Advanced Structural Dynamics and Active Control of Structures

Advances in control theory have often led to solutions of a variety of difficult practical problems. One such application is control of flexible structures, which are typically characterized by large numbers of nearly undamped elastic modes. The primary challenges in control design for flexible structures are: 1) large model order, 2) oscillatory behavior with small natural damping, 3) inherent modeling errors due to finite-dimensional modeling of essentially infinite-dimensional systems, i.e., unmodeled/ignored elastic modes, 4) inaccuracies in model parameters (e.g., elastic mode frequencies, mode shapes, damping), and 5) nonlinearities (kinematic and actuator-sensor). Items 3) and 4) require controller robustness in order to ensure stability and performance, while 5) arises mainly in large-angle motion of single-body and multibody articulated systems. This book essentially focuses on items 1) and 2) in a finite-dimensional linear time-invariant (FDLTI) setting, in a thorough and detailed manner. This book is an expanded version of the author’s 1998 book (Dynamics and Control of Structures—a Modal Approach) by the same publisher. The intended readership is researchers and practitioners working on structural dynamics and control, and graduate students specializing in that area. It is well-written and contains an in-depth treatment of certain aspects of this important (albeit specialized) control problem. The treatment is limited to FDLTI structural models and controllers. The first six chapters provide a nice and easily understandable introduction to structural dynamics, and basic results in standard linear system theory particularized to flexible structures by exploiting their special characteristics. Chapter 1 presents a brief qualitative introduction to structures and structural dynamics. Chapter 2 contains the basic finite-dimensional linear nodal elastic model, transformation to standard modal forms, and the resulting state–space and transfer-function models. Chapter 3 presents models with rigid-body dynamics, with “proof-mass” actuators to reduce elastic motion, as well as inertial forceand moment-inputs. Chapter 4 introduces controllability and observability, and presents closed-form expressions for approximately balanced realizations of structural dynamic systems obtained by scaling the modal coordinates. Useful approximations for Hankel singular values are derived. Timeand frequency-limited controllability and observability grammians are defined, for subsequent use in model reduction (Chapter 6). Chapter 5 presents definitions of H2, H1, and Hankel norms of LTI systems and derives norm expressions for flexible structures. Real-life structural systems often contain very large numbers of elastic modes. Therefore model order reduction is essential, and is discussed in Chapter 6 viaH2,H1, and Hankel norm approaches. Model reduction in finite time and frequency intervals is discussed (their use appears to be rather limited). Chapters 7–9 address actuator/sensor placement, modal excitation and sensing, and system identification. Chapter 7 presents methods of selecting the most effective locations (out of a large discrete set of lo-