On H/sup /spl infin// optimal repetitive controllers

In this paper we consider a two degree of freedom repetitive controller design for a SISO finite dimensional plant. We pose an H/sup /spl infin// optimal control problem, which we then convert to a two block problem involving a MIMO plant with a scalar time delay, by constraining the solution to have a certain "standard" repetitive structure. We solve a generalization of this two block infinite dimensional MIMO H/sup /spl infin// optimal control problem by an extension/modification of results for similar SISO systems. The resulting two degree of freedom H/sup /spl infin// optimal repetitive controller leads to a more general repetitive control structure.<<ETX>>

[1]  P. Khargonekar.  Control System Synthesis: A Factorization Approach (M. Vidyasagar) , 1987 .

[2]  George Anwar,et al.  Low Velocity Friction Compensation and Feedforward Solution based on Repetitive Control , 1991, 1991 American Control Conference.

[3]  Allen Tannenbaum,et al.  Some Explicit Formulae for the Singular Values of Certain Hankel Operators with Factorizable Symbol , 1988 .

[4]  D. Sarason.  Generalized interpolation in , 1967 .

[5]  F. Kobayashi,et al.  Reduction of motor speed fluctuation using repetitive control , 1990, 29th IEEE Conference on Decision and Control.

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

[7]  K. Srinivasan,et al.  Discrete-Time Repetitive Control System Design Using the Regeneration Spectrum , 1993 .

[8]  Shinji Hara,et al.  Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem , 1987, 26th IEEE Conference on Decision and Control.

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

[10]  Nader Sadegh,et al.  Synthesis and Stability Analysis of Repetitive Controllers , 1991, 1991 American Control Conference.

[11]  K. Srinivasan,et al.  Analysis and Design of Repetitive Control Systems using the Regeneration Spectrum , 1990, 1990 American Control Conference.

[12]  Hong Yang,et al.  H∞ mixed sensitivity design for a real multivariable delay problem , 1991, 1991 American Control Conference.

[13]  Allen Tannenbaum,et al.  Mixed-sensitivity optimization for a class of unstable infinite-dimensional systems , 1993 .

[14]  M. Tomizuka,et al.  Digital control of repetitive errors in disk drive systems , 1990, IEEE Control Systems Magazine.

[15]  C. Foias,et al.  The commutant lifting approach to interpolation problems , 1990 .

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

[17]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

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

[19]  Allen Tannenbaum,et al.  On the Four Block Problem, I , 1988 .

[20]  Masayoshi Tomizuka,et al.  Adaptive And Repetitive Digital Control Algorithms for Noncircular Machining , 1988, 1988 American Control Conference.

[21]  G. Zames,et al.  On H ∞ -optimal sensitivity theory for SISO feedback systems , 1984 .

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