H infinity controller design for adaptive optics systems

Adaptive optics is used to enhance the capability of optical systems by actively compensating for aberrations. These aberrations, such as atmospheric turbulence, optical fabrication errors, thermally induced distortions, or laser device aberrations, reduce the peak intensity and smear an image or a laser beam propagating to a target. The twinkling of stars or distorted images across a paved road on a hot summer day is caused by turbulence in the atmosphere. Distortions like these were corrected by adaptive optics for a long time. The principal uses for adaptive optics are improving image quality in optical and infrared astronomical telescopes, imaging and tracking rapidly moving space objects, and compensating for laser beam distortion through the atmosphere. Adaptive optics system consists of a wave front sensor, deformable mirror and a control unit. The basic operating principle of adaptive optics system is detection, calculation and activation. First the distortion in the wavefront is determined by the sensors. Then, the control unit derive DM up to takes the shape in the reverse form of distorted wavefront and the wave reflected front face of the mirror would be corrected. Many problems particularly (long distance secure wireless communication, laser weapons, imaging systems etc.) needed for adaptive optics systems in the defense industry, not yet produced in our country at the moment. The main reason is that the system can not easily be controlled with conventional methods or the inability to reach the desired success rate with this method. For example, because of absence of the adaptive optic system in laser damage or blinding system, manufacturers are forced to enhance their laser power. Sufficient energy density to destroy the target cannot be formed without eliminated atmospheric distortions. In order to obtain an applicable control system, the problem needs to be solved as an optimization problem with a proper definition of the performance index. The main objective of the adaptive optics system is to handle the deformation control because the main component of the system is deformable mirror. Deformable mirror consist of a flexible reflective surface derived by the piezoelectric or MEMS type actuators. The realistic model of the system's surface derived by actuators under the flexible layer includes spatial changes with temporal changes. The mathematical model of DM can be expressed by Kirchhoff-Love Surface theory which is derived from Euler Bernoulli's flexible rods equation generalized in two dimension. This representation is hosted in the class of infinite-dimensional system due to partially differential equations (PDE). Model reduction must be used to control such a system optimally. By this way, infinite-dimensional systems can be reduced approximately to finite-dimensional systems. the aim of this project is to provide H sonsuz optimal controller for adaptive optical systems.