Wave-based control of flexible mechanical systems

There are many contexts, from space structures to disk drive heads, from medical mechanisms to long-arm manipulators, from cranes to robots, in which it is desired to achieve rapid and accurate position control of a system end-point by an actuator working through a flexible system. The system´s actuator must then attempt to reconcile two, potentially conflicting, demands: position control and active vibration damping. Somehow each must be achieved while respecting the other´s requirements. Wave-based control is a powerful, relatively new strategy that has many advantages over most existing techniques. The central idea is to consider the actuator motion as launching mechanical waves into the flexible system while simultaneously absorbing returning waves. This simple, intuitive idea leads to robust, generic, highly efficient, adaptable controllers, allowing rapid and almost vibrationless re-positioning of the remote load (tip mass). For the first time there is a generic, high-performance solution to this important problem that does not depend on an accurate system model. The lecture will investigate the mathematical foundation for a wave-based interpretation of flexible system dynamics, both lumped and continuous. It will then show how this view can be used to interpret the actuator-system interface as a two-way energy flow, leading to the design of controllers that give close-to-optimal performance by controlling this energy flow, in ways that are simple, robust, generic, and energy efficient.