Probabilistic Methods for Performance Evaluation of Actively Controlled Structures

Abstract

Abstract Active Structures have significant practical applications in areas such as vibration, noise and shape control. In recent times, several studies on modeling of the response and control of these structural systems have been undertaken. Most of these studies use deterministic procedures for designing the required active control systems, with the underlying assumption that the design parameters are accurately known. However, for most practical situations, the values of the design parameters are not known exactly and must therefore be treated as random variables. Parametric uncertainties can degrade the performance of an otherwise well designed control system, sometimes leading to instability. In this paper probabilistic models for evaluating the performance of actively controlled structures is presented. A closed loop damping ratio formulation is proposed for the determination of the probability of instability for such structures in the presence of real parameter uncertainties. Furthermore, a probabilistic model for evaluating the performance robustness of actively controlled systems in terms of margin of stability is developed. Advanced probabilistic reliability analysis algorithms namely the first order reliability methods (FORM) and the second order reliability methods (SORM) are used for the estimation of robustness. A comparison of estimates of the probabilistic stability robustness from the proposed closed loop damping ratio formulation and the eigenvalue model which has been employed in recent studies (Field, 1996; Spencer 1992) is undertaken. It is shown that both procedures yield the same result. However, the novel technique has the added advantage of computational efficiency for FORM and SORM applications. Furthermore, it is shown that for the class of controllers considered in this study, robustness estimates from FORM is adequate for meaningful engineering decisions. Sensitivities of the controlled structure stability robustness to uncertainties in model parameters is evaluated using the novel approach.