In several practical applications actuators are interconnected to a controlled plant through long cables. If the actuator operates at a fast sampling rate (with respect to the propagation delay of the cable) and its impedance cannot be neglected, wave reflections will occur and the transmitted pulse will be deformed-degrading the control quality. In this note, exploiting the scattering variables representation of the transmission line, we provide a framework for the design of active compensators to reduce the wave reflection problem. The compensators, implementable with regulated current and voltage sources, can be placed either on the actuator side or the plant side, and the only required prior knowledge is the transmission line characteristic impedance and the propagation delay. An adaptive implementation that obviates the need of the lines characteristic impedance, but still requires the knowledge of the propagation delay, is also presented. We prove the existence of an ideal scheme that transforms the line into a pure delay transfer which, unfortunately, yields an ill-posed interconnection and therefore has to be approximated for its practical application. The proposed design method is illustrated with a benchmark ac drives example consisting of a pulsewidth modulation inverter and an induction motor.
['R. Ortega', 'A. de Rinaldis', 'Mark W. Spong', 'Sangcheol Lee', 'Kwanghee Nam']
On compensation of wave reflections in transmission lines and applications to the overvoltage problem AC motor drives