Enhancement of sound transmission through an aircraft structure modeled as a doubly curved shell under uncertainty considering robust H ∞ controller

Abstract

This study aims to design a robust $H_{\infty }$ based piezoelectric active controller to enhance sound transmission loss (STL) of a doubly curved bimorph shell replicating aircraft structural parts under uncertain operating conditions. Mach number, incidence, and azimuth angles are considered as the sources of uncertainty since their values change according to the atmospheric conditions. The open-loop generalized plant of the bimorph shell is formed by using the shear deformation shallow shell theory and Hamilton’s principle considering piezoelectric constitutive equations. Weighting transfer functions are employed to bound the STL response, controller voltage, and incidence acoustic wave disturbance. The closed-loop simulation results show both effects on uncertainty minimization and STL enhancement when applying the relatively simple $H_{\infty }$ controller. This controller proposes more enhancement in STL compared to classical control algorithms. Also, by applying the performance weights, the piezoelectric actuator voltage is decreased which prevents controller overload and actuator rupture. Hence, this design provides a sufficient replacement for relatively classical controllers considering robust STL enhancement in doubly curved shells.