On equivalence between internal and external model‐based repetitive learning controllers for nonlinear passive systems

In this paper a new class of globally stable finite dimensional repetitive controllers for nonlinear passive systems is proposed. The proposed internal model-based repetitive controller has a structure in the form of a parallel connection of linear oscillators and one integrator. The passive interconnection of the controller and the nonlinear passive systems provides the same stability conditions as the controller with the exact feed-forward compensation of system dynamics. The existing internal and external model-based repetitive controllers can be derived as the special cases of the proposed controller. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

[1]  Warren E. Dixon,et al.  Repetitive learning control: a Lyapunov-based approach , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[2]  Masayoshi Tomizuka,et al.  A Comparison of Four Discrete-Time Repetitive Control Algorithms , 1992, 1992 American Control Conference.

[3]  Jie Huang,et al.  On a robust synchronization problem via internal model approach , 2009 .

[4]  Masayoshi Tomizuka,et al.  Analysis and Synthesis of Discrete-Time Repetitive Controllers , 1989 .

[5]  Myung Jin Chung,et al.  Repetitive control for the track-following servo system of an optical disk drive , 1998, IEEE Trans. Control. Syst. Technol..

[6]  Masayoshi Tomizuka,et al.  A unified approach to the design of adaptive and repetitive controllers for robotic manipulators , 1990 .

[7]  Danko Brezak,et al.  Passive Finite-Dimensional Repetitive Control of Robot Manipulators , 2008, IEEE Transactions on Control Systems Technology.

[8]  Jayati Ghosh,et al.  Nonlinear repetitive control , 2000, IEEE Trans. Autom. Control..

[9]  Rafael Kelly,et al.  PD control with feedforward compensation for robot manipulators: analysis and experimentation , 2001, Robotica.

[10]  Roberto Horowitz,et al.  A new adaptive learning rule , 1991 .

[11]  Masayoshi Tomizuka,et al.  Discrete-Time Domain Analysis and Synthesis of Repetitive Controllers , 1988, 1988 American Control Conference.

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

[13]  Nader Sadegh,et al.  Design and implementation of adaptive and repetitive controllers for mechanical manipulators , 1992, IEEE Trans. Robotics Autom..

[14]  Nader Sadegh,et al.  A new repetitive controller for mechanical manipulators , 1991, J. Field Robotics.