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Control Design for a Bilinear System. Reachable Sets and Exact Linearization

Axelsson, Jan Peter and Hagander, Per LU (1990) 29th IEEE Conference on Decision and Control, 1990
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to conference
publication status
published
subject
keywords
reversed control action, Lie brackets, differential geometry, control system synthesis, fermentation, linear syste, bilinear system reachable sets, exact linearization, continuous tank reactor, fermenter, reachable set expressions, time-optimal controller
conference name
29th IEEE Conference on Decision and Control, 1990
external identifiers
  • Scopus:0025530080
language
English
LU publication?
yes
id
2dc63ecd-5893-4022-b8a2-c27f273028f9 (old id 8517544)
date added to LUP
2016-01-19 13:23:05
date last changed
2016-04-16 11:18:56
@misc{2dc63ecd-5893-4022-b8a2-c27f273028f9,
  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.},
  author       = {Axelsson, Jan Peter and Hagander, Per},
  keyword      = {reversed control action,Lie brackets,differential geometry,control system synthesis,fermentation,linear syste,bilinear system reachable sets,exact linearization,continuous tank reactor,fermenter,reachable set expressions,time-optimal controller},
  language     = {eng},
  title        = {Control Design for a Bilinear System. Reachable Sets and Exact Linearization},
  year         = {1990},
}