Ning Ji - Boundary Control of Flexible Three-Dimensional Euler–Bernoulli Beams

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Compared with rigid materials, flexible materials have the advantages of lightweight, low-energy consumption and flexible operation, which are widely applied in aerospace, seabed exploration, medical industry, robotics, machinery manufacturing and other fields. The mechanical systems made of flexible materials are also different from the systems made of rigid materials. The rigid mechanical systems are traditional lumped parameter systems, and the models can be described by ordinary differential equations (ODEs). While the flexible mechanical systems are typical distributed parameter systems, the model states are not only related to time, but also to spatial position, so they should be described by partial differential equations (PDEs) more precisely. The flexible mechanical systems have some advantages mentioned above, but it inevitably leads to vibration because of the flexibility in the process of working. Therefore, vibration suppression is a key problem to be solved in order to ensure the normal operation of the flexible mechanical systems.

Typical distributed parameter systems include flexible manipulators, flexible satellite panels, flexible aircraft wings, flexible aerial refueling hose and flexible marine riser. Due to the fact that the above mechanical systems have slender structures, they are usually regarded as EulerBernoulli beams for dynamic modeling. Meanwhile, in order to meet the actual working environment, the deflections of an EulerBernoulli beam are considered in three-dimensional space in this book. The PDEs of flexible three-dimensional mechanical systems are more complex than those of plane systems, and there are strong couplings between deflections in three directions, which brings more challenges to the control law design and stability analysis.

Based on PDEs of a flexible three-dimensional EulerBernoulli beam, the book is structured as follows:

Chapter is the introduction section. Some specific examples of mechanical systems are listed for illustrating the application background and research significance of three-dimensional EulerBernoulli beams. Then modeling methods, control strategies and control methods, stability analysis and simulation methods are introduced for distributed parameter systems. Finally, a series of common practical engineering problems are introduced which will be considered in this book.