IIR Youla–Kucera Parameterized Adaptive Feedforward Compensators for Active Vibration Control With Mechanical Coupling

Adaptive feedforward broadband vibration (or noise) compensation requires a reliable correlated measurement with the disturbance (an image of the disturbance). The reliability of this measurement is compromised in most of the systems by a “positive” internal feedback coupling between the compensator system and the correlated measurement of the disturbance. The system may become unstable, if the adaptation algorithms do not take into account this positive feedback. Instead of using classical infinite impulse response (IIR) or finite impulse response (FIR) feedforward compensators, this paper proposes and analyses an IIR Youla-Kucera parametrization of the feedforward compensator. A model-based central IIR stabilizing compensator is used, and its performance is enhanced by the adaptation of the parameters (Q-parameters) of an IIR Youla-Kucera filter. Adaptation algorithms assuring the stability of the system in the presence of the positive internal feedback are provided. Their performances are evaluated experimentally on an active vibration control system. Theoretical and experimental comparisons with FIR Youla-Kucera parameterized feedforward compensators and IIR feedforward compensators are provided.

[1]  Ioan Doré Landau,et al.  Adaptive feedforward compensation algorithms for active vibration control with mechanical coupling , 2011, Autom..

[2]  Ioan Doré Landau,et al.  Adaptive Suppression of Multiple Time-Varying Unknown Vibrations Using an Inertial Actuator , 2011, IEEE Transactions on Control Systems Technology.

[3]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[4]  C.R. Johnson,et al.  Stability of active noise control algorithms , 2001, IEEE Signal Processing Letters.

[5]  T. J. Sutton,et al.  Performance of feedforward and feedback systems for active control , 1996, IEEE Trans. Speech Audio Process..

[6]  Max Rotunno,et al.  DESIGN OF MODEL-BASED FEEDFORWARD COMPENSATORS FOR VIBRATION COMPENSATION IN A FLEXIBLE STRUCTURE , 2004 .

[7]  Jwu-Sheng Hu,et al.  Feedforward active noise controller design in ducts without independent noise source measurements , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[8]  S.J. Elliott,et al.  Active noise control , 1993, IEEE Signal Processing Magazine.

[9]  Mingsian R. Bai,et al.  COMPARISON OF ACTIVE NOISE CONTROL STRUCTURES IN THE PRESENCE OF ACOUSTICAL FEEDBACK BY USING THEH∞SYNTHESIS TECHNIQUE , 1997 .

[10]  Stephen J. Elliott.  Active Control Of Structure-Borne Noise , 1994 .

[11]  Michel Verhaegen,et al.  Convergence analysis of the Filtered-U LMS algorithm for active noise control in case perfect cancellation is not possible , 2003, Signal Process..

[12]  Brian D. O. Anderson,et al.  From Youla-Kucera to Identification, Adaptive and Nonlinear Control , 1998, Autom..

[13]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[14]  I. Landau,et al.  Recursive algorithms for identification in closed loop-a unified approach and evaluation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[15]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[16]  Ioan Doré Landau,et al.  Design and Tuning of Reduced Order H-Infinity Feedforward Compensators for Active Vibration Control , 2012, IEEE Transactions on Control Systems Technology.

[17]  John B. Moore,et al.  High Performance Control , 1997 .

[18]  A. Franco,et al.  A methodology for the design of feedback active vibration control systems , 2001, 2001 European Control Conference (ECC).

[19]  Charles E. Kinney,et al.  ROBUST ESTIMATION AND ADAPTIVE CONTROLLER TUNING FOR VARIANCE MINIMIZATION IN SERVO SYSTEMS , 2010 .

[20]  Jie Zeng,et al.  Recursive filter estimation for feedforward noise cancellation with acoustic coupling , 2006 .

[21]  Lennart Ljung,et al.  On positive real transfer functions and the convergence of some recursive schemes , 1977 .

[22]  Ioan Doré Landau,et al.  An IIR Youla-Kucera parametrized adaptive feedforward compensator for active vibration control with mechanical coupling , 2011, IEEE Conference on Decision and Control and European Control Conference.

[23]  Sen M. Kuo,et al.  Active noise control: a tutorial review , 1999, Proc. IEEE.

[24]  Ioan Doré Landau,et al.  A Youla-Kucera parametrized adaptive feedforward compensator for active vibration control , 2011 .

[25]  Wei Ren,et al.  Convergence analysis of the filtered-U algorithm for active noise control , 1999, Signal Process..

[26]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[27]  Foued Ben Amara,et al.  Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs , 2008 .

[28]  Javad Poshtan,et al.  A Computationally Efficient Adaptive IIR Solution to Active Noise and Vibration Control Systems , 2010, IEEE Transactions on Automatic Control.