Based on control theory, a new method to investigate initial conditions induced by the application of a step command on linear or nonlinear systems is given in this paper. Examples are provided to illustrate the proposed method.
Get full access to this article
View all access options for this article.
References
1.
Ord-SmithR. and StephensonJ., Computer Simulation of Continuous Systems, Cambridge University Press (1975)
2.
MeditchJ. and HostetterG., ‘Technique for initial condition estimation in linear systems’, Int. J. of Control, 22, No. 3, pp. 409–419 (1975)
3.
Louvass-NagyV. and PowersD., ‘On under-and-over determine initial value problems’, Int. J. of Control, 19, No. 3, pp. 653–656 (1974)
4.
VibetC., ‘Initial condition check in differential equations’, Simulation, Int. J. of Software Applic. (May, 1987). See also: Systèmes Non-Linéaires. Lectures course notes, Institut National des Télécommunications, Evry (ISBN 2-5331-03-8, Bibliothèque Nationale)
5.
KuY., Analysis and Control of Nonlinear Systems, The Ronald Press Company (1958)
6.
GearC., Differential-algebraic equations. Computer Analysis and Optimization of Mechanical System Dynamics, Iowa Univ. (August, 1983). Ed. HaugE., NATO ASI Series, Springer Verlag, pp. 323–334 (1984)
7.
SastryS.DesoerC. and VaraiyaP., ‘Jump behavior of circuits and systems’, MEMO No. UCB/ERL M80-44, Electr. Research Lab., Univ. of California Berkley (October, 1980)
8.
KuY., ‘Acceleration plane method for nonlinear oscillations’, Proc. of the Symp. on Nonlinear Circuit Analysis, N.Y., pp. 129–153 (April, 1953)
9.
VibetC., ‘General method of finding initial conditions’, IEEE Trans. on Educ. (Feb., 1988)
10.
DavisB., ‘Finding initial conditions in electr. circuits’, IEEE Trans. on Educ.E-29, No. 3, pp. 173–174 (August, 1986)
11.
VibetC., Cinématique, Dynamique et Contrôle des Robots, Ellipses Publish., Paris, in French (Summer, 1987)
12.
CotsaftisM. and VibetC., ‘Consistent impulse conditions in Lagrangian system dynamics’Robotica, 6, part 2 (1988)