Design of the oscillatory systems with the extremal dynamic properties

Bulletin of the Polish Academy of Sciences. Technical Sciences

M. ZaczykAGH University of Science and Technology, Department of Automatics and Biomedical Engineering, 30 Mickiewicza Ave., 30-059 Kraków, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹  H. GóreckiAGH University of Science and Technology, Department of Automatics and Biomedical Engineering, 30 Mickiewicza Ave., 30-059 Kraków, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, 30 Mickiewicza Ave., 30-059 Kraków, Poland

关键词: Keywords: extremal dynamic properties;    oscillatory systems;    symmetrical equations;    regions of the roots;   

DOI  :  10.2478/bpasts-2014-0024

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

In this article the problem of determination of such coefficients a1, a2, ..., an and eigenvalues s1, s2, ..., sn of the characteristic equation which yield required extremal values of the solution x(t) at the extremal value τ of time is solved. The extremal values of x(τ ) and τ are treated as functions of the roots s1, s2, ..., sn. The analytical formulae enable us to design the systems with prescribed dynamic properties. For solution of the problem the properties of symmetrical equations are used. The method is illustrated by an example of the equation of 4-th degree. The regions of the different kinds of the roots: real, with one pair of complex and two pairs of complex roots are illustrated. A practical problem is shown.

【 授权许可】

Unknown