Sensitivity reduction of adaptive repetitive control system with asymptotical rejection against uncertain periodic disturbance

This paper deals with a repetitive control problem for the cases where the period of periodic disturbances to be rejected is uncertain but is within known lower and upper bound. A new adaptive repetitive control system with on-line estimation of the period is proposed not only to guarantee stability of the overall system but also both to reject any periodic disturbances with the uncertain period and to reduce sensitivity against any disturbances, for example, non-periodic persistent ones. The design problem is reduced to a simple and feasible l1 norm minimization problem. The controller can be obtained easily by solving a simple linear programming problem. Simulations show the effectiveness of the proposed controller for rejection of periodic disturbances and sensitivity reduction.

[1]  W. Wonham,et al.  The internal model principle for linear multivariable regulators , 1975 .

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

[3]  T. Tsao,et al.  Asymptotic Rejection of Periodic Disturbances with Uncertain Period , 1992, 1992 American Control Conference.

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

[5]  M. Dahleh,et al.  Control of Uncertain Systems: A Linear Programming Approach , 1995 .

[6]  Masayoshi Tomizuka,et al.  Steady-State and Stochastic Performance of a Modified Discrete-Time Prototype Repetitive Controller , 1990 .

[7]  Jwu-Sheng Hu.  Variable Structure Digital Repetitive Controller , 1992, 1992 American Control Conference.

[8]  M. B. Zarrop,et al.  Self-Tuning Systems: Control and Signal Processing , 1991 .

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

[10]  Manabu Yamada,et al.  Design of discrete-time repetitive control system for pole placement and application , 1999 .

[11]  Manabu Yamada,et al.  Adaptive Repetitive Control with On-line Estimation of Multiple Periods , 2009 .

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

[13]  Manabu Yamada,et al.  Robust Repetitive Control System With On-Line Identification of the Period of Periodic Disturbances , 2004 .

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