Abstract-Iterative learning control (ILC) is a very effectivetechnique to reduce systematic errors that occur in systems that repetitively perform the same motion or operation. However, several characteristics have prevented standard ILC from being widely used for high precision motion systems. Most importantly, the learned feedforward signal depends on the motion profile (setpoint trajectory) and if this is altered, the learning process has to be repeated. Secondly, ILC amplifies non-repetitive disturbances and noise. Finally, its performance may be limited due to position-dependent dynamics. This paper presents the design and implementation of a time-frequency adaptive ILC that is applicable for motion systems which executes the same motion or operation. It employs the same control system block diagram as standard ILC, but instead of a fixed robustness filter it uses a time-varying filter. By using the results of the time-frequency adaptive ILC, i.e., the shape of the learned feedforward signal, a "piecewise ILC" is proposed that leads to the design of a single learned feedforward signal suitable for different setpoints. The results are experimentally shown to work for a high precision motion system.

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A new prototype adaptive deformable mirror for future AO-systems is presented that consists of a thin continuous membrane on which push-pull actuators impose out-of-plane displacements. Each actuator has ±10µm stroke, nanometer resolution and only mW's heat dissipation. The mirror's modular design makes the mechanics, electronics and control system extendable towards large numbers of actuators. Models of the mirror are derived that are validated using influence and transfer function measurements. First results of a prototype with 427 actuators are also presented.

Future large optical telescopes require adaptive optics (AO) systems whose deformable mirrors (DM) have ever more degrees of freedom. This paper describes advances that are made in a project aimed to design a new AO system that is extendible to meet tomorrow's specifications. Advances on the mechanical design are reported in a companion paper , whereas this paper discusses the controller design aspects. The numerical complexity of controller designs often used for AO scales with the fourth power in the diameter of the telescope's primary mirror. For future large telescopes this will undoubtedly become a critical aspect. This paper demonstrates the feasibility of solving this issue with a distributed controller design. A distributed framework will be introduced in which each actuator has a separate processor that can communicate with a few direct neighbors. First, the DM will be modeled and shown to be compatible with the framework. Then, adaptive turbulence models that fit the framework will be shown to adequately capture the spatio-temporal behavior of the atmospheric disturbance, constituting a first step towards a distributed optimal control. Finally, the wavefront reconstruction step is fitted into the distributed framework such that the computational complexity for each processor increases only linearly with the telescope diameter.

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