Adaptive influence-coefficient methods have proven successful at controlling unbalance-induced vibration of rotating machinery without requiring a priori knowledge of machine dynamics. If initial influence estimates are inaccurate, however, vibration may become worse temporarily before the estimation converges. An auto-tuning method is presented here that adjusts adaptive gain parameters during control convergence. The auto-tuning method limits worst-case vibration while allowing the same convergence rate as conventional fixed-parameter adaptive control. A supervisory control method is also introduced that automatically selects vibration thresholds for enabling and disabling control based on estimated plant dynamics. Experimental results verify the effectiveness of the auto-tuning approach.