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.