Dynamics and Control of Membrane Mirrors for Adaptive Optic Applications
Current and future space exploration operations rely heavily on space-borne telescopes, of which mirrors are an integral component. However, traditional solid mirrors are heavy and require a big storage space. Deploying membrane mirrors can alleviate many of these obstacles. Membrane mirrors are light and can be compactly stowed resulting in cheap launching costs. It was also demonstrated that membrane mirror would provide quality optical imaging capabilities.
However, membrane mirrors exhibit undesirable vibrations that can be caused by thermal gradients or internally-induced excitations. The undesirable vibration degrades the performance of these mirrors. Hence, it is proposed to augment membrane mirrors with smart actuators around their outer rim. Smart actuators can be used to suppress the undesirable vibration. More importantly, such a system provide the capability to form appropriate surfaces to correct for aberrations in an incoming wavefront.
In this spirit, this work aims at modeling and control a membrane mirror augmented with smart actuators. The approach here to consider a membrane strip augmented with smart actuators as a prelude for studying circular membranes. We consider strips of membrane material, and treat two such structures: a membrane strip augmented with a single piezoceramic bimorph acting in bending, and a membrane strip augmented with multiple macro-fiber composite bimorphs. The later structure is studied under two actuation configurations. In the first configuration, both actuators act in bending. In the other configuration, one actuator acts in bending and the second acts in tension. The developed models of both structures were validated experimentally. Then, control laws were derived for both structures. An optimal proportional-integral controller is used for the membrane strip augmented with a single piezoceramic bimorph. For the membrane strip augmented with two macro-fiber composite bimorphs, a sliding mode controller with a switching command is used. Simulation results are presented to demonstrate the efficacy of the proposed control laws.
Then, a circular membrane augmented with macro-fiber composite bimorph actuators is considered. We derive the governing equation of the structure for the general configuration, where actuators are producing bending moments and radial loading. Then, we seek a reduced order model of the structure. We work on obtaining a Galerkin expansion of the model where the test functions used are the mode shapes of the structure as obtained from a finite element analysis conducted in a commercial software package. Then the control problem is considered. The objective is to correct for optical aberrations, so the Zernike polynomial basis functions are used. A transformation from the optical modes to the mechanical modes is presented and an augmented adaptive controller is used to correct for image aberrations. The results presented show the efficacy of the controller.