Previous work on stabilization of compressor surge is extended to include control of the angular velocity of the compressor. A low-order centrifugal compressor model is presented, where the states are mass flow, pressure rise, and rotational speed of the spool. Energy transfer considerations are used to develop a compressor characteristic. In order to stabilize equilibria to the left of the surge line, a close coupled valve is used in series with the compressor. Controllers for the valve pressure drop and spool speed are derived. Semiglobal exponential stability is proved using a Lyapunov argument.