Boundary-controlled travelling and standing waves in cascaded lumped systems

This paper describes how pure travelling waves in cascaded, lumped, uniform, mass-spring systems can be defined, established, and maintained, by controlling two boundary actuators, one at each end. In most cases the control system for each actuator requires identifying and measuring notional component waves, propagating in opposite directions, through the actuator-system interfaces. These measured component waves are then used to form the control inputs to the actuators. The paper also shows how the boundaries can be actively controlled to establish and maintain standing waves of arbitrary standing wave ratio, including those corresponding to classical modes of vibration with textbook boundary conditions. The proposed control systems are also robust to system disturbances: they react quickly to overcome external transient disturbances to re-establish the desired steady motion.