Component Based Modeling of Electromechanical Systems

2005 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Single Step ◽  
System Response ◽  
Algebraic Equations ◽  
System Behavior ◽  
Governing Equations ◽  
Electromechanical Systems ◽  
System Equations ◽  
Saturation Effects

Simulation methods for electromechanical systems should accommodate their interdisciplinary nature and the fact that these systems often display qualitative changes in system behavior during operation, such as saturation effects and changes in kinematic structure. Current approaches are either based on deriving the system equations by applying a single formulation to all problem domains, or they are based on trying to integrate different software packages/modules to solve the interdisciplinary problem. In this paper, we present a component-based approach which allows the governing equations of each component to be defined in terms of its natural variables. The different component equations are then brought together to form a single system of differential-algebraic equations (DAE’s), which can be numerically solved to obtain the system response. The fact that we have an explicit, unified form of the system governing equations means that this formulation can be easily extended to design sensitivity analysis and optimization of electromechanical systems (EMS). The formulation includes monitor functions which can be used to detect when a qualitative system change has occurred, and to switch to a new set of governing equations to reflect this change. A single step integrator is used to make it easier to switch to a new system behavior, since this will always require a restart of the integrator. There is considerable flexibility in how the components can be defined, and connections between components are themselves modeled as special types of components. Examples of components from the mechanical and electrical side are presented, and two numerical examples are solved to illustrate the efficacy of the proposed method. One example is a link that is driven by a DC motor through a gearbox. The results of this example were verified against Simulink, and good agreement was observed. The second example is a motor driven slider-crank mechanism. The method can be extended to include components from any domain, such as hydraulics, thermal, controls, etc., as long as the governing equations can be written as DAE’s.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

Null Space Method of Differential Equation Type for Motion Analysis of Multibody Systems

2017 ◽  
Author(s):  
Keisuke Kamiya ◽  
Yusaku Yamashita
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Null Space ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Accurate Analysis ◽  
Dependent Variables ◽  
Space Matrix ◽  
Space Method

The governing equations of multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called null space method and Maggi’s method eliminate the Lagrange multipliers by using the null space matrix for the constraint Jacobian. In previous reports, one of the authors presented methods which use the null space matrix. In the procedure to obtain the null space matrix, the inverse of a matrix whose regularity may not be always guaranteed. In this report, a new method is proposed in which the null space matrix is obtained by solving differential equations that can be always defined by using the QR decomposition, even if the constraints are redundant. Examples of numerical analysis are shown to validate the proposed method.

scholarly journals Multibody Modeling Method for UHV Porcelain Arresters Equipped with Lead Alloy Isolation Device

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xiaochao Su ◽  
Lei Hou ◽  
Zhubing Zhu ◽  
Yushu Chen
Keyword(s):  
Seismic Isolation ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Modeling Method ◽  
Lead Alloy ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Multibody Modeling ◽  
Isolation Device

This paper presents a multibody modeling method for seismic analysis of UHV porcelain surge arresters equipped with a kind of seismic isolation device. An UHV arrester is modeled as a planar multibody system whose number of DOF is equal to the number of the arrester units. Joint coordinate method is adopted to construct the governing equations of motion. The seismic isolation device utilizing a number of lead alloy dampers as its core energy dissipation components is also investigated. An analytical model of this device is given by modeling each lead alloy damper as a hysteretic spring and reducing the entire device to a planar system consisting of a range of hysteretic springs. Its mechanical characteristic is derived theoretically, and the obtained moment-angle relationship is expressed as a system of differential algebraic equations. The initial rotational stiffness of the device is formulated in terms of the structural and mechanical parameters of the device. This analytic expression is used in estimating the fundamental frequency of the isolated equipment. By this modeling method, it is easy to construct the governing equations of motion for the isolated system. An UHV arrester specimen is analyzed by this proposed method. The effectiveness of the isolation device in terms of reducing the internal base moment is significant and the influence of system parameters on the effectiveness is also discussed. The proposed method shows its potential usefulness in optimal design of the isolation device.

Solution Numerical of Stiff ODEs and DAEs in Mechanical and Other Systems

1997 ◽  
Author(s):  
H. Pasic
Keyword(s):  
Formal Solution ◽  
Differential Algebraic Equations ◽  
Single Step ◽  
Algebraic Equations ◽  
Stiff Differential Equations ◽  
Index Zero ◽  
Initial Value ◽  
Polynomial Coefficients ◽  
Multi Stage ◽  
Index 2

Abstract Presented is a formal solution of the initial-value problem of the system of general implicit differential-algebraic equations (DAEs) F(x, y, y’) = 0 of index zero or higher, based on perturbations of the polynomial coefficients of the vector y(x). The equation is linearized with respect to the coefficients and brought into a form suitable for implementation of the weighted residual methods. The solution is advanced by a single-step multi-stage collocation qadrature formula which is stiffly accurate and suitable for solving stiff differential equations and DAEs that arise in many mechanical and other systems. The algorithm is illustrated by two index-2 and index-3 examples — one of which is the well known pendulum problem.

