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

Recent work in Adaptive Disturbance Rejection Control has shown this method to be effective to reject forces due to imbalance, runout and base motion disturbances on magnetically supported flywheels over a large span of frequencies. The method, however, requires certain properties (such as almost -strict positive realness) that active magnetic bea rings do not possess, limiting the applicability of the method. In this work, the adaptive disturbance rejection control law is modified (with relaxed assumptions) and a design methodology is presented to allow for a much wider range of frequencies to be r ejected. The ideas used here include using a reduced order model, appropriate state estimator design, and modifying the original adaptive gains. Computer simulation and experimental results are given to validate the ideas presented.

Modification of Adaptive Disturbance Rejection Control for an Active Magnetic Bearing

Methods and systems for controlling a physical system (plant) are disclosed. The plant is modeled as a linear, finite-dimensional system having a state vector, a control input vector, a plant output vector, and a disturbance vector comprising disturbances having known basis functions and unknown amplitudes. An adaptive control law is used with separate adaptive gains for an error vector associated with the plant output vector, and the disturbance vector, plus a fixed gain for a disturbance estimator. The adaptive control law is operable to adjust the control input vector so as to minimize the error vector. The plant includes modes which are not Almost Strictly Positive Real (ASPR).

Residual mode filters

Recent developments in flow control technology have resulted in small-sized, powerefficient devices, as microtabs, which is capable of impacting flow field over rotating wind turbine blade to generate control forces. The model of the rotatory blade is considered as an aeroelastic system with unsteady periodic aerodynamic loads, simulated by BeddoesLeishman stall model. The traditional control technique as PID control can not address the problem of blade fluttering or multiple performance goals arising from wind turbine operation. Therefore, novel approach for control design, as Adaptive Control, is required. The stability of the designed controller is revealed by good performance of simulation results in open-loop and closed-loop tests, showing robustness and effectiveness of the controller in flutter suppression with Microtabs. Moreover, The stability of the feedback system is proved theoretically by the given Adaptive Stability Theorem for periodic time-varying system. The demonstration of the stability theorem is also given by certain cases.

Flutter Suppression of Rotating Wind Turbine Blade Based on Beddoes-Leishman model using Microtabs

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for mildly non-linear systems with unknown time varying input delays. This controller can also reject bounded disturbances of known waveform but unknown amplitude, e.g. steps or sinusoids. In this paper a robustness result is developed for DMRAC of mildly non-linear systems with unknown small constant or time varying input delays using the concept of undelayed ideal trajectories.We will show that the adaptively controlled system is globally stable, but the adaptive tracking error is no longer guaranteed to approach the origin. However, exponential convergence to a neighborhood can be achieved as a result of the control design. A simple example will be provided to illustrate this adaptive control method. The proof of the corollary for the application and further examples are provided in the paper: Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delay - Part II.

Mark J. Balas

Papers

Modification of Adaptive Disturbance Rejection Control for an Active Magnetic Bearing

Residual mode filters

Flutter Suppression of Rotating Wind Turbine Blade Based on Beddoes-Leishman model using Microtabs

Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delays – Part I

Adaptive Output Tracking and Disturbance Rejection with Saturation Constraints