A compensator for attenuation of wave reflections in long cable actuator–plant interconnections with guaranteed stability

The wave reflection phenomenon that appears when actuator and plant are connected through long cables is studied in this paper. In several applications, the perturbation induced by the presence of these reflected waves is non-negligible and seriously degrades the performance of the control and the operation of the system. Standard compensation schemes are based on matching impedances at specific frequencies (possibly infinity) and are realized with the addition of linear RLC filters. Impedance matching is ineffective if there is no single dominant frequency in the system and/or the plant is highly uncertain. In a recent paper the authors proposed a novel compensator design framework, based on the scattering representation of the transmission line, which is applicable for the latter scenario. In contrast with standard schemes the compensators are active and require for their implementation regulated sources placed either on actuator or on plant side. The use of active compensators raises the issues of well-posedness and stability of the design. The former was addressed in our previous work making a critical discretization assumption that generated an approximated finite-dimensional model; on the other hand, the stability question was left open. Both issues are fully solved in the present note for the complete infinite-dimensional system. We propose a family of adaptive compensators that requires only knowledge of the line propagation delay and guarantees stable asymptotic regulation for all (unknown) linear plants and actuators with passive impedances. Furthermore, under some additional reasonable assumptions, transient performance improvement is ensured. Some simulation results on a benchmark example of voltage overshoot suppression in AC drives are shown.