City Research Online

Optimisation of condition number for eigenstructure problems

Sayyad, Ali (2016). Optimisation of condition number for eigenstructure problems. (Unpublished Doctoral thesis, City, University of London)


This thesis deals with a new solution for the problem of eigenstructure assignment in control systems design. A wide range of challenging issues is examined involving the problem of eigenstructure assignment and associated system properties through different forms of complexity which are strongly related to control system design. In this thesis, specific attention has been given to the issue of skewness of the closedloop eigenframe of the state matrix. In fact