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2004 | Buch

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Advanced Structural Dynamics and Active Control of Structures

herausgegeben von: Wodek K. Gawronski

Verlag: Springer New York

Buchreihe : Mechanical Engineering Series

Enthalten in: Professional Book Archive

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Über dieses Buch

Science is for those who learn; poetry for those who know. —Joseph Roux This book is a continuation of my previous book, Dynamics and Control of Structures [44]. The expanded book includes three additional chapters and an additional appendix: Chapter 3, “Special Models”; Chapter 8, “Modal Actuators and Sensors”; and Chapter 9, “System Identification. ” Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and -frequency grammians and reduction, almo- balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The appendices have also been updated and expanded. Appendix A consists of thirteen new Matlab programs. Appendix B is a new addition and includes eleven Matlab programs that solve examples from each chapter. In Appendix C model data are given. Several books on structural dynamics and control have been published. Meirovitch’s textbook [108] covers methods of structural dynamics (virtual work, d’Alambert’s principle, Hamilton’s principle, Lagrange’s and Hamilton’s equations, and modal analysis of structures) and control (pole placement methods, LQG design, and modal control). Ewins’s book [33] presents methods of modal testing of structures. Natke’s book [111] on structural identification also contains excellent material on structural dynamics. Fuller, Elliot, and Nelson [40] cover problems of structural active control and structural acoustic control.

Inhaltsverzeichnis

Frontmatter

1. Introduction to Structures

Abstract

Flexible structures in motion have specific features that are not a secret to a structural engineer. One of them is resonance—strong amplification of the motion at a specific frequency, called natural frequency. There are several frequencies that structures resonate at. A structure movement at these frequencies is harmonic, or sinusoidal, and remains at the same pattern of deformation. This pattern is called a mode shape, or mode. The modes are not coupled, and being independent they can be excited separately. More interesting, the total structural response is a sum of responses of individual modes. Another feature—structural poles—are complex conjugate. Their real parts (representing modal damping) are typically small, and their distance from the origin is the natural frequency of a structure.

2. Standard Models

Abstract

In this and the following chapter we explain structural models that describe standard —or more common—structures. The standard models include structures that are stable, linear, continuous-time, and with proportional damping.

3. Special Models

Abstract

Models described in the previous chapter include typical structural models, which are continuous-time, stable, and with proportional damping. In this chapter we consider models that are not typical in the above sense but, nevertheless, often used in engineering practice. Thus, we will consider models with rigid-body modes (which are unstable), models with nonproportional damping, discrete-time structural models, models with acceleration measurements, and generalized structural models. The latter include two kinds of inputs: controlled (or test) inputs and disturbance inputs, and also two kinds of outputs: measured outputs and outputs where the system performance is evaluated.

4. Controllability and Observability

Abstract

Controllability and observability are structural properties that carry information useful for structural testing and control, yet they are not fully utilized by structural engineers. The usefulness can be found by reviewing the definitions of the controllability and observability of a structure. A structure is controllable if the installed actuators excite all its structural modes. It is observable if the installed sensors detect the motions of all the modes. This information, although essential in many applications (e.g, in the placement of sensors and actuators), is too limited. It answers the question of mode excitation or detection in terms of yes or no. The more quantitative answer is supplied by the controllability and observability grammians, which represent a degree of controllability and observability of each mode.

5. Norms

Abstract

System norms serve as a measure of intensity of its response to standard excitations, such as unit impulse, or white noise of unit standard deviation. The standardized response allows comparing different systems. Three system norms, H₂, H_∞, and Hankel are used in this book. We show that for flexible structures the H₂ norm has an additive property: it is a root-mean-square (rms) sum of the norms of individual modes. We also show that the H_∞ and Hankel norms are determined from the corresponding modal norms, by selecting the largest one. All three norms of a mode with multiple inputs (or outputs) can be decomposed into the rms sum of norms of a mode with a single input (or output). Later in this book these two properties allow for the development of unique and efficient model reduction methods and actuator/sensor placement procedures.

6. Model Reduction

Abstract

Model reduction is a part of dynamic analysis, testing planning, and the control design of structures. Typically, a model with a large number of degrees of freedom, such as one developed for static analysis, causes numerical difficulties in dynamic analysis, to say nothing of the high computational cost. In system identification, on the other hand, the order of the identified system is determined by the reduction of the initially oversized model that includes a noise model. Finally, in structural control design the complexity and performance of a model-based controller depends on the order of the structural model. In all cases the reduction is a crucial part of the analysis and design. Thus, the reduced-order system solves the above problems if it acquires the essential properties of the full-order model.

