Control design for a bilinear system reachable sets and exact linearization

Author

Axelsson, Jan Peter ; Hagander, Per

Author_Institution

Dept. of Autom. Control, Lund Inst. of Technol., Sweden

fYear

1990

fDate

5-7 Dec 1990

Firstpage

2828

Abstract

A bilinear system model of a continuous tank reactor from a biotechnology application (F. Mandenius et al., 1987) is studied. The concentrations of the substrate sugar and the product ethanol were measured on-line and utilized to control the flow-rate through the fermenter. The system can be integrated analytically making it possible to describe the reachable sets. Limited controllability is found on a line in the state space. These reachable set expressions are used to obtain a time-optimal controller that for large disturbances implies reversed control action as compared to linear control. Transformations used when applying exact linearization are described. The lack of controllability, also obtained using the Lie brackets of differential geometry, shows up as singularities in the transformations

Keywords

control system synthesis; fermentation; linear systems; linearisation techniques; nonlinear systems; optimal control; set theory; Lie brackets; bilinear system reachable sets; continuous tank reactor; differential geometry; exact linearization; fermenter; reachable set expressions; reversed control action; time-optimal controller; Biotechnology; Control design; Controllability; Design methodology; Equations; Ethanol; Inductors; Nonlinear systems; Optimal control; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1990., Proceedings of the 29th IEEE Conference on

Conference_Location

Honolulu, HI

Type

conf

DOI

10.1109/CDC.1990.203294

Filename

203294