TY - CHAP
T1 - Some Applications of Differential Geometry in Control
AU - Schlacher, Kurt
AU - Fuchshumer, Stefan
AU - Holl, Johann
PY - 2004
Y1 - 2004
N2 - Differential geometry has been introduced to control about 25 years ago. This contribution shows, how one can identify dynamic systems with geoemtric objects defined on certain manifolds such that one obtains a coordinate free description of the systems. Based on this approach basic properties like accessibility and observability will be introduced. After that, tests, whether a system shows these properties, are presented. To show the power of the geometric approach for the control loop design, the two methods input to output and input to state linearization have been selected, finally, it is worth mentioning that all the presented methods can easily be implemented in any advanced computer algebra system.
AB - Differential geometry has been introduced to control about 25 years ago. This contribution shows, how one can identify dynamic systems with geoemtric objects defined on certain manifolds such that one obtains a coordinate free description of the systems. Based on this approach basic properties like accessibility and observability will be introduced. After that, tests, whether a system shows these properties, are presented. To show the power of the geometric approach for the control loop design, the two methods input to output and input to state linearization have been selected, finally, it is worth mentioning that all the presented methods can easily be implemented in any advanced computer algebra system.
UR - http://regpro.mechatronik.uni-linz.ac.at
U2 - 10.1007/978-3-7091-2774-2_13
DO - 10.1007/978-3-7091-2774-2_13
M3 - Chapter
SN - 3-211-22867-5
T3 - CISM Courses and Lectures No. 444
BT - Advanced Dynamics and Control of Structures and Machines
PB - Springer Wien New York
ER -