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Active Vibration Control and Stability Analysis of Flexible Beam Systems

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Control of flexible beam systems constitutes an important benchmark problem in many application areas, such as flexible manipulators for grasping, marine mooring lines for station keeping, marine risers for oil transportation, and crane cables for positioning the payload. Flexible systems have a number of advantages such as lightweight, efficiency, higher operation speed, and lower cost. The dynamics of the flexible beam system is essentially a distributed parameter system (DPS). Different from lumped parameter systems, the DPS has an infinite-dimensional state space. The dynamics of DPS modeled by the coupled partial differential equations (PDEs)–ordinary differential equations (ODEs) is difficult to control due to the infinite dimensionality of the beam system.

Since the flexible beam system becomes lighter and more flexible, the external disturbances will lead to the mechanical vibrations of flexible beam systems. Therefore, the control strategy should be designed to suppress the vibrations of flexible beam systems. Driven by practical needs and theoretical challenges, flexible beam systems and their vibration suppression have received great attention. Boundary control is an effective control strategy for vibration suppression of the flexible beam system which is described by hybrid PDEs–ODEs. By using sensors and actuators at the boundary, the dynamic model of the system is not affected, and boundary control can be derived from a Lyapunov function which is relevant to the mechanical energy based on the dynamics of the system.

The purpose of this book is to investigate the fundamental issues including dynamic analysis and control design for flexible beam systems by theoretical analysis and numerical simulations. A comprehensive study is provided to develop boundary control methods for the vibration suppression of flexible beam systems with input nonlinearities and output constraint. In addition, the book presents theoretical explorations for advanced control methods of flexible beam systems, including distributed control, iterative learning control, and neural network control. The control designs are coupled with numerical simulations to illustrate the effectiveness.
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