There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Robust Model-Based Fault Diagnosis for Dynamic Systems

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

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Essentials of Robust Control

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

An investigation about the influence of internal damping on the rotordynamic stability of high-speed flywheel energy storage systems made from carbon fiber epoxy is presented. The research effort consists of simulation studies coupled with experimental testing and evaluation. Damping values obtained from composite beam samples and a composite rotor hub design are shown. The effect of vibration frequency on damping is examined and discussed. These parameters are then used in a series of simulation studies that examine the effects of internal damping on rotordynamic behavior. An experimental model has been developed to verify the conclusions made from the simulations. The experimental testing consisted of creating a prototype rig, characterizing the system parameters, applying these parameters to determine the expected critical speed and experimentally determine the actual critical speed. These results are presented and their implications for flexible hub flywheel designs discussed.Copyright © 2005 by ASME

The Influence of Internal Damping on the Rotordynamic Stability of a Flywheel Rotor With Flexible Hub

A mathematic rotating blade model is introduced in conjunction with periodic time-varying aerodynamic load, which is described by Beddoes-Leishman dynamic stall model. The consequent aeroelastic model is utilized to analyze blade dynamics and design control strategy for blade flutter suppression application. Aeroelastic stability of rotating blade is indicated by Floquet Theory, and the stability indications show good agreement with results of open-loop simulation test for critical flutter speed study. It's shown that the Adaptive Controller is capable of restraining flutter vibration with the actuation of the trailing-edge flap. The robustness and effectiveness of the controller are shown by closed-loop tests with a wide range of aerodynamic loads. The stability analysis proves the stability of the Adaptive Controller by the Adaptive Stability Theorem.

Aeroelastic Control of Wind Turbine Blade Using Trailing-Edge Flap

This paper is focused on adaptively controlling a linear infinite-dimensional system to cause it to regulate the output to zero in the presence of persistent disturbances. The plant (A, B, C) is described by a closed, densely defined linear operator A that generates a continuous semigroup of bounded operators on a Hilbert space of states; the input-output operators B & C are finite rank linear operators. We show that there exists a direct model reference adaptive control law that regulates the output in the presence of disturbances of known waveform but unknown amplitude and phase. The conditions needed for the success of the direct adaptive controller include the need for (A, B, C) to be almost strictly dissipative (ASD). In finite dimensional space, ASD is equivalent to two simple open-loop requirements: the high frequency gain CB is sign-definite and the open-loop transfer function P(s) is minimum phase. Our main result will prove infinite-dimensional versions of these conditions for a large class of infinite-dimensional systems.

Adaptive regulation in the presence of persistent disturbances for linear infinite-dimensional systems in Hilbert space: Conditions for almost strict dissipativity

New theory is presented for evolving systems, which are autonomously controlled subsystems that self-assemble into a new evolved system with a higher purpose. Evolving systems of aerospace structures often require additional control when assembling to maintain stability during the entire evolution process. This is the concept of Adaptive Key Component Control that operates through one specific component to maintain stability during the evolution. In addition, this control must often overcome persistent disturbances that occur while the evolution is in progress. Theoretical results will be presented for Adaptive Key Component control for persistent disturbance rejection. An illustrative example will demonstrate the Adaptive Key Component controller on a system composed of rigid body and flexible body modes.

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Mark J. Balas

Papers

The Influence of Internal Damping on the Rotordynamic Stability of a Flywheel Rotor With Flexible Hub

Aeroelastic Control of Wind Turbine Blade Using Trailing-Edge Flap

Adaptive regulation in the presence of persistent disturbances for linear infinite-dimensional systems in Hilbert space: Conditions for almost strict dissipativity

Evolving Systems: An Outcome of Fondest Hopes and Wildest Dreams

Model Reference Adaptive Control of Linear Systems with Time Varying Input/Output Delays