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Modelling and parameter estimation for distributed vibratory systems. (English) Zbl 0602.93022
Distributed parameter systems, Proc. 2nd Int. Conf., Vorau/Austria 1984, Lect. Notes Control Inf. Sci. 75, 280-311 (1985).
[For the entire collection see Zbl 0572.00027.]
As noted in the subtitle, this paper is a survey of research projects and, therefore, does not constitute a research paper as such, but is a manifest of how mathematical theory, numerical analysis and empirical facts should be brought together to constitute a praxis-oriented control theory. As for its relevance in engineering problems, experimental investigations of the frequency distribution of several thin elastic beams of different complexity are presented. It is found that, according to the frequency dependent damping, due to the action of internal parameters, a dissipation term should be taken into account. One of the inverse problems outlined in an exemplaric manner is as follows: given the empirical distribution of the frequencies (or power spectrum) find the mass density (etc.) of the underlined vibratory system. The theoretical treatment usually culminates in a moment problem. The principle is demonstrated with the aid of some particular string and beam models, part of them have come to be known as flexible structures.
Reviewer: G.Leugering

MSC:
93B30 System identification
74H45 Vibrations in dynamical problems in solid mechanics
93C20 Control/observation systems governed by partial differential equations
35P15 Estimates of eigenvalues in context of PDEs
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
68U20 Simulation (MSC2010)
93C05 Linear systems in control theory