Iterative learning control with advanced output data for nonminimum phase systems

This paper investigates iterative learning control of discrete time nonminimum phase systems. First, an iterative learning control scheme of linear maximum phase systems is briefly discussed. It is shown that the inverse mapping from desired output to input is stable for maximum phase systems with the proposed method. Next, the results are extended to nonminimum phase systems. The stability of the inverse mapping from the desired output to the input can be shown based on the results of maximum phase systems. The input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros. Also, the results are extended to the nonlinear systems and the boundedness of the desired input is proven locally around the origin. An example is given to indicate the importance of proper advances of output in the input update law.

[1]  Masayoshi Tomizuka,et al.  Experimental flexible beam tip tracking control with a truncated series approximation to uncancelable inverse dynamics , 1994, IEEE Trans. Control. Syst. Technol..

[2]  M. Morari,et al.  A normal form approach to approximate input-output linearization for maximum phase nonlinear SISO systems , 1996, IEEE Trans. Autom. Control..

[3]  B. Paden,et al.  Iterative learning control for nonlinear nonminimum phase plants with input disturbances , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[4]  Masayoshi Tomizuka,et al.  Zero Phase Error Tracking Algorithm for Digital Control , 1987 .

[5]  P. Lucibello.  Inversion of linear square systems by learning , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[6]  Masaru Uchiyama,et al.  Formation of High-Speed Motion Pattern of a Mechanical Arm by Trial , 1978 .

[7]  B. Paden,et al.  Nonlinear inversion-based output tracking , 1996, IEEE Trans. Autom. Control..

[8]  Myung Jin Chung,et al.  ILC for non-minimum phase system , 1996, Int. J. Syst. Sci..

[9]  C. Melchiorri,et al.  Comparison of noncausal inversion techniques for discrete time linear systems: application to a flexible link , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

[10]  Chong-Ho Choi,et al.  A feedforward controller by modified series approximation , 1998 .

[11]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[12]  B. Paden,et al.  Pseudo-inverse based iterative learning control for plants with unmodelled dynamics , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  P. Lucibello,et al.  Inversion of nonlinear time-varying systems , 1993, IEEE Trans. Autom. Control..

[14]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[15]  Chong-Ho Choi,et al.  Iterative learning control for linear discrete time nonminimum phase systems , 2002, Autom..