Constant and switching gains in semi-active damping of vibrating structures

摘要

We consider the problem of optimal control of vibrating structures and we analyse the solution provided by collocated semiactive decentralised damping devices. We mainly consider the H _∞ criterion and we first study the case of constant dampers, showing that in the case of a single damper the performance is a quasi-convex function of friction so there is a single local minimum which is a global one. The case of multiple dampers does not exhibit this feature and time-expensive computations may be required. Secondly, we consider the case in which dampers may be tuned on line, and in particular the case in which they work in a switching on-off mode. We propose a state-switching feedback control strategy, which outperforms the constant damping approach with the optimal static gain performance as an upper bound. For large distributed flexible structures, state feedback is unrealistic and so we propose a stochastic strategy based on a Markov-jump criterion for which the transition probability are not assigned but designed to optimise average performance, with guaranteed asymptotic stability. Finally, we show that the same result provided for the H _∞ case holds for the H _2 and the l _1 criteria.