Research Papers

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

[+] Author and Article Information
Sachit Rao1

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, Indiasachit@aero.iisc.ernet.in

Vadim Utkin

Department of Electrical Engineering, Ohio State University, Columbus, OH 43210utkin@ece.osu.edu

Martin Buss

Institute of Automatic Control Engineering (LSR), Technische Universitaet Muenchen, Munich, 80290 Germanymb@tum.de


Corresponding author.

J. Comput. Nonlinear Dynam 5(4), 041005 (Jun 30, 2010) (8 pages) doi:10.1115/1.4001904 History: Received November 28, 2008; Revised October 22, 2009; Published June 30, 2010; Online June 30, 2010

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventional simulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 2

LRC circuit simulation

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Figure 3

Accuracy and finite time convergence

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Figure 1

LRC circuit with a common node

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Figure 6

SMC discretization

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Figure 7

i(0,t): SMC and modal expansion techniques

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Figure 8

Elements of the EB cantilever on a circle

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Figure 9

Varying number of elements and modes

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Figure 10

Comparing responses in close-up

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Figure 4

FEM discretization

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Figure 11

SMC, FEM, and modal expansion techniques




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