A class of relaxation algorithms for finding the periodic steady-state solution in nonlinear systems

Author

Frey, Douglas R.

Author_Institution

Dept. of Comput. Sci. & Electr. Eng., Lehigh Univ., Bethlehem, PA, USA

Volume

45

Issue

6

fYear

1998

fDate

6/1/1998 12:00:00 AM

Firstpage

659

Lastpage

663

Abstract

An improvement in the author´s previous algorithm for computing periodic steady-state solutions in nonautonomous systems is proposed that enables efficient computation of the solutions in autonomous systems. In addition, the derivations more clearly demonstrate the impact that the s- to z-plane mapping has on the equation formulation, specifically in the computation of the “A” and “B” matrices. A class of relaxation algorithms is proposed for the efficient solution of both nonautonomous and autonomous systems. Finally, simulation results on a van der Pol oscillator are presented that demonstrate the potential of the proposed algorithms. In addition, these simulations show how the use of different mappings from the s- to z-plane effect the solution estimates, and how the use of different mappings may be exploited to improve the efficiency of finding solutions

Keywords

nonlinear network analysis; nonlinear systems; relaxation oscillators; relaxation theory; autonomous systems; equation formulation; nonautonomous systems; nonlinear circuits; nonlinear systems; periodic steady-state solution; relaxation algorithms; s- to z-plane mapping; van der Pol oscillator; Application software; Bifurcation; Computational modeling; Computer networks; Nonlinear circuits; Nonlinear equations; Nonlinear systems; Oscillators; Relaxation methods; Steady-state;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.678483

Filename

678483