Two-degree-of-freedom l2-optimal tracking with preview

  • Authors:

  • David N. Hoover;Roland Longchamp;Joachim Rosenthal

  • Affiliations:

  • STI-IPR-LCSM, ícole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland;STI-I2S-LA, ícole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland;Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5641, USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2004

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Abstract

A simple SISO two-degree-of-freedom pole-placement design method is presented that provides @?"2-optimal tracking of a given reference signal. The closed-loop pole locations are first chosen by the system designer. The closed-loop zeros are then placed in an optimal fashion by a computationally inexpensive algorithm to achieve asymptotic tracking with an optimal transient response. The preview approach, which has become a common method for dealing with systems which have non-minimum phase behavior, can then optionally be used to further improve the transient behavior for both minimum phase and non-minimum phase systems. Unlike previous results based on the preview approach, the solution presented here takes into consideration the closed-loop pole dynamics, and is @?"2 optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the H"2 model matching problem, where the design parameter Q is not rational, but polynomial, is the heart of the solution method.