A discrete time-varying internal model based approach for high precision tracking

In this paper, we consider the discrete time case of a time-varying internal model-based control design for high precision tracking of frequency-varying reference trajectories. Thanks to a recently proposed parallel time-varying internal model structure, the asymptotic tracking conditions for the design of internal model units are developed, and a low order robust stabilizer is synthesized. In a discrete time setting, the high precision tracking control architecture is deployed on a Voice Coil Motor (VCM) actuated servo gantry system, where numerical simulation and real time experimental results are given to validate the proposed method.

[1]  Shang-Liang Chen,et al.  Repetitive control design and implementation for linear motor machine tool , 2007 .

[2]  Peiqing Ye,et al.  An Internal Model-Based Tracking Control for a Class of Uncertain Linear Time-Varying Systems , 2010 .

[3]  S. Verma,et al.  Multi-axis maglev nanopositioner for precision manufacturing and manipulation applications , 2005, IEEE Transactions on Industry Applications.

[4]  Andrew G. Alleyne,et al.  A Cross-Coupled Iterative Learning Control Design for Precision Motion Control , 2008, IEEE Transactions on Control Systems Technology.

[5]  Chao Lu,et al.  Time-varying internal model-based tracking control for a voice coil motor servo gantry , 2013, 2013 American Control Conference.

[6]  S. Hara,et al.  Repetitive control system: a new type servo system for periodic exogenous signals , 1988 .

[7]  Hayato Yoshioka,et al.  A Newly Developed Linear Motor-Driven Aerostatic X-Y Planar Motion Table System for Nano-Machining , 2007 .

[8]  Tsu-Chin Tsao,et al.  Optimal Suppression of Laser Beam Jitter by High-Order RLS Adaptive Control , 2008, IEEE Transactions on Control Systems Technology.

[9]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[10]  Masayoshi Tomizuka,et al.  Robust adaptive and repetitive digital tracking control and application to a hydraulic servo for noncircular machining , 1994 .

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

[12]  Michio Nakano,et al.  High Accuracy Control of a Proton Synchrotron Magnet Power Supply , 1981 .

[13]  Valter J. S. Leite,et al.  Gain scheduled state feedback control of discrete-time systems with time-varying uncertainties: an LMI approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Zhen Zhang,et al.  A discrete time-varying internal model based approach for high precision tracking , 2013 .

[15]  A. Isidori Nonlinear Control Systems , 1985 .

[16]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[17]  Akira Ichikawa,et al.  Output regulation of time-varying systems , 2006, Syst. Control. Lett..

[18]  Roberto Horowitz,et al.  A variable structure multirate State estimator for seeking control of HDDs , 2005, IEEE Transactions on Control Systems Technology.

[19]  Zongxuan Sun,et al.  Robust stabilizer design for Linear time varying internal model based control , 2012, 2012 American Control Conference (ACC).

[20]  Zongxuan Sun,et al.  Robust Stabilization of Discrete Linear Time Varying Internal Model Based System , 2012 .

[21]  Zongxuan Sun,et al.  A Novel Internal Model-Based Tracking Control for a Class of Linear Time-Varying Systems , 2010 .

[22]  Andrea Serrani,et al.  Adaptive Robust Output Regulation of Uncertain Linear Periodic Systems , 2009, IEEE Transactions on Automatic Control.

[23]  B. Francis The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[24]  Andrea Serrani,et al.  The Linear Periodic Output Regulation Problem , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[25]  Zhen Zhang,et al.  Trajectory tracking and disturbance rejection for linear time-varying systems: Input/output representation , 2009, Syst. Control. Lett..