Header

UZH-Logo

Maintenance Infos

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


Hoover, D; Longchamp, R; Rosenthal, J (2004). Two-degree-of-freedom ℓ2-optimal tracking with preview. Automatica, 40(1):155-162.

Abstract

A simple SISO two-degree-of-freedom pole-placement design method is presented that provides ℓ2-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 ℓ2 optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the H2 model matching problem, where the design parameter Q is not rational, but polynomial, is the heart of the solution method.

Abstract

A simple SISO two-degree-of-freedom pole-placement design method is presented that provides ℓ2-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 ℓ2 optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the H2 model matching problem, where the design parameter Q is not rational, but polynomial, is the heart of the solution method.

Statistics

Citations

14 citations in Web of Science®
16 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

36 downloads since deposited on 11 Mar 2010
5 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Discrete-time control; Non-minimum phase systems; Optimality; Zero assignment; Two-degree-of-freedom controllers; Trajectory tracking; Preview control
Language:English
Date:2004
Deposited On:11 Mar 2010 09:20
Last Modified:06 Dec 2017 20:48
Publisher:Elsevier
ISSN:0005-1098
Publisher DOI:https://doi.org/10.1016/j.automatica.2003.09.003

Download

Download PDF  'Two-degree-of-freedom ℓ2-optimal tracking with preview'.
Preview
Filetype: PDF (Preprint)
Size: 1MB
View at publisher