Research on nonsmooth H∞ control for the adaptive optics system

To design an adaptive optics robust controller with the characteristics of simple structure and low orders, a nonsmooth H∞ control method for the adaptive optics system was proposed. The full order H∞ controller and the reduced order H∞ controller were designed by conventional H∞ control method combined with model reduction based on Hankel singular values. And the orders of the controllers are 226 and 163 respectively, whereas the nonsmooth H∞ controller designed for the system is simply the product of a constant matrix and a 4 order single input single output transfer function. For the sake of control performance verification and comparation, the dynamic atmospheric turbulence wavefront phase was simulated, as well as the residual wavefront phase corrected by adaptive optics systems with the full order H∞ controller and with the nonsmooth H∞ controller. The simulation demonstrates that the two adaptive optics systems achieve approximate control performance, and proves the efficiency of nonsmooth H∞ control method for the adaptive optics system.