Boundary-controlled travelling and standing waves in cascaded lumped systems

This paper shows 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 the notional component waves propagating in opposite directions at 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 the classical modes of vibration of such systems with textbook boundary conditions. These vibration modes are achieved and maintained by controlled reflection of the pure travelling wave components. The proposed control systems are also robust to system disturbances: they react to overcome external disturbances quickly and so to re-establish the desired steady motion.

► We define travelling and standing waves in cascaded, lumped, mass–spring strings. ► We control two boundary actuators to achieve arbitrary travelling and standing waves. ► We quickly establish target standing wave ratios and classical vibration modes. ► We control transients and disturbances while establishing waves and modes. ► The theory and practical implementation of the control are presented.