- Development of Fixed-Order Hinf sub-Optimal Controller for Adaptive Optical Systems
- Principle Investigator: Akın Delibaşı, Researcher: Mustafa Kurt
- 2018 – 2021
Adaptive optics are 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, already cannot be produced in our country at the moment. The main reason is that the system can not be easily controlled with conventional methods or the inability to reach the desired success rate with these methods. For example, because of absence 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 solve 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 partial differential equations (PDE). Model reduction must be used for providing to optimal control in such system. By this way, infinite-dimensional systems can be reduced approximately to finite-dimensional systems. Moreover, the main disturbance factors in an optic system are atmospheric turbulences. It is need to be a high degree expression for realistic atmospheric turbulence model (the combination of the first 15 functions of Zernike polynomials can be defined realistic models in accuracy 92). As a result, the degree of the entire system model is very high and It cannot produce satisfactory results in practice be controlled by a controller of the same order of the system.
The aim of this project is to provide fixed-order H? sub-Optimal Controller for Adaptive Optical Systems. Order of standard optimal H? controller needs to be at least the same order as system?s one. This type of controller is named as full degree controller in the literature. Due to the limitation in design, the final degree of closed loop system is doubled. Engineers, who work in the space and aerospace industry, always avoid using high order controller, because high order systems can be highly sensitive to changes in the parameters. In addition, to implement embedded systems with full order controllers is quite difficult. Therefore, one of the major problems in the computer aided controller systems is to design fixed-order controller. The main difficulty in the development of fixed-order controllers is that the associated stability region in the space of coefficients of the closed-loop characteristic polynomial is non-convex in general. In order to cope with this problem, inner and outer convex approximation techniques are used. Due to the outer approximations can only provide the necessary condition on the stability, we focus on inner approximation techniques on this project to obtain a sufficient condition.