An analysis of signal transformation approach to triangular waveform tracking

This paper is concerned with the mathematical analysis of the signal transformation approach to triangular waveform tracking. We provide necessary and sufficient conditions for stability and convergence of tracking error for a general class of plants and compensators. A procedure is offered to incorporate robustness against plant uncertainties and disturbances in the signal transformation method. Moreover, effectiveness of the method compared to an ordinary 2-DoF feedback control system is investigated. Simulation results are presented that reveal the conditions under which the incorporation of signal transformation blocks in a linear feedback loop may introduce control performance improvements.

[1]  Paolo Pennacchi.  Robustness of Command Input Preshaping Technique Applied to Residual Vibration Reduction , 2004 .

[2]  Yea-Chin Yeh,et al.  Application of the continuous no-reset switching iterative learning control on a novel optical scanning system , 2009 .

[3]  S. O. Reza Moheimani,et al.  High-Performance Control of Piezoelectric Tube Scanners , 2007, IEEE Transactions on Control Systems Technology.

[4]  Warren P. Seering,et al.  Using input command pre-shaping to suppress multiple mode vibration , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[5]  Qingze Zou,et al.  Iterative control of dynamics-coupling-caused errors in piezoscanners during high-speed AFM operation , 2005, IEEE Transactions on Control Systems Technology.

[6]  Warren P. Seering,et al.  Preshaping Command Inputs to Reduce System Vibration , 1990 .

[7]  S. O. Reza Moheimani,et al.  Sensor fusion for improved control of piezoelectric tube scanners , 2007, 2007 IEEE/ASME international conference on advanced intelligent mechatronics.

[8]  Kam K. Leang,et al.  Design and Analysis of Discrete-Time Repetitive Control for Scanning Probe Microscopes , 2009 .

[9]  F. Allgöwer,et al.  High performance feedback for fast scanning atomic force microscopes , 2001 .

[10]  Kenji Hirata,et al.  Reference Governor for Constrained Systems with Time-varying References , 2006, 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

[11]  Toshiharu Sugie,et al.  Off-Line Reference Shaping of Periodic Trajectories for Constrained Systems With Uncertainties , 2008, IEEE Transactions on Automatic Control.

[12]  Yuen Kuan Yong,et al.  Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning , 2009, IEEE Transactions on Nanotechnology.

[13]  Chen Youping,et al.  A linear drive system for the dynamic focus module of SLS machines , 2007 .

[14]  S O Reza Moheimani,et al.  Invited review article: accurate and fast nanopositioning with piezoelectric tube scanners: emerging trends and future challenges. , 2008, The Review of scientific instruments.

[15]  A. Sebastian,et al.  Control of MEMS-Based Scanning-Probe Data-Storage Devices , 2007, IEEE Transactions on Control Systems Technology.

[16]  S. S. Aphale,et al.  High-bandwidth control of a piezoelectric nanopositioning stage in the presence of plant uncertainties , 2008, Nanotechnology.

[17]  Abu Sebastian,et al.  Signal transformation approach to fast nanopositioning. , 2009, The Review of scientific instruments.

[18]  Paolo Pennacchi,et al.  Pre-shaping motion input for a rotating flexible link , 2001 .

[19]  Santosh Devasia,et al.  A Survey of Control Issues in Nanopositioning , 2007, IEEE Transactions on Control Systems Technology.

[20]  Toshiharu Sugie,et al.  Robust reference shaping of periodic trajectories for systems with state/input constraints using impulse and step responses , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[21]  Goele Pipeleers,et al.  Optimal Performance Tradeoffs in Repetitive Control: Experimental Validation on an Active Air Bearing Setup , 2009, IEEE Transactions on Control Systems Technology.

[22]  Ilya V. Kolmanovsky,et al.  Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor , 2002, Autom..

[23]  Tae Gyoon Lim,et al.  Model-based reference trajectory generation for tip-based learning controller , 2005 .

[24]  Theodore Antonakopoulos,et al.  Probe-based ultrahigh-density storage technology , 2008, IBM J. Res. Dev..

[25]  I.A. Mahmood,et al.  Tracking Control of a Nanopositioner Using Complementary Sensors , 2009, IEEE Transactions on Nanotechnology.

[26]  Murti V. Salapaka,et al.  High bandwidth nano-positioner: A robust control approach , 2002 .

[27]  Otto J. M. Smith,et al.  Feedback control systems , 1958 .

[28]  S.O.R. Moheimani,et al.  PVPF control of piezoelectric tube scanners , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[29]  William L. Luyben,et al.  Design of low-frequency compensators for improvement of plantwide regulatory performance , 1997 .