H∞ optimal and suboptimal controllers for infinite dimensional SISO plants

This paper presents a simple formula for H/sup /spl infin// optimal and suboptimal controllers for unstable SISO distributed plants, with rational weighting functions. The controller is expressed in terms of i) inner and outer parts of the plant, ii) a finite dimensional spectral factor obtained from the weighting functions, and iii) a rational function satisfying certain interpolation conditions. Under certain genericity assumptions, this rational function is of dimension less than or equal to n/sub 1/+l-1 (n/sub 1/+l in the suboptimal case), where l is the number of unstable poles of the plant and n/sub 1/ is the order of the sensitivity weighting function. There are 2(n/sub 1/+l) (2(n/sub 1/+l+1) in the suboptimal case) linear equations, which determine this rational function. These linear equations can be written directly from the structure of the controller. >

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

[2]  Edmond A. Jonckheere,et al.  On computing the spectral radius of the Hankel plus Toeplitz operator , 1988 .

[3]  M. Kreĭn,et al.  ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM , 1971 .

[4]  Malcolm C. Smith,et al.  On the optimal two block H∞ compensators for distributed unstable plants , 1992, 1992 American Control Conference.

[5]  Sanjoy K. Mitter,et al.  A note on essential spectra and norms of mixed Hankel-Toeplitz operators , 1988 .

[6]  Allen Tannenbaum,et al.  Optimal H∞ interpolation: A new approach , 1986, 1986 25th IEEE Conference on Decision and Control.

[7]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[8]  Malcolm C. Smith.  On stabilization and the existence of coprime factorizations , 1989 .

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

[10]  Allen Tannenbaum,et al.  Abstract model and controller design for an unstable aircraft , 1992 .

[11]  Ruth F. Curtain,et al.  H/sub infinity /-control for distributed parameter systems: a survey , 1990, 29th IEEE Conference on Decision and Control.

[12]  Hitay Özbay,et al.  Tutorial review H∞ optimal controller design for a class of distributed parameter systems , 1993 .