Modeling and Control of a 1-D Membrane Strip With an Integrated PZT Bimorph

Abstract

Ultra-lightweight, ultra-large and deployable satellite technology is at the forefront of research efforts for future on-orbit reconnaissance missions. The minimal mass and stowage volume associated with the technology are attractive traits for getting larger bandwidth satellites on-orbit. One of the key components for such a satellite is the membrane lens or aperture for optical or radar applications, and understanding the membrane’s dynamics is critical for mission success. As either an optical reflector or radar antenna, the vibration levels of the membrane must be minimized and eliminated. This work examines the possibility of integrating a PZT bimorph near the boundary of a strip sample to eliminate detrimental vibration. By starting with a 1-D model, the dominant governing phenomena of the system dynamics can be established and used to build more complex models with confidence. A physics-based finite element (FE) model of a thin strip of Kapton HN material with a monolithic PZT bimorph bonded near a boundary is developed in a MatLab environment and verified experimentally. The membrane strip under tension is modeled as a beam under axial load. In doing so, the FE model is able to capture the relevant transverse dynamics of the experimental setup. Having verified the FE model, an LQR controller is developed and simulated to demonstrate effective control over the transverse dynamics of the membrane sample.