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

Symmetric Hyperbolic Systems of partial differential equations describe many physical phenomena such as wave behavior, electromagnetic fields, and quantum fields. 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. Here we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. We apply the results to control of symmetric hyperbolic systems with coercive boundary conditions.

Robust adaptive model tracking control for linear infinite dimensional Symmetric Hyperbolic Systems

This paper presents an introduction to Evolving Systems, which are autonomously controlled subsystems which 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 which operates through one specific component to maintain stability during the evolution. In addition this control must overcome persistent disturbances that occur while the evolution is in progress. We present theoretical results for the successful operation of Adaptive Key Component control in the presence of such disturbances and an illustrative example.Copyright © 2011 by ASME

Evolving Systems: Adaptive Key Component Control With Persistent Disturbance Rejection

A direct adaptive control theory to control the onshore wind turbine in partial loading operation and offshore wind turbine in full loading operation is presented in this paper. Adaptive controllers are designed based on the proposed theory and then implemented to 5 MW FAST wind turbine models.

Modeling and direct adaptive control of utility-scale wind turbines for both onshore and offshore operation

The Kreisselmeier discrete adaptive observer is analyzed for the case in which the observer order is less than that of the plant. The state and parameter estimates from the observer are compared to the states and parameters for an arbitrary reduced-order model (ROM) of the plant, where the observer and ROM are of equal dimension. Conditions sufficient for ultimate boundedness of the observation errors are given, and expressions for the error bounds are derived.

Error Analysis for a Reduced-Order Discrete Adaptive Observer

This paper is focused on adaptively controlling a linear infinite-dimensional system to cause it to track an infinite-dimensional reference model 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 Both the plant and the reference model are described by closed, densely defined linear operators that generate continuous semigroups of bounded operators on the Hilbert space of states An extension of the Barbalat-Lyapunov result for infinite dimensional Hilbert spaces is used to determine conditions under which a linear Infinite-dimensional system can be directly adaptively controlled to follow such a reference model In particular we examine conditions for a set of ideal trajectories to exist for the tracking problem and show the solvability of the infinite dimensional matching conditions under the simple condition that the high frequency gain CB is nonsingular and the reference system is a normal operator with compact resolvent

Mark J. Balas

Papers

Robust adaptive model tracking control for linear infinite dimensional Symmetric Hyperbolic Systems

Evolving Systems: Adaptive Key Component Control With Persistent Disturbance Rejection

Modeling and direct adaptive control of utility-scale wind turbines for both onshore and offshore operation

Error Analysis for a Reduced-Order Discrete Adaptive Observer

Adaptive tracking of infinite-dimensional reference models for linear infinite-dimensional systems in Hilbert space