Title: A response spectral decomposition approach for the control of nonlinear mechanical systems

Authors: Corina Sandu, Adrian Sandu, Brendan J. Chan, Mehdi Ahmadian

Addresses: Assistant Professor, Mechanical Engineering Department, Director, Advanced Vehicle Dynamics Laboratory, Center for Vehicle Systems and Safety, Virginia Polytechnic Institute and State University, 104 Randolph Hall, Blacksburg, VA 24061, USA. ' Associate Professor, Computer Science Department, Center for Vehicle Systems and Safety, Virginia Polytechnic Institute and State University, 2224 Knowledgeworks 2, 2200 Kraft Dr., Blacksburg, VA 24061, USA. ' Mechanical Engineering Department, Advanced Vehicle Dynamics Laboratory, Center for Vehicle Systems and Safety, Virginia Polytechnic Institute and State University, 9A Randolph Hall, Blacksburg, VA 24061, USA. ' Professor, Mechanical Engineering Department, Director, Center for Vehicle Systems and Safety, Director, Railway Technology Laboratory, Virginia Polytechnic Institute and State University, 123 Randolph Hall, Blacksburg, VA 24061, USA

Abstract: This study investigates a control methodology for dynamic systems based on representing all possible system responses under all possible values of the control variables. The underlying idea is to extend the system along the |control dimension| and explicitly account for the dependence of the system state on control variables. A spectral discretisation along the |control dimension| is employed. The optimal control values are chosen to obtain the desired parameterised system response. This approach has the advantage of allowing an inexpensive search for the optimal control values at each time increment without having to run the full nonlinear dynamic model. Numerical studies for the control of linear and nonlinear quarter-car models riding on various terrain profiles show promising results.

Keywords: nonlinear control; mechanical systems; optimal control; orthogonal polynomials; spectral decomposition; dynamic systems; quarter-car models; vehicle control.

DOI: 10.1504/IJHVS.2008.017982

International Journal of Heavy Vehicle Systems, 2008 Vol.15 No.1, pp.27 - 52

Published online: 25 Apr 2008 *

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