Zhizheng Wu

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

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.

Control of Magnetic-Fluid-Deformable Mirrors

Abstract Motivated by practical applications such as active vibration control and noise attenuation, this paper presents an adaptive Youla ( Q ) parameterized regulation approach to reject unknown sinusoidal exogenous inputs representing disturbance or reference signals. A weighted Ritz-type Q parameter is adopted to implement the adaptation algorithm and to shape the sensitivity functions of the resulting adaptive system. The proposed regulation approach is applied to a benchmark problem involving unknown vibration attenuation in an active suspension system. Both simulation and real time experimental results are discussed and analyzed to illustrate the effectiveness of the proposed adaptive regulation approach.

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

An adaptive regulation approach in linear systems against exogenous inputs consisting of a linear combination of sinusoids with unknown amplitudes, frequencies and phases is proposed within the framework of Youla parameterized stabilizing controllers. The goal of the developed adaptation algorithm is to search, within the set of weighted Ritz-type Youla parameters, for a controller that yields regulation in the closed-loop system. The proposed approach is applied to an active vibration control problem, and the performance of the developed regulator is illustrated by considering the vibration cancellation against exogenous inputs represented as a linear combination of unknown stationary as well as time-varying sinusoidal disturbances.

Youla parameterized adaptive regulation against sinusoidal exogenous inputs applied to a benchmark problem

The number of new adaptive optics applications has soared during the last decade, demonstrating the need for low-cost, high-stroke deformable mirrors with a large number of actuators. Magnetic fluid deformable mirrors (MFDMs) were proposed a few years ago as an alternative to conventional membrane deformable mirrors used in wavefront correctors. Though the idea of these magnetic fluid deformable mirrors is quite recent, they have been appraised by a number of preliminary studies as a promising future technology. This chapter first presents a brief review of the MFDM development history. The operating principle and composition of MFDMs are discussed, including a brief description of important properties of magnetic fluids and metal liquid-like films (MELLFs)—the key constituents of an MFDM. The known advantages, limitations, and potential applications of this new type of deformable mirrors are also discussed, followed by an outline of the research developments presented in the following chapters.

Youla parameterized adaptive regulation against unknown multiple narrow-band disturbances:

Motivated by a class of contact vibration control problems in mechanical systems, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against partially known deterministic and unknown random exogenous signals. First, a set of observer-based Youla parameterized stabilizing controllers is constructed, based on which the regulation conditions for the switched system against the deterministic signals along with an performance constraint against the unknown random signals are derived. Then a corresponding regulator synthesis algorithm is developed based on solving properly formulated linear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence, demonstrating the effectiveness of the proposed regulation approach.

Magnetic Fluid Deformable Mirrors

In this paper, the shape control problem for a magnetic fluid deformable mirror using a discrete-time multivariable PID controller is studied. First, the design of a stabilizing multivariable PID controller for discrete-time systems subject to a pole clustering constraint is proposed based on properly formulated linear matrix inequalities. The design approach is then extended to include an H2 performance constraint. The proposed design method is applied for the shape control of a magnetic fluid deformable mirror and the controller performance is experimentally evaluated in an adaptive optics system. The experimental results indicate the proposed controller can successfully provide the desired shape tracking performance in the closed loop adaptive optics system.

Output Regulation in Discrete-Time Switched Bimodal Systems Based on Youla Parameterized Stabilizing Controllers

This chapter presents the development of an adaptive optics experimental setup to be used in the validation of the analytical model presented in Chap. 4 and in testing the controllers presented in Chaps. 7 and 8. The setup represents a closed-loop AO system built around a prototype MFDM with novel design features. The system can be complemented further by an imaging system to realize a functional ophthalmic imaging AO system. This chapter first provides in Sect. 5.1 a description of the important considerations in the design of the mirror and the encompassing AO system. The conceptual and detailed design of the prototype MFDM are presented in the Sects.5.1.1 and 5.1.2, respectively. A prototype MFDM developed for the experimental validation of the analytic model is presented in Sect. 5.1.3. The design of the experimental AO system and a description of its main components are presented in Sect. 5.2. The analytical model is experimentally evaluated in Sect. 5.3, where some preliminaries of the AO setup are first introduced, the analytic model is validated by comparing the predictions made by the model with the corresponding experimental results, and the effects of the linearization of the MFDM response under the strong uniform magnetic field generated using a Helmholtz coil are investigated and verified.

Magnetic fluid deformable mirror shape control with a multivariable PID controller

This chapter presents an overview of adaptive optics (AO) systems, including a brief summary of their development history and their importance in high-resolution imaging systems. The first section of this chapter introduces the basic optical concepts of wavefronts and aberrations. The operating principle of AO systems and the primary components of these systems are then presented. Covered in the last section is a review of retinal imaging AO systems, including a brief review of the history of ophthalmic imaging systems and the requirements and challenges to their practical implementation using AO systems.