Minimum‐variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling

Abstract

International audienceAdaptive optic (AO) systems are now routinely used in ground-based telescopes to counter the effects of atmospheric turbulence. A deformable mirror (DM) generates a correction wavefront, which is subtracted from the turbulent wavefront using measurements of the residual phase provided by a wavefront sensor (WFS). Minimizing the variance of the residual phase defines a sampled data control problem combining a continuous time minimum-variance (MV) performance criterion with a discrete-time controller. For a fairly general class of linear time-invariant DM and turbulence WFS models, this control problem can be transformed into an equivalent discrete-time LQ optimization problem involving a set of (discrete-time) control-sufficient statistics of the incoming continuous-time turbulence. This paper shows how to constructively solve this MV problem in the presence of DM's dynamics, starting from continuous-time models of DM and turbulence. This result is extended to the case of asynchronous DM/WFS sampling. An illustrative application to optimal control of tip-tilt turbulent modes for the European extremely large telescope in the presence of first-order DM's dynamics is presented

SPHERE eXtreme AO control scheme: final performance assessment and on sky validation of the first auto-tuned LQG based operational system

“…As a result, in this mode, vibration filtering is shut down at the LQG control level (corresponding parts of matrices set to zero). This is a clear limitation that could be easily corrected accounting for global delay in the pseudo-open loop data computation and in the control law as discussed in [18] for instance.…”

Mirrors' dynamics: A plague for adaptive optics systems performance?

“…, u M −1 which minimizes J p M thus defines a sampled-data MV control problem, which will be reformulated as a standard discrete-time LQG control problem. As noted in the introduction, this particular result is not new: constructive formula enabling to solve this equivalent LQG problem have been proposed in previous contributions and applied to a number of different AO systems and configurations ( [1], [4], [10], [8], [6], [11], [7]). …”

“…The approach in this paper is a streamlined version of the construction in ( [4], [6], [7]). The main difference is that in those papers the complete information case was defined as knowledge value of the disturbance φ tur up to time t = (k + 1)T s .…”

“…The proposed approach streamlines and extends the sampled-data LQG approach proposed in previous papers ( [1], [4], [5], [6], [7], [8]), which yielded constructive but (relatively) cumbersome to compute solutions. The new formulation enables to break down the original control performance criterion (continuoustime residual phase variance) into a sum of contributions which, for a given linear time-invariant controller, can all be computed using standard state-space control design routines.…”

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data

“…A proportional-integral (PI) controller is a widely used control algorithm in AO [ 27 , 28 , 29 ]. However, with the construction of extremely large telescopes, the demanding requirements and challenging features increase, which causes the new generation of AO systems to require the implementation of more sophisticated identification and control techniques [ 1 ], such as linear-quadratic Gaussian (LQG) [ 1 , 5 , 7 , 29 ], minimum variance control (MVC) [ 26 , 30 ], or model predictive control (MPC) [ 31 ]. Notice that, in [ 26 ], the authors show that MVC is an equivalent representation of the typically used LQG controller for AO systems.…”