Active control law design for flutter suppression and gust alleviation of a panel withpiezoelectric actuators

Abstract

This paper presents an active optimal integral/feedforward control for a supersonic panelunder gust disturbance effects with piezoelectric actuators. Classical laminate theory withinduced strain actuation and a generalized form of Hamilton’s principle are used toformulate the governing equations of motion. The total charge developed on thesensor layer is calculated from the direct piezoelectric equation. The piezoelectricsensor distributed output is also integrated, since the output voltage is dependenton the integrated strain rates over the sensor area. Aerodynamic modeling isaccomplished by first-order piston theory with gust velocity effects. The modelreduction is performed to the state space system of equations for the controldesign and the time domain simulation. Moreover, the disturbance dynamics aremodeled through the addition to the equations of motion for various conditions.The optimal control problem is set up to minimize the panel deflection usinga linear quadratic regulator (LQR). Using an integral control model as a partof the feedback loop, together with a feedforward of the disturbances, greatlyenhances the transient response, and the steady state error characteristics of thissystem are observed. Also, parametric studies for three piezoelectric actuatorconfigurations are demonstrated. Simulation results show that the controller model iseffective for flutter suppression and gust alleviation for various piezo configurations.