Nonlinear Control Methodologies for Hysteresis in PZT Actuated On-Blade Elevons

Abstract

While piezoelectric (PZT) actuators exhibit only mild nonlinear response at low voltage levels, it is well known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise induces sources of mechanical hysteresis (friction, backlash, etc.) that can couple with this material nonlinearity to yield a structural scale nonlinearity that is nonnegligible. These two sources of hysteresis, due to mechanism response and nonlinear material response, are not easily decoupled. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the results of previous papers for the derivation of closed loop control for active material actuated devices. The goal is to derive a control methodology that accounts for the overall, total hysteresis due to material nonlinearities and mechanism response. In this technique, a compensator derived from an offline identification of a Krasnoselskii-Pokrovskii hysteresis operator is cascaded with the plant. We show that the methodology is well posed for the class of problems under consideration; we describe relevant closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results.