Optimal Placement of Piezoelectric Actuated Trailing-Edge Flaps for Helicopter Vibration Control

Abstract

This study aims to determine the optimal locations for dual trailing-edge flaps on a helicopter blade in the presence of actuator hysteresis. An aeroelastic analysis based on a finite element approach in space and time is used in conjunction with an optimal control algorithm to determine the actuator control input for vibration minimization. The reduced hub-vibration level and the flap power are the two optimization indices considered in this study. The location of the flaps along the blade are the design variables. The hysteresis in the piezo-actuators is modeled using a dynamic hysteresis model based on an extension to the classical Preisach model. It is found that second-order polynomial response surfaces based on the central composite design of the theory of design of experiments describe both objectives adequately. Numerical studies for a four-bladed hingeless rotor show that both objectives are more sensitive to outboard flap location compared with inboard flap location. Optimization studies indicate that the dual-flap configuration for the least hub-vibration level is different from the configuration for the least flap power. The Pareto front between the two objectives is found to be discontinuous. However, a reasonable tradeoff configuration is obtained by careful inspection of the Pareto front. This configuration yields about a 70% reduction in hub-vibration levels from the baseline conditions at an advance ratio of 0.30, while requiring about 21% more flap power from the initial configuration of the optimization study.