  
Feedback Control System ◽  
Physical Systems ◽  
Modular Modeling ◽  
Index Reduction ◽  
Analytical System

Abstract Layton’s Analytical System Dynamics theory for modeling multidisciplinary physical systems with Lagrangian differential algebraic equations (DAEs) is extended by introducing a technique for using hierarchical reusable modules. Connections between submodels are represented in a systematic manner using kinematic constraints and Lagrange multipliers. Simulation software design issues are discussed: data structures, consistent initial conditions, index reduction, and DAE solvers. An example of an electromechanical feedback control system is presented in detail.

scholarly journals A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2057
Author(s):  
Juan Tang ◽  
Yongsheng Rao
Keyword(s):  
Large Scale ◽  
Differential Algebraic Equations ◽  
Coupled Systems ◽  
Algebraic Equations ◽  
Triangular Form ◽  
Large Scale Systems ◽  
Index Reduction ◽  
Dae Systems ◽  
New Generation ◽  
Block Structures

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

scholarly journals Index Reduction for Differential-algebraic Equations with Mixed Matrices

2019 ◽  
Vol 66 (5) ◽  
pp. 1-34 ◽  
Author(s):  
Satoru Iwata ◽  
Taihei Oki ◽  
Mizuyo Takamatsu
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Index Reduction

scholarly journals Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

2019 ◽  
Vol 5 ◽  
pp. e227
Author(s):  
Volodymyr B. Kopei ◽  
Oleh R. Onysko ◽  
Vitalii G. Panchuk
Keyword(s):  
Solution Procedure ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Third Party ◽  
Modeling Languages ◽  
Algebraic Equations ◽  
Basic Set ◽  
Sucker Rod ◽  
Acausal Modeling ◽  
Model Equations

Typically, component-oriented acausal hybrid modeling of complex dynamic systems is implemented by specialized modeling languages. A well-known example is the Modelica language. The specialized nature, complexity of implementation and learning of such languages somewhat limits their development and wide use by developers who know only general-purpose languages. The paper suggests the principle of developing simple to understand and modify Modelica-like system based on the general-purpose programming language Python. The principle consists in: (1) Python classes are used to describe components and their systems, (2) declarative symbolic tools SymPy are used to describe components behavior by difference or differential equations, (3) the solution procedure uses a function initially created using the SymPy lambdify function and computes unknown values in the current step using known values from the previous step, (4) Python imperative constructs are used for simple events handling, (5) external solvers of differential-algebraic equations can optionally be applied via the Assimulo interface, (6) SymPy package allows to arbitrarily manipulate model equations, generate code and solve some equations symbolically. The basic set of mechanical components (1D translational “mass”, “spring-damper” and “force”) is developed. The models of a sucker rods string are developed and simulated using these components. The comparison of results of the sucker rod string simulations with practical dynamometer cards and Modelica results verify the adequacy of the models. The proposed approach simplifies the understanding of the system, its modification and improvement, adaptation for other purposes, makes it available to a much larger community, simplifies integration into third-party software.

scholarly journals A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations

2020 ◽  
Author(s):  
Juan Tang ◽  
Yongsheng Rao
Keyword(s):  
Large Scale ◽  
Differential Algebraic Equations ◽  
Coupled Systems ◽  
Algebraic Equations ◽  
Structural Index ◽  
Triangular Form ◽  
Large Scale Systems ◽  
Index Reduction ◽  
New Generation ◽  
Block Structures

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

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