Youla parameterized adaptive vibration control against deterministic and band-limited random signals

•A H∞ controller with augmented Youla (Q) parameterized adaptive regulation approach is proposed to reject both random and deterministic vibrations.•By incorporating Youla parameterization scheme into the controller, the internal model of the disturbances may implicitly be contained in the controller with the appropriately designed Q parameters.•The parameter Q is converged to the desired value by online tune of a recursive least squares (RLS) algorithm based on the Internal Model Principle.•An experimental evaluation on a lathe system has been carried out to indicate the effectiveness of this adaptive approach to attenuate both the band-limited random disturbance and the narrow-band unknown deterministic disturbance.