Optimal sizing and placement of piezo-actuators for active flutter suppression

Abstract

The purpose of this work is to design an active control system for flutter suppression of a laminated plate wing model using segmented piezo-actuators. We describe investigations pertaining to the optimal size, thickness and locations of piezo-actuators on a laminated plate-wing structure for flutter suppression. The analysis for the laminated composite wing model is conducted by the Ritz solution technique, which represents the displacement on the plate in terms of power series in spanwise and chordwise directions. The active control system design for flutter suppression requires the equation of motion to be expressed in a linear time-invariant state-space form. The doublet-lattice method is used to compute unsteady aerodynamic forces, which are approximated as the transfer functions of the Laplace variable by the minimum-state method combined with an optimization technique. To design the control system, linear quadratic regulator theory with output feedback is considered in this study. The feedback control gains are obtained by solving coupled nonlinear matrix equations via numerical optimization routines. The optimal geometry of piezo-actuators which minimizes the control performance index is determined by the optimization technique referred to as the sequential linear programming method. The numerical result shows a substantial saving in control effort compared with the initial model.