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

• 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

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

Publikations- och innehållstyp

kon (ämneskategori)

ref (ämneskategori)