Naslov
Lyapunov optimization of a damped system

Autori
Cox, Steven J. ; Nakić, Ivica ; Rittmann, Annette ; Veselić, Krešimir

Izvornik
Systems & control letters (0167-6911) 53 (2004), 3-4; 187-194

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Damped vibrational systems ; Optimal damping ; Parametrized damping

Sažetak
Our aim is to optimize the damping of a linear vibrating system. The penalty function is the average total energy, which is equal to the trace of the corresponding Lyapunov solution. We prove the existence and the uniqueness of the global minimum, if the damping varies over the set of all possible positive definite matrices. The minimum is shown to be taken on the so-called modal critical damping, thus confirming a long existing conjecture. We also give some preliminary results concerning dampings which depend linearly on the viscosity parameters whereas the damper positions are kept fixed. We produce physical examples on which the minimum is taken on a negative viscosity or which have several local minima. Both phenomena seem to be a consequence of a bad choice of the damper positions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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