Modeling and control of massively actuated, magnetically levitated, adaptive mirrors

Abstract

The successful design of non contact, magnetically levitated, massively actuated deformable mirrors and their control system requires the use of medium to high fidelity hybrid multidisciplinary simulation models, encompassing: deformable structures, fluid dynamics of the air film interposed between the mirror and its reference backplane, sensor and actuator dynamics, the control system. Such models must serve the diverse needs for the analysis, design and verification of a fully decentralized control solution and to simulate all of on the field operational phases including initial feedback design, the identification of the static feed-forward matrix and control self tuning. The paper presents the related modeling techniques along with a few results and experimental correlations validating various aspects of the presented capabilities.

Servo-fluid-elastic modeling of contactless levitated adaptive secondary mirrors

“…In this work it is also assumed that capacitive position sensors are ideally co-located to the actuation points. More detailed analyses proved the substantial negligibility of real measurements non co-location in assessing the dynamic response of a controlled mirror [12,13]. It is however worth noticing that the modeling of position sensors non co-location remains important for obtaining accurate evaluations of the control system forces, which do not represent an issue for the present work.…”

Self-Tuning Shape Control of Massively Actuated Adaptive Mirrors

“…On the contrary a constant α = 0.75 parameter (α scheme in Figs. 13) can assure stability as well as a smoother signal tracking. In this way average and absolute rms tracking error can be kept lower, as shown in Fig.…”

“…As shown in [15] the non co-location of the measures can be modeled through the computation of the motion dependent variable capacitance of the sensors circular electrodes. The present work highlights the importance to model such a non co-location, not only in order to correctly estimate the required system control forces, as shown in [13], [14], but also to obtain a realistic evaluation of the system stability. In fact, the intrinsic distributed nature of the position measures acts as a band-stop spatial filter with respect to a non negligible portion of the structural modal shapes, so limiting possible instabilities linked to spillover phenomena (see Subsec.…”

“…The resulting multiphysics problem has been handled through the development of appropriate models and ad hoc simulation tools. An accurate description of all the modeling choices, together with further details about the simulation code implementation and its ability to correlate with experimental data have already been presented in previous works [2], [13], [14], [3]. The aim of such detailed modeling is the development of an accurate simulator, not a system description suitable for the control system design.…”

“…The aim is to tune the feedback and FF parameters through a model free optimization to be carried out on the real system. Instead of looking for a globally optimal solution by a simultaneous optimization of all the control parameters [17], the strategy proposed here improves on an already suggested self-tuning [13], [15] by using a two steps optimization performed by repeatedly imposing a predefined training command vector time history d r (t).…”