A Compensator for Attenuation of Wave Reflections in Long Cable Actuator–Plant Interconnections with Guaranteed Transient Performance Improvement

The wave reflection phenomenon that appears when actuator and plant are connectedthrough long cables is studied in this paper.In a recent work the authors proposed a novel compensator design framework,based on the scattering representation of the transmission line, that is applicable for the latter scenario.In contrast with the standard schemes the compensators are active and require for their implementation regulated sources placed either on actuator or plant side.The use of active compensators raises the issue of ensuring stability of the design,a point left openin our previous work,that is fully solved in the present note.We propose a family of compensators that requires only knowledge of cable characteristics and—under some practically reasonable assumptions—guarantees transient performance improvement and asymptotic tracking for all (unknown) plants with passive impedance.