Continuous Null Space Method for Constrained Mechanical Systems

2011 ◽  
Author(s):  
Keisuke Kamiya ◽  
Makoto Sawada ◽  
Yuji Furusawa
Keyword(s):  
Lagrange Multipliers ◽  
Null Space ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Accurate Analysis ◽  
Constrained Mechanical Systems ◽  
Dependent Variables ◽  
Space Matrix ◽  
Space Method

The governing equations for multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. It is desirable for efficient and accurate analysis to eliminate the Lagrange multipliers and dependent variables. As a method to solve the DAEs by eliminating the Lagrange multipliers, there is a method called the null space method. In this report, first, it is shown that using the null space matrix one can eliminate the Lagrange multipliers and reduce the number of velocities to that of the independent ones. Then, a new method to obtain the continuous null space matrix is presented. Finally, the presented method is applied to four-bar linkages.

scholarly journals THE INVERSE SIMULATION STUDY OF AIRCRAFT FLIGHT PATH RECONSTRUCTION

Transport ◽  
2002 ◽  
Vol 17 (3) ◽  
pp. 103-107 ◽  
Author(s):  
Wojciech Blajer ◽  
Jacek A. Goszczyński ◽  
Mariusz Krawczyk
Keyword(s):  
Differential Algebraic Equations ◽  
Velocity Variation ◽  
State Variables ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Inverse Simulation ◽  
Time Variations ◽  
Aircraft Motion ◽  
Additional Constraints ◽  
Program Constraint

This paper presents a uniform approach to the modelling and simulation of aircraft prescribed trajectory flight. The aircraft motion is specified by a trajectory in space, a condition on airframe attitude with respect to the trajectory, and a desired flight velocity variation. For an aircraft controlled by aileron, elevator and rudder deflections and thrust changes a tangent realization of trajectory constraints arises which yields two additional constraints on the airframe attitude with respect to the trajectory. Combining the program constraint conditions and aircraft dynamic equations the governing equations of programmed motion are developed in the form of differential-algebraic equations. A method for solving the equations is proposed. The solution consists of time variations of the aircraft state variables and the demanded control that ensures the programmed motion realization.

Group Preserving Correction Methods for Differential Algebraic Equations

2016 ◽  
Vol 13 (10) ◽  
pp. 7719-7725
Author(s):  
Jianguang Lu ◽  
Yong Feng ◽  
Xiaolin Qin ◽  
Juan Tang
Keyword(s):  
High Accuracy ◽  
Differential Algebraic Equations ◽  
Single Step ◽  
Euler Scheme ◽  
Cayley Transform ◽  
Exponential Mapping ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Time Integrators ◽  
Correction Scheme

The group preserving methods proposed by Liu [Int. J. Non-Linear Mech., 2001 and CMES-Comp. Model. Eng., 2006] for ordinary differential equations or differential algebraic equations (DAEs) adopted the Cayley transform or exponential mapping to formulate the Lie group from its Lie algebra. In this paper, we combine the Euler scheme with the group preserving methods to obtain the high accuracy group preserving techniques. We propose a group preserving correction scheme (GPCS) via exponential mapping and a modified group preserving correction scheme (MGPCS) by considering constraint. The two schemes provide single-step explicit time integrators for systems of DAEs. Some numerical examples are examined, showing that the GPCS and MGPCS work very well and have good computational efficiency and high accuracy.

A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations

2006 ◽  
Vol 1 (3) ◽  
pp. 230-239 ◽  
Author(s):  
Dan Negrut ◽  
Jose L. Ortiz
Keyword(s):  
Heterogeneous Systems ◽  
Reference Method ◽  
Nonholonomic Constraints ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Constrained Mechanical Systems ◽  
Friction Control ◽  
Constrained Multibody Dynamics ◽  
Space Formulation

The paper presents an approach to linearize the set of index 3 nonlinear differential algebraic equations that govern the dynamics of constrained mechanical systems. The proposed method handles heterogeneous systems that might contain flexible bodies, friction, control elements (user-defined differential equations), and nonholonomic constraints. Analytically equivalent to a state-space formulation of the system dynamics in Lagrangian coordinates, the proposed method augments the governing equations and then computes a set of sensitivities that provide the linearization of interest. The attributes associated with the method are the ability to handle large heterogeneous systems, ability to linearize the system in terms of arbitrary user-defined coordinates, and straightforward implementation. The proposed approach has been released in the 2005 version of the MSC.ADAMS/Solver(C++) and compares favorably with a reference method previously available. The approach was also validated against MSC.NASTRAN and experimental results.

Subset Selection Methods for Design Sensitivity Analysis of Constrained Dynamic Systems

1990 ◽  
Author(s):  
Jun-Tien Twu ◽  
Prakash Krishnaswami ◽  
Rajiv Rampalli
Keyword(s):  
Dynamic Systems ◽  
Correct Choice ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Selection Methods ◽  
Constrained Motion ◽  
Differentiation Formula ◽  
Backward Differentiation Formula ◽  
Solution Methods

Abstract In the Lagrangian formulation of the constrained motion of mechanical systems, a system of Differential-Algebraic Equations is generally encountered. The popular Backward Differentiation Formula for the numerical solution of such problems leads to an over-determined system of equations. The correct choice of a proper exactly determined subset can greatly enhance the performance of a solution algorithm. In this paper, we discuss four solution methods with different choices of subsets. Three numerical examples are solved to compare the accuracy and efficiency of these methods.

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