A COMPENSATOR FOR ATTENUATION OF WAVE REFLECTIONS IN LONG CABLE ACTUATOR-PLANT INTERCONNECTIONS WITH GUARANTEED TRANSIENT PERFORMANCE IMPROVEMENT

Abstract

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 operativity 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 clearly 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, 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 open in 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.