Foued Ben Amara

Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems

Magnetic-fluid deformable mirrors (MFDMs) offer a simple alternative to the costly yet inefficient wavefront correctors currently in use in adaptive optics (AO) systems. They have been found particularly suitable for AO systems used in ophthalmic applications, such as retinal imaging. However, their practical implementation in clinical devices is contingent on the development of effective methods to model and control their surface-shape. This article presents a model of the dynamic response of the surface of a MFDM to the applied magnetic field. The resulting model allows the development of high-performance shape control algorithms for the mirror surface.

Regulator Synthesis for Bimodal Linear Systems

This technical note presents a regulator synthesis approach for switched bimodal linear systems where it is desired to achieve regulation against known disturbance or reference signals. First, a set of observer-based Q-parameterized stabilizing controllers for the switched system is constructed. Then regulation conditions for the switched system are obtained and a regulator synthesis method is derived based on iteratively solving a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

Mixed-Sensitivity

This paper presents an H∞ controller designed to cancel dynamic wavefront aberrations in an adaptive optics (AO) system based on a magnetic-fluid-deformable mirror (MFDM). MFDMs are a recently proposed novel type of active optical elements called wavefront correctors, which constitute the central part of AO systems. They offer cost and performance advantages over existing wavefront correctors. MFDMs have been found particularly suitable for ophthalmic imaging systems where they can be used to compensate for the complex optical aberrations in the eye that blur the images of the internal parts of the eye. However, their practical implementation in clinical devices is hampered by the lack of effective methods to control the shape of their deformable surface. Specifically, control algorithms that can be used to cancel dynamically varying wavefront aberrations need to be developed. This paper presents one such control algorithm that can be used to compensate for high-order time-varying optical aberrations using an MFDM. The control algorithm is developed using the mixed-sensitivity H∞ design method that enables the tracking of the desired MFDM surface shape and also limits the magnitude of the control currents applied to the MFDM. Experimental results showing the performance of a closed-loop system comprising the developed controller and a 19-channel prototype MFDM are presented.

H_\infty

This article presents an analytical model for the dynamic surface shape of a magnetic fluid deformable mirror (MFDM) in cylindrical coordinates. Such a mirror is proposed as a high-performance alternative to existing costly and fragile wavefront correctors in ophthalmic adaptive optics systems. Results of an experimental investigation aimed at validating the developed analytical model are also presented. A novel approach to linearize and amplify the response of the MFDM surface to the applied magnetic field is introduced and experimentally validated. The developed model will make it possible to design effective surface shape control algorithms for the mirror.

Control of Magnetic-Fluid-Deformable Mirrors

In this paper, the design of multivariable proportional-integral-derivative (PID) controllers for discrete-time systems based on linear matrix inequalities (LMIs) is studied. First the stability problem of the closed-loop system with the multivariable PID controller is investigated. To adjust the transient response of the resulting closed-loop system, the design method is extended to account for a pole clustering constraint. PID controller design methods that yield closed-loop systems with H∞ and H2 performance specifications are then investigated. Algorithms based on properly formulated LMIs are developed for the above different cases. Finally, the performance of the proposed controllers is experimentally evaluated in an adaptive optics system where it is desired to control the shape of a magnetic fluid deformable mirror. The experimental results indicate the proposed controllers can successfully provide the desired shape tracking performance in the closed-loop adaptive optics system.

Modeling and Experimental Evaluation of a Circular Magnetic-Fluid Deformable Mirror

This paper presents the first-ever experimental evaluation of a closed-loop adaptive optics system based on a magnetic fluid deformable mirror (MFDM). MFDMs are a new type of wavefront correctors used in adaptive optics systems to compensate for complex optical aberrations. They have been found particularly suitable for ophthalmic imaging systems where they can be used to compensate for the aberrations in the eye that lead to blurry retinal images. However, their practical implementation in clinical devices requires effective methods to control the shape of their deformable surface. This paper presents one such control method which is based on an innovative technique used to linearize the response of the MFDM surface shape. The design of the controller is based on a DC-decoupled model of the multi-input multi-output system and on considering a decentralized PI controller. Experimental results showing the performance of the closed-loop system comprising the developed controller and a 19-channel prototype MFDM are presented.

LMI-Based Multivariable PID Controller Design and its Application to the Control of the Surface Shape of Magnetic Fluid Deformable Mirrors

Maintaining a constant small flying height of the read/write head is an important target in the design of the ultra high storage density hard disk drives. One effective way to achieve this goal is to use a feedback regulator to suppress the flying height variations. For low flying heights, the read/write head enters into intermittent contact with the disk surface, which results in a switched system regulation problem. In this paper a new control method is proposed to maintain the flying height at its desired value based on the switched system models, despite the unknown microwaviness in the disk surface profile and the unpredictability in the switching times. First, a switched system model is constructed. Then, a Q parameterized set of switched regulators is constructed and the stability of the resulting switched closed loop system is analyzed. Online adaptive regulator tuning is then performed by adjusting the Q parameter in the controller to achieve regulation. Simulation results are presented to illustrate the effectiveness of the proposed method.Copyright

Closed-loop control of magnetic fluid deformable mirrors.

This article presents a systematic approach to the design of a decentralized robust PID controller to regulate the surface shape of a magnetic fluid deformable mirror (MFDM). The proposed approach offers the simplicity of the decentralized controller implementation while accounting for robustness and performance constraints. The controller design problem is formulated as a multi-objective H ∞/H 2 static output feedback problem. The desired controller is obtained by iteratively solving properly formulated linear matrix inequalities (LMIs). Finally, the experimental evaluation of the proposed controller performance on a MFDM-based adaptive optics system illustrates the effectiveness of the proposed MFDM surface shape control approach.

Flying Height Control for a 2-DOF Tripad Slider in Hard Disk Drives With Switched Regulator

This paper presents experimental results on the adaptive exact output regulation in a switched bimodal mechanical system subject to unknown sinusoidal exogenous inputs representing reference or disturbance signals. The adaptive regulator design exploits the Q parameterization of regulators for the switched system, and where the Q parameter is tuned online to yield the desired regulator. The proposed adaptive regulator is evaluated on an experimental setup motivated by the flying height regulation problem in hard disk drives. In the experimental setup, the tip of a flexible beam is supposed to maintain a constant separation with respect to a surface with an unknown profile, while also being subject to an unknown disturbance force. The system exhibits a switching behaviour depending on whether contact takes place between the surface to be tracked and the tip of the beam. The experimental results successfully demonstrate the effectiveness of the proposed approach in achieving exact output regulation against unknown sinusoidal exogenous inputs and in the presence of switching in the system dynamics.

A Decentralized Robust PID Controller Design for the Shape Control of a Magnetic Fluid Deformable Mirror

A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.