Mathematical Tools and Software for Analysis and Design of Nonlinear Control Systems
1992 (English)Doctoral thesis, monograph (Other academic)
The theory of nonlinear control systems has developed rapidly <luring the last decades, but still only small parts of this theory have become standard tools for a control engineer in practice. There are at least two reasons for that. One is that the theory still lacks many results related to practical issues, such as constructive computational methods and robustness results. The other reason is that there are few software tools available to support the new theory.
In this thesis we will give a survey of some mathematical tools, in which we focus on constructive theory. In particular we will describe the theory of Volterra series and exact linearization in detail, since we believe that these theories have the potential to become standard mathematical tools in control theory.
With this theory as a background, we then study some issues of practical importance. We investigate structural questions for Volterra series and derive some results on complexity and computational aspects. The use of a reduced Kronecker product formalism is pointed out, and an attempt to connect the input-output behavior of a nonlinear system and the controller design is made.
Then, we investigate some robustness issues arising when exact linearization is used as a design method. We study the robustness properties of an LQ design and show how Volterra series descriptions can be used to analyze the effect of model errors.
In order to make the theory useful and available for the user in a more practical situation, some algorithms for nonlinear computations are presented and a software package for computer algebra systems is developed. Examples and implementations are made in two such systems, and some aspects of using those are given.
Place, publisher, year, edition, pages
Linköping: Linköping University , 1992. , 174 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 285
IdentifiersURN: urn:nbn:se:liu:diva-98083ISBN: 91-7870-989-XOAI: oai:DiVA.org:liu-98083DiVA: diva2:652089
1992-09-25, C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)