Theory of Wave Analysis of Lumped Flexible Systems

Flexible systems such as robots and space structures are frequently represented by lumped models. In the mechanics of lumped systems, wave concepts have been avoided, generally for good reasons. In the control of lumped flexible systems however, wave concepts prove very fruitful. This tutorial paper provides a foundation for the wave-based control application by exploring the validity and nature of wave concepts in lumped systems. A new wave-based model of mass- spring systems is proposed and verified. The model is exact but not unique. Useful simplifications and approximations are also presented. As seen in a companion paper, the model leads to control strategies for flexible robotic systems that are simple, powerful, robust, and generic. The wave approach also provides a new analysis tool and conceptual framework for lumped dynamic systems.