Structure of LQG Controllers Based on a Hybrid Adaptive Optics System Model

The effects of a controller on the residual wavefront variance in an adaptive optics system can be represented by a discrete-time system. Consequently, the controller design that minimizes the wavefront is given by the solution of a discrete-time Linear-Quadratic-Gaussian (LQG) problem. The purpose of this paper is to analyze the structure of the LQG controller that minimizes the residual wavefront variance. It is shown that the LQG controller is an integral controller when the DM has no dynamics, there is no computational delay (the total loop delay is one frame), and the PSD of the incident wavefront decreases by f–2 at all frequencies. Non-zero computational delays result in a multivariable generalization lead element being added to the controller with the zero of the lead element at the origin.