Optimal control of supersonic pre-twisted rotating functionally graded thin-walled blades

Abstract

In this paper, the optimal vibration control of a rotating, pre-twisted, single-celled box thin-walled beam made of functionally graded material is discussed. This beam is under aerothermoelastic loading and warping restraint. A first-order shear deformation theory enabling satisfaction of traction-free boundary conditions is employed to achieve governing dynamical model. These equations include the effects of the presetting angle, the secondary warping, temperature gradient through the wall thickness of the beam, and also the rotational speed. Moreover, quasi-steady aerodynamic pressure loadings are determined using first-order piston theory, and steady beam surface temperature is obtained from gas dynamics theory. The extended Galerkin method is then used to transform the blade partial differential equations into a set of ordinary differential equations. Transversely isotropic sensor-actuator piezoelectric pairs that are surface embedded along the blade are also considered for the purpose of closed-loop control. An optimal observer-based output feedback control scheme is used to stabilize the closed-loop system. Simulation studies demonstrate the effectiveness of the proposed method.

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