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

Using an FEM, it is shown that all linear flexible structures have convergent second-order observers, but that some are unnatural, involving a corrector term obtained from a filter.

Do all linear flexible structures have convergent second-order observers?

Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result is an extension of Barbalat-Lyapunov result for infinite dimensional Hilbert spaces. This is used to determine conditions under which a linear Infinite-dimensional system can be directly adaptively regulated. Our results are applied to adaptive control of general linear diffusion systems.

Distributed Parameter Direct Adaptive Control Using a New Version of the Barbalat-Lyapunov Stability Result in Hilbert Space

Feedback Control of Dissipative Hyperbolic Distributed Parameter Systems with Finite Dimensional Controllers

https://ti.arc.nasa.gov/publications/1595/download/

Evolving Systems: Adaptive Key Component Control and Inheritance of Passivity and Dissipativity

Recent work in the area of adaptive control has seen the development of techniques for the adaptive rejection of persistent disturbances for structural systems. They have been implemented and tested for large-scale structural systems, with promising results, but have not been widely applied to smallerscale systems and devices. Rotor systems are subject to a variety of persistent disturbances (for example, due to mass imbalance, blade-pass effects) that occur at the rotor running speed or multiples of the running speed. The frequencies of such disturbance forces are generally known, but their magnitudes tend to vary over time. Adaptive techniques to counter the effects of such disturbances would appear to be a promising strategy in this regard. In order to assess the effectiveness of adaptive disturbances rejection for rotor applications and identify issues associated with implementation, and adaptive disturbance rejection control is developed, implemented, and tested for a magnetic-bearing-supported rotor system. Some conclusions and insights concerning the application of this method to rotor system vibration suppression are presented and discussed.Copyright © 2003 by ASME

Mark J. Balas

Papers

Do all linear flexible structures have convergent second-order observers?

Distributed Parameter Direct Adaptive Control Using a New Version of the Barbalat-Lyapunov Stability Result in Hilbert Space

Feedback Control of Dissipative Hyperbolic Distributed Parameter Systems with Finite Dimensional Controllers

Evolving Systems: Adaptive Key Component Control and Inheritance of Passivity and Dissipativity

Suppression of Persistent Rotor Vibrations Using Adaptive Techniques