Over the past few decades, an international effort has been undertaken to develop electric generators using rotors with super-conducting windings. The main differences between superconducting generators (SCGs) and the conventional generators are that (i) the SCG has a double rotor screen and (ii) the SCG’s field windings on the rotor are made up of super-conductors that have zero resistance at cryogenic temperature and, therefore, completely eliminate resistive losses from the rotor. In order to enhance power system stability, a conventional power system stabilizer (CPSS) is commonly applied to the conventional generator excitation system to damp oscillations. In an SCG, due to the long field time-constant and the shielding effect of the double rotor screen, it is not effective to control through the generator excitation system. A possibility, considered here, is to control the SCG through an electro-hydraulic governor as its time-constant is much less than that of the field winding. The objective of this research is to test the performance of an adaptive power system stabilizer for a SCG based on the pole-shift linear feedback control algorithm and acting through the SCG electro-hydraulic governor. The system considered is a single SCG – infinite-bus power system driven by a three stage turbine that includes a re-heater. The turbine is controlled by an electro-hydraulic governor. A third order autoregressive moving average (ARMA) model is used to represent the plant that can be controlled by an adaptive pole-shift controller through the electro-hydraulic governor