| Adaptive optics, one of the most exciting advances in optical imaging in decades,is a discipline developed for the sake of astronomical observation. Almost all groundtelescopes are equipped with adaptive optics systems nowadays. With the deepeningof the research, several subfields of adaptive optics are developed to solve morepractical problems. Adaptive optics systems have been applied to space borne opticalsystems, airborne laser weapons systems, laser fusion systems, laser communicationsystems, human retinal imaging systems，and so on. The research on control foradaptive optics is an important direction for adaptive optics. Focusing on improvingstability and performance of adaptive optical systems, theoretical and experimentalstudies are carried out in this study.The research is started on a test platform for the adaptive optics system inFraunhofer Institute for Applied Optics and Precision Mechanics in Germany. Thepiezoelectric deformable mirror, which is adopted as the wavefront corrector in thistest platform, is the most commonly used wavefront corrector in adaptive optics. Ithas many advantages, such as low cost, rapid correction and large deformation. Thedisadvantage is the presence of hysteresis phenomenon, which is a typical nonlinearphenomenon. To compensate for the effects caused by the hysteresis phenomenon,we must first measure the hysteresis. I participated in building the test platform forthe adaptive optics system, which can achieve not only hysteresis measurement butalso real-time disturbance correction. The major hysteresis loop of the piezoelectricdeformable mirror is measured and researched. An adaptive optics system controlmethod based on linear fitting and an adaptive optics system control method basedon lookup table are proposed to compensate the hysteresis, and achieve stablecontrol of the system. LabVIEW programs are written to realize the control of theadaptive optics system. Experimental results show that the both proposed methodsachieve a real-time and stable disturbance correction.Hysteresis of the deformable mirror, thermal effects, and so on, can be modeledas multiplicative uncertainty. The robust control methods can ensure the systemstability in the presence of the multiplicative uncertainty. The robust stability meansthat the system remains stable in the presence of uncertainty. H-infinity control is a typical robust control method. Over the past decade, H-infinity control for theadaptive optics system has been proposed and applied preliminarily. In this study, thesystem modeling was based on a test platform for adaptive optics system in Xi’anInstitute of Optics and Precision Mechanics of Chinese Academy of Science. Thisstudy proposes a mixed H2/H-infinity control method for the adaptive optics systemto ensure system robust stability and to further improve system performance. Theproposed method is compared with the H-infinity control for adaptive optics systemsand the integral control which is the most common adaptive optics system controller.The simulation programe of static and dynamic atmospheric turbulence wavefrontphase is developed based on Taylor’s frozen hypothesis and atmospheric turbulencewavefront simulation method by Zernike polynomials. The residual wavefront phasecorrected by adaptive optics systems with the three kinds of controller is compared.The robust stability of the three systems is compared as well. The simulationexperiment result shows that the system with the mixed H2/H-infinity controllerachieved not only small residual wavefront phase but also good robust stability.Under the premise of the same robust stability, the residual wavefront phase rms ofthe mixed H2/H-infinity control system is16.7%smaller than that of the H-infinitycontrol system and37.1%smaller than that of the classic integral control system.Meanwhile, the order of the mixed H2/H-infinity controller and the order of theH-infinity controller are both equal to the order of the generalized plant, whichmeans the mixed H2/H-infinity control method neither introduces more complexitynor achieves higher order controller than the H-infinity control method. The resultproves the superiority of the mixed H2/H-infinity control method for the adaptiveoptics system.How to achieve the low-order and simple-structured robust controller, andguarantee the performance as well, is an important research direction for robustcontrol. That the low-order and simple-structured robust controller is adopted in theadaptive optical system can reduce the delay of operation time and the difficulty ofcontroller realization. The nonsmooth H-infinity control method is proposed todesign an adaptive optics system controller with the characteristics of simplestructure and low orders. The controller for our system is simply the product of aconstant matrix and a four-order single-input single-output transfer function. Tocompare with the nonsmooth H-infinity control method, the full order H-infinitycontroller and the reduced-order H-infinity controller are designed by the conventional H-infinity control method and balanced model reduction method. Theorders of the two controllers are226and163respectively. For the sake of controlperformance verification and comparison, the residual wavefront phase corrected byadaptive optics systems with the nonsmooth H-infinity controller and with the fullorder H-infinity controller is simulated. The simulation demonstrates that the twoadaptive optics systems achieve approximate control performance, which proves theefficiency of the nonsmooth H-infinity control method for the adaptive opticssystem. |
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