Self-tuning MIMO disturbance feedforward control for active hard-mounted vibration isolators

Abstract This paper proposes a multi-input multi-output (MIMO) disturbance feedforward controller to improve the rejection of floor vibrations in active vibration isolation systems for high-precision machinery. To minimize loss of performance due to model uncertainties, the feedforward controller is implemented as a self-tuning generalized FIR filter. This filter contains a priori knowledge of the poles, such that relatively few parameters have to be estimated which makes the algorithm computationally efficient. The zeros of the filter are estimated using the filtered-error least mean squares (FeLMS) algorithm. Residual noise shaping is used to reduce bias. Conditions on convergence speed, stability, bias, and the effects of sensor noise on the self-tuning algorithm are discussed in detail. The combined control strategy is validated on a 6-DOF Stewart platform, which serves as a multi-axis and hard-mounted vibration isolation system, and shows significant improvement in the rejection of floor vibrations.

[1]  Wei Ren,et al.  Convergence analysis of the multi-variable filtered-X LMS algorithm with application to active noise control , 1999, IEEE Trans. Signal Process..

[2]  Brett Ninness,et al.  Frequency domain analysis of tracking and noise performance of adaptive algorithms , 1998, IEEE Trans. Signal Process..

[3]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[4]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[5]  Hideaki Sakai,et al.  Mean-Square Performance of the Filtered-Reference/ , 2005 .

[6]  Johannes van Dijk,et al.  Active vibration isolation control: Comparison of feedback and feedforward control strategies applied to Coriolis mass-flow meters , 2015, 2015 American Control Conference (ACC).

[7]  Herman Soemers,et al.  Sensor fusion for active vibration isolation in precision equipment , 2012 .

[8]  Ryota Shimizu,et al.  Systematic analyses of vibration noise of a vibration isolation system for high-resolution scanning tunneling microscopes. , 2011, The Review of scientific instruments.

[9]  Dean Karnopp,et al.  Comparative Study of Optimization Techniques for Shock and Vibration Isolation , 1969 .

[10]  Stephen J. Elliott,et al.  Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances , 2000, IEEE Trans. Signal Process..

[11]  Mf Marcel Heertjes,et al.  Self-tuning in master–slave synchronization of high-precision stage systems , 2013 .

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

[13]  Andrew J. Fleming,et al.  Optimal integral force feedback for active vibration control , 2015 .

[14]  Georg Schitter,et al.  Atomic force microscopy using voice coil actuators for vibration isolation , 2015, 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM).

[15]  Arthur P. Berkhoff,et al.  Combined MIMO adaptive and decentralized controllers for broadband active noise and vibration control , 2009 .

[16]  Sen M. Kuo,et al.  Residual noise shaping technique for active noise control systems , 1994 .

[17]  Bernard Widrow.  Adaptive inverse control , 1990, Defense, Security, and Sensing.

[18]  Marcel François Heertjes,et al.  Performance trade-offs in disturbance feedforward compensation of active hard-mounted vibration isolators , 2015, 2015 American Control Conference (ACC).

[19]  André Preumont,et al.  FORCE FEEDBACK VERSUS ACCELERATION FEEDBACK IN ACTIVE VIBRATION ISOLATION , 2002 .

[20]  Dayong Zhou,et al.  Hybrid filtered error LMS algorithm: another alternative to filtered-x LMS , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Eric A. Wan,et al.  Adjoint LMS: an efficient alternative to the filtered-x LMS and multiple error LMS algorithms , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[22]  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..

[23]  J. Shynk.  Adaptive IIR filtering , 1989, IEEE ASSP Magazine.

[24]  MF Marcel Heertjes,et al.  Self-tuning feedforward control for active vibration isolation of precision machines , 2014 .

[25]  Elias Bjarnason.  Analysis of the filtered-X LMS algorithm , 1995, IEEE Trans. Speech Audio Process..

[26]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[27]  Charles E. Kinney,et al.  Active noise control in a forced-air cooling system , 2010 .

[28]  D. Tjepkema,et al.  Active hard mount vibration isolation for precision equipment , 2008 .

[29]  A NEW FILTERED LMS ALGORITHM FOR ACTIVE NOISE CONTROL , 1999 .

[30]  Shunsuke Ishimitsu,et al.  Improvement of the convergence property of adaptive feedforward controllers and their application to the active control of ship interior noise , 2004 .

[31]  Michel Verhaegen,et al.  Robustness of the Filtered-X LMS Algorithm— Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty , 2007, IEEE Transactions on Signal Processing.

[32]  Sen M. Kuo,et al.  Active Noise Control Systems: Algorithms and DSP Implementations , 1996 .

[33]  Daniel Y. Abramovitch,et al.  Mitigating rotational disturbances on a disk drive with mismatched linear accelerometers , 2015, 2015 IEEE Conference on Control Applications (CCA).

[34]  Ali H. Sayed,et al.  Fundamentals Of Adaptive Filtering , 2003 .

[35]  Ronald G.K.M. Aarts,et al.  A linearized input–output representation of flexible multibody systems for control synthesis , 2009 .

[36]  Gerrit Wijnand van der Poel,et al.  An exploration of active hard mount vibration isolation for precision equipment , 2010 .

[37]  Marcel François Heertjes,et al.  Switching Control in Vibration Isolation Systems , 2013, IEEE Transactions on Control Systems Technology.

[38]  Issa M. S. Panahi,et al.  A novel feedforward active noise control structure with spectrum-tuning for residual noise , 2010, IEEE Transactions on Consumer Electronics.

[39]  Geoffrey A. Williamson,et al.  Globally convergent adaptive IIR filters based on fixed pole locations , 1996, IEEE Trans. Signal Process..