Hybrid Position Feedback Controller for Inducing Cross-Well Motion of Bistable Structures

Abstract

A hybrid position feedback controller based on the well-known positive position feedback controller for bistable structures is presented. The proposed controller is a hybrid unstable-then-stable position feedback controller, which is a second-order single-degree-of-freedom system in nature. The controller takes advantage of the resonant mode of a bistable system about one equilibrium position, destabilizes the system, and dynamically induces snapthrough between the two equilibria. The proposed method is demonstrated on a bistable unsymmetric cross-ply composite platelike structure with surface-bonded piezoelectric actuators. The control scheme is shown to eliminate undesirable cross-well oscillations leading to a monotonic state crossover. An experimentally validated parametric analysis is also presented. Essential properties observed in theoretical and numerical analyses, such as the nondynamic stability and stability gain limit for the positive position feedback controller and the wide unstable bandwidth for the negative position feedback controller, are validated with experiments.