TY - GEN
T1 - Exact periodic solution for control system containing static nonlinear function
AU - Boiko, I.
PY - 2006
Y1 - 2006
N2 - A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity and linear dynamics is presented. The solution is designed as an iterative algorithm of refinement of the approximate solution obtained via application of the describing function (DF) method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system and the concept of the periodic signal mapping applied to the latter. The solution is sought for as a fixed point of the periodic signal mapping. It is shown that the DF method can be viewed as a method of approximate calculation of the periodic signal mapping. It is proved via the exact approach that for the considered type of nonlinear systems, the necessary conditions of sliding mode existence, previously obtained via the DF method, are valid. The proposed approach is illustrated by examples of analysis of periodic motions in nonlinear systems.
AB - A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity and linear dynamics is presented. The solution is designed as an iterative algorithm of refinement of the approximate solution obtained via application of the describing function (DF) method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system and the concept of the periodic signal mapping applied to the latter. The solution is sought for as a fixed point of the periodic signal mapping. It is shown that the DF method can be viewed as a method of approximate calculation of the periodic signal mapping. It is proved via the exact approach that for the considered type of nonlinear systems, the necessary conditions of sliding mode existence, previously obtained via the DF method, are valid. The proposed approach is illustrated by examples of analysis of periodic motions in nonlinear systems.
UR - http://www.scopus.com/inward/record.url?scp=33845579820&partnerID=8YFLogxK
U2 - 10.1109/VSS.2006.1644509
DO - 10.1109/VSS.2006.1644509
M3 - Conference contribution
AN - SCOPUS:33845579820
SN - 1424402085
SN - 9781424402083
T3 - Proceedings of the 2006 International Workshop on Variable Structure Systems, VSS'06
SP - 149
EP - 154
BT - Proceedings of the 2006 International Workshop on Variable Structure Systems, VSS'06
T2 - 2006 International Workshop on Variable Structure Systems, VSS'06
Y2 - 5 June 2006 through 7 June 2006
ER -