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Operability enhancement is one of the major goals for active control of rotating stall and surge in aeroengines. The model developed by Moore and Greitzer exhibits the qualitative behavior of rotating stall and surge dynamics and thus can be used for controller designs. Based on this model, we derive a normal form from which explicit relations between the stall and surge inception process and the shape of compressor characteristics are obtained via bifurcation analysis. Analysis for the normal form with bleed valve actuator dynamics shows that under certain circumstances the optimal control is the "bang-on" control law that drives the bleed valve to open against its rate limit once the disturbances grow out of the noise level.