When is a controller in automatic not able to do anything to reduce an oscillation? When will a controller amplify an oscillation? In both of these cases, the controller is doing more harm than good by wearing out valves and upsetting other loops.
Fast oscillations are particularly insidious because the best thing a PID controller can do is ignore them. Action taken by PID controller can do more harm than good in terms of resonance, amplification, and perpetuation leading to increased process variability and premature valve failure.