A backwards error analysis approach for simulation and control of nonsmooth mechanical systems

David Pekarek; Todd D. Murphey

doi:10.1109/CDC.2011.6160975

A backwards error analysis approach for simulation and control of nonsmooth mechanical systems

David Pekarek^*, Todd D. Murphey

^*Corresponding author for this work

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

This paper presents an original structured integration scheme for Lagrangian systems undergoing elastic impacts due to unilateral constraints. In deriving the method, a backwards error analysis approach establishes a discrete time conservation law for impacts using the notion of a modified system Hamiltonian. Shortcomings of existing simulation methods that do not use this conservation law are demonstrated both analytically and in simulation. Relative to these methods, our scheme provides advantages in terms of discrete time energy behavior, accuracy of trajectories, and consistent order of accuracy of the method.

Original language	English (US)
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages	6942-6949
Number of pages	8
DOIs	https://doi.org/10.1109/CDC.2011.6160975
State	Published - 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: Dec 12 2011 → Dec 15 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country	United States
City	Orlando, FL
Period	12/12/11 → 12/15/11

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2011.6160975

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author = "David Pekarek and Murphey, {Todd D.}",

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Pekarek, D & Murphey, TD 2011, A backwards error analysis approach for simulation and control of nonsmooth mechanical systems. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160975, Proceedings of the IEEE Conference on Decision and Control, pp. 6942-6949, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160975

A backwards error analysis approach for simulation and control of nonsmooth mechanical systems. / Pekarek, David; Murphey, Todd D.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 6942-6949 6160975 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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A backwards error analysis approach for simulation and control of nonsmooth mechanical systems

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