Nonlinear control of PZT actuated trailing edge flaps

While PZT exhibits 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 designto amplify the stroke of PZT-based actuation likewise can couple with this material nonlinearity to yield a structural level nonlinearity that is non-negligible. 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 recent results of [18,19] for the derivation of closed loop control for active material actuated devices. In this technique, a compensator derived from an offline identification of a Krasnoselski-Pokrovski hysteresis operator is cascaded with the plant. We show that the methodology is well-posed for the class of problems under consideration; we derive 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.