In conjunction with the deregulated energy market, more energy must be transported over longer distances with greater flexibility. And it is difficult to obtain the right of way for new transmission lines. Therefore the existing lines must be better used, e.g. by increasing the operating voltage. Since the isolation voltage must not be exceeded in any case, the oscillations due to switching actions at the ends of the line must be reduced, by active damping. Based on the measurement of the voltage, an additional current is injected at the same location. This current is to be generated by a FACTS (Flexible AC Transmission System). An appropriate controller is designed using the H ∞ optimization method, where the closed loop transfer functions are tuned, and the tuning weights follow directly from the specifications. However such a controller will invert the plant. For plants with resonances and antiresonances, as considered here, the resulting closed loop behavior is not acceptable. The method proposed here avoids this inversion. It can also be used to design robust controllers. The H ∞ approach is based on a plant model. Since the electric power transmission line is described by a partial differential equation, the model must be approximated by a set of ordinary differential equations before common engineering tools may be applied. This is done by using the Euler-Lagrange equation and the eigenfunctions of the line. Significantly better results are obtained than with the well known 7r-model. The active damping of the line, that is the performance of the controller, is demonstrated by simulations.