Open AccessSampled‐data control of coupled harmonic oscillators using measured position states only
Author(s) -
Zhang Hua,
Ji Jinchen,
Wu Quanjun
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.1232
Subject(s) - eigenvalues and eigenvectors , control theory (sociology) , laplacian matrix , correctness , position (finance) , harmonic oscillator , mathematics , sampling (signal processing) , harmonic analysis , range (aeronautics) , harmonic , laplace operator , topology (electrical circuits) , computer science , mathematical analysis , algorithm , control (management) , physics , engineering , finance , quantum mechanics , filter (signal processing) , artificial intelligence , combinatorics , economics , computer vision , aerospace engineering
This brief study investigates the synchronisation of undirected coupled harmonic oscillators by using a sampled‐data control strategy. In the absence of measured velocity information, each of the networked oscillators can only obtain the measurements of the position states relative to its neighbours at the sampling moments. A distributed protocol based on the sampled relative position measurements at a series of time instants is proposed for the coupled harmonic oscillators. Necessary and sufficient conditions for achieving synchronisation are analytically established in virtue of the graph theory, matrix analysis theory and Schur stability theory of cubic polynomials. Theoretical results indicate that the explicit range that contains all the desirable sampling periods is uniquely determined by the largest eigenvalue of the Laplacian matrix associated with the network graph and the position gain of the harmonic oscillators. An effective simple iterative method is then developed to calculate the range in which the desirable sampling periods fall. Finally, numerical simulations are performed to illustrate the correctness of the theoretical results and effectiveness of the proposed protocol.