A Design Method for Two-Degree-of-Freedom Simple Multi-Period Repetitive Control Systems

The multi-period repetitive (MPR) control system is a type of servomechanism for periodic reference inputs. Using MPR controllers, transfer functions from the reference input to the output and from the disturbance to the output of the MPR control system have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed MPR control systems, named simple multi-period repetitive (simple MPR) control systems, where these transfer functions have finite numbers of poles. In addition, Yamada and Takenaga clarified the parameterization of all stabilizing simple MPR controllers. However, using the simple MPR repetitive controller by Yamada and Takenaga, we cannot specify the input-output characteristic and the disturbance attenuation characteristic separately. From the practical point of view, it is desirable to specify the input-output characteristic and the disturbance attenuation characteristic separately. The purpose of this paper is to propose the parameterization of all stabilizing two-degree-of-freedom (TDOF) simple MPR controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately.

[1]  Masao Ikeda,et al.  Repetitive control for systems with nonzero relative degree , 1988, 29th IEEE Conference on Decision and Control.

[2]  Graham C. Goodwin,et al.  A parameterization for the class of all stabilizing controllers for linear minimum phase plants , 1994, IEEE Trans. Autom. Control..

[3]  Takaaki Hagiwara,et al.  The Parameterization of All Stabilizing Multi-Period Repetitive Controllers for Time-Delay Plants with the Specified Input-Output Characteristic , 2011 .

[4]  R. G. Molyet,et al.  A new approach to phase cancellation in repetitive control , 1994, Proceedings of 1994 IEEE Industry Applications Society Annual Meeting.

[5]  Dante C. Youla,et al.  Modern Wiener--Hopf design of optimal controllers Part I: The single-input-output case , 1976 .

[6]  Kou Yamada,et al.  A Design Method for Repetitive Control Systems with a Multi-Period Repetitive Compensator , 2002 .

[7]  Shinji Hara,et al.  Stability of Multivariable Repetitive Control Systems , 1986 .

[8]  Yasuyuki Funahashi,et al.  A Design Method of Repetitive Controllers , 1996 .

[9]  Kou Yamada,et al.  A Design Method for Multi-period Repetitve Controllers : Design Method Using the Parametrization of All Multi-period Repetitive Controllers , 2005 .

[10]  Keiji Watanabe,et al.  Stabilization of Repetitive Control Systems-Spectral Decomposition Approach , 1986 .

[11]  Michio Nakano,et al.  High Accuracy Control of Play-Back Servo Systems , 1981 .

[12]  Shinji Hara,et al.  The Internal Model Principle and Stabilizability of Repetitive Control Systems , 1986 .

[13]  M. Vidyasagar.  Control System Synthesis : A Factorization Approach , 1988 .

[14]  Maarten Steinbuch,et al.  Repetitive control for systems with uncertain period-time , 2002, Autom..

[15]  Hidehiko Sugimoto,et al.  A Design Method for Modified Repetitive Control System with Corrected Dead Time , 1998 .

[16]  Toru Omata,et al.  Nonlinear repetitive control with application to trajectory control of manipulators , 1987, J. Field Robotics.

[17]  Michio Nakano,et al.  High Accuracy Control for Magnet Power Supply of Proton Synchrotron in Recurrent Operation , 1980 .

[18]  Hidehiko Sugimoto,et al.  A Proposition of Modified Repetitive Control with Corrected Dead Time , 1998 .

[19]  功 山田,et al.  多重周期繰返し補償器を用いた繰返し制御系の一設計法(機械力学,計測,自動制御) , 2003 .

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

[21]  K. Yamada,et al.  A Design Method of Simple Multi-period Repetitive Controllers , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[22]  Michio Nakano,et al.  Stability Condition and Synthesis Methods for Repetitive Control Systems , 1986 .