Dynamic Modeling and Vibration Control for a Nonlinear Three-Dimensional Flexible Manipulator

In the previous chapters, modeling and vibration control of the flexible mechanical systems are restricted to one dimensional space, and only transverse deformation is taken into account. However, flexible systems may move in a three-dimensional (3D) space in practical applications. The control performance will be affected if the coupling effects between motions in three directions are ignored. In spatial and industrial environment, flexible manipulators have been widely used due to their advantages such as light weight, fast motion and low energy consumption [3, 7]. For dynamic analysis, the flexible manipulator system is regarded as a distributed parameter system (DPS) which is mathematically represented by partial differential equations (PDEs) and ordinary differential equations (ODEs) [2, 5, 8], however, these works are only considered in one dimensional space. To improve accuracy and reliability analysis, modeling and control of the flexible manipulator system in a 3D space is necessary. Therefore, several works have been done in dynamics modeling and control design when the coupling effect are taken into account.