ABSTRACT
The dynamics of flexible mechanical systems that require vibration reduction are usually mathematically represented by partial differential equations (PDEs). Flexible systems are modeled by a PDE that is satisfied over all points within a domain and a set of boundary conditions. PDE-based models for flexible systems have been discretized via modal analysis in order to facilitate the control design process. This chapter provides a motivating example to illustrate in a heuristic manner how a boundary controller is derived via the use of a Lyapunov-like approach. In many flexible mechanical systems such as flexible link robots, helicopter rotor/blades, space structures, and turbine blades, the flexible element can be modeled as a beam-type structure. A more sophisticated boundary control law is often required for more complicated flexible, mechanical system models. The chapter presents a model-based boundary controller that regulates the angular position of a flexible-link robot arm while simultaneously regulating the link vibrations.