7. Actuator and Sensor Placement

Abstract

A typical actuator and sensor location problem for structural dynamics testing can be described as a structural test plan. The plan is based on the available information on the structure itself, on disturbances acting on the structure, and on the required structural performance. The preliminary information on structural properties is typically obtained from a structural finite-element model. The disturbance information includes disturbance location and disturbance spectral contents. The structure performance is commonly evaluated through the displacements or accelerations of selected structural locations. The actuator and sensor placement problem was investigated by many researchers, see, for example, [1], [7], [24], [47], [55], [86], [89], [90], [96], [97], [101], [103], [105], [106], [127], and a review article [131].

8. Modal Actuators and Sensors

Abstract

In some structural tests it is desirable to isolate (i.e., excite and measure) a single mode. Such a technique considerably simplifies the determination of modal parameters, see [116]. This was first achieved by using the force appropriation method, also called the Asher method, see [107], or phase separation method, see [21]. In this method a spatial distribution and the amplitudes of a harmonic input force are chosen to excite a single structural mode. Modal actuators or sensors in a different fonnulation were presented in [38], [93], [75], and [114] with application to structural acoustic problems. In this chapter we present two techniques to determine gains and locations of actuators or sensors to excite and sense a target mode or a set of targeted modes.

9. System Identification

Abstract

The LQG and H_∞ controllers, analyzed later in this book, are model-based ones, i.e., such that the plant model (used as an estimator) is a part of the controller. In this case the performance of the closed-loop system depends on the accuracy of the plant model. The accuracy is defined as a discrepancy between the dynamics of the actual plant and its model. For this reason, analytical models of a plant obtained, for example, from the finite-element model, are inaccurate and are acceptable in the simulation stages only. In implementation the test data are used to determine the accurate plant model—in a procedure known as system identification.

10. Collocated Controllers

Abstract

Collocated controllers have their sensors collocated with actuators. They are a special case of the dissipative controllers, which are designed based on the passivity principle. In this book we select the collocated controllers as a first step to controller design, since they are simple, always stable, and some of their properties are similar to the more advanced controllers described later in this book. A good introduction to the collocated control of structures—but from a different point of view—can be found in the book by Preumont [120].

11. LQG Controllers

Abstract

The control issues, as applied to structures, include precise positioning or tracking. It is expected that the positioning and tracking requirements should be satisfied for structures with natural frequencies within the controller bandwidth and within the disturbance spectra. LQG (Linear system, Quadratic cost, Gaussian noise) controllers can typically meet these conditions and they are often used for tracking and disturbance rejection purposes. A good insight into the problems of analysis and design of LQG controllers can be obtained from the books by Kwakernaak and Sivan [91], Maciejowski [104], Anderson and Moore [3], Furuta, Sano, and Atherton [41], Lin [100], Skogestad and Postlethwaite [129], Dorato, Abdallah, and Cerone [28], Burl [13], and Fairman [34].

12. H∞ and H2 Controllers

Abstract

In the LQG controller design we assumed that the control inputs were collocated with disturbances, and that the control outputs were collocated with the performance. This assumption imposes significant limits on the LQG controller possibilities and applications. The locations of control inputs do not always coincide with the disturbance locations, and the locations of controlled outputs are not necessarily collocated with the location where the system performance is evaluated. This was discussed earlier, when the generalized structure was introduced. The H₂ and H_∞ controllers address the controller design problem in its general configuration of non-collocated disturbance and control inputs, and noncollocated performance and control outputs. Many books and papers have been published addressing different aspects of H_∞ controller design, and [12], [30], [94], [99], [100], [104], [122], and [129] explain the basic issues of the method. The H_∞ method addresses a wide range of the control problems, combining the frequency- and time-domain approaches. The design is an optimal one in the sense of minimization of the H_∞ nonn of the closed-loop transfer function. The H_∞ model includes colored measurement and process noise. It also addresses the issues of robustness due to model uncertainties, and is applicable to the single-input-single-output systems as well as to the multiple-input-multiple-output systems.

Backmatter

Titel: Advanced Structural Dynamics and Active Control of Structures
herausgegeben von: Wodek K. Gawronski
Verlag: Springer New York
Electronic ISBN: 978-0-387-72133-0
Print ISBN: 978-0-387-40649-7
DOI: https://doi.org/10.1007/978-0-387-72133-0

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Inhaltsverzeichnis

Frontmatter

1. Introduction to Structures

2. Standard Models

3. Special Models

4. Controllability and Observability

5. Norms

6. Model Reduction

7. Actuator and Sensor Placement

8. Modal Actuators and Sensors

9. System Identification

10. Collocated Controllers

11. LQG Controllers

12. H∞ and H2 Controllers

Backmatter