Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

1998 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Dynamics and Control of Structures

A Modal Approach

verfasst von: Wodek K. Gawronski

Verlag: Springer New York

Buchreihe : Mechanical Engineering Series

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

Robots, aerospace structures, active earthquake-damping devices of tall buildings, and active sound suppression are examples of the application of structural dynamics and control methods. This book addresses the structural dynamics and control problems encountered by mechanical, civil, and control engineers. Many problems presented in this book originated in recent applications in the aerospace industry, and have been solved using the approach presented here. Dynamics analysis and controller design for flexible structures require a special approach due to the large size of structural models, and because flexible structure testing and control typically requires massive instrumentation (sensors and actuators). But the rapid development of new technologies and the increased power of computers allows for the formulation and solution of engineering problems that seemed to be unapproachable not so very long ago. The modal approach was chosen in this book. It has a long tradition in structural engineering (see, e.g., [84], [87], and [26]) and is also used in control system analysis, e.g., [93]. Its usefulness, thoroughly tested, does not need extensive justification. Both structural testing and analysis give priority to the modal representation, due to its compactness, simplicity, and explicit physical interpretation. Also, many useful structural properties are properly exposed only in modal coordinates. In this book the modal approach, preferred by structural engineers, is extended into control engineering, giving new analytical results, and narrowing the gap between structural and control analysis.

Inhaltsverzeichnis

Frontmatter

Dynamics

Frontmatter
Chapter 1. Introduction
Abstract
A flexible structure is a linear system of specific properties. What are the special features that distinguish a flexible structure from other systems? For structural or mechanical engineers its special properties include periodic vibrations with dominating few frequencies, resonances, and natural modes of vibrations. The term “flexible structure” is commonly used within the control engineering community to refer to a linear system with oscillatory properties characterized by strong amplification of a harmonic signal for certain frequencies, a system with weakly correlated states, and which complex conjugate poles have small real parts.
Wodek K. Gawronski
Chapter 2. Models
Abstract
System analytical models are given in the form of equations. Linear models are represented by linear differential equations. Structural models are represented in the form of second-order differential equations or in the form of first-order differential equations as a state-space representation. In the first case, the system dynamics is typically represented by the system degrees of freedom, and in the second case by the system states. Preferred by structural engineers, second-order differential equations of structural dynamics have a series of nice mathematical and physical properties. In this representation of a long tradition many important results have been derived. The state-space model is a standard model used by control engineers. Most linear control system analysis and design methods are given in state-space form. In this chapter we use both: second-order and state-space models.
Wodek K. Gawronski
3. Controllability and Observability
Abstract
Controllability and observability are structural properties that carry useful information for structural testing and control, yet are often overlooked by structural engineers. 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, is too limited: it answers the question of excitation or detection in terms of yes or no. The quantitative answer is supplied by the controllability and observability grammians, which represent a degree of controllability and observability of each mode. In this chapter the controllability and observability properties of flexible structures are discussed. The fundamental property of a flexible structure in modal coordinates consists of a set of weakly coupling of the modes, as shown in Property 2.1. The weak coupling allows one to treat each individual mode separately specifically, to combine the controllability and observability properties of the whole system out of the properties of individual modes. These controllability and observability properties are used later in this book in the evaluation of structural testing and in control analysis and design.
Wodek K. Gawronski
Chapter 4. Norms
Abstract
System norms serve as a measure of system “size” and in this capacity they are used in the model reduction and in the actuator/sensor placement procedures. Three system norms: H2, H∞, and Hankel are analyzed in this book. It is shown that for flexible structures the H2 norm has an additive property: it is a rootmean-square (rms) sum of the norms of individual modes. The H∞ and Hankel norms are also determined from the corresponding modal norms, by choosing the largest one. All three norms of a structure with multiple inputs (or outputs) can be decomposed into the rms sum of norms of a structure with a single input (or output). These two properties allow for the development of unique and efficient model reduction methods and actuator/sensor placement procedures.
Wodek K. Gawronski
Chapter 5. Model Reduction
Abstract
Model reduction is a part of dynamic analysis, testing, and the control of flexible structures. Typically, a model with a large number of degrees of freedom, such as the one developed for the static analysis of structures, 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 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.
Wodek K. Gawronski
Chapter 6. Assignment
Abstract
The sensor and actuator locations of an open-loop system influence the controllability and observability properties of a system. Therefore one can modify the sensor and/or actuator locations to obtain the required (or assigned) values of the controllability and observability grammians. In particular, one can find the locations such that all Hankel singular values are identical. This is a case of a uniform controllability and observability assignment.
Wodek K. Gawronski
7. Actuator and Sensor Placement
Abstract
A typical actuator and sensor location problem for structural testing can be described as follows. The structural test plan is based on the available information on the structure itself, on disturbances acting on the structure, and on the expected structural performance. The first information is typically in the form of 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 at certain structural locations.
Wodek K. Gawronski

Control

Frontmatter
Chapter 8. Dissipative Controllers
Abstract
The most direct approach to controller design is to implement a proportional gain between the input and output. This approach, however, seldom gives a superior performance, since the performance enhancement in this case is tied to the reduction of the stability margin. If some conditions are satisfied, one obtains a special type of proportional controllers — dissipative ones. As stated by Joshi [64, p. 45] “the stability of dissipative controllers is guaranteed regardless of the number of modes controlled (or even modeled), and regardless of parameter errors.” Therefore, for safety reasons, they are the most convenient candidates for implementation. However, the simplicity of the control law does not simplify the design. For example, in order to obtain the required performance a multi-input—multi-output controller with a large number of inputs and outputs has to be designed. Determining the gains for this controller is not an obvious task. In this chapter we investigate the properties of the dissipative controllers, and show how to design dissipative controllers for flexible structures in order to meet certain objectives.
Wodek K. Gawronski
Chapter 9. LQG Controllers
Abstract
The control issues for flexible structures include the maintenance of precise positioning or tracking. It is expected that these requirements should be satisfied for structures with natural frequencies within the controller bandwidth and within the disturbance spectra. LQG controllers (Linear system, Quadratic cost, Gaussian noise) 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 [71], Maciejowski [81], Anderson and Moore [3], Furuta and Sano [31], Lin [78], Skogestad and Postlethwaite [102], and Dorato et al. [22].
Wodek K. Gawronski
10. H∞ and H2 Controllers
Abstract
In the LQG controller design we assumed that the control inputs are collocated with disturbances, and that the control output was 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 output are not necessarily collocated with the location where the system performance is evaluated. The H2 and H∞ controllers address the controller design problem in its general configuration of noncollocated 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 [24], [81], [73], [78], [12], [77], [95], and [102] explain the basic issues of the method. The H∞ method addresses 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∞ norm 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 singleinput-single—output systems as well as to the multiple-input—multiple-output systems.
Wodek K. Gawronski
Backmatter
Metadaten
Titel
Dynamics and Control of Structures
verfasst von
Wodek K. Gawronski
Copyright-Jahr
1998
Verlag
Springer New York
Electronic ISBN
978-0-387-21855-7
Print ISBN
978-1-4757-5033-1
DOI
https://doi.org/10.1007/978-0-387-21855-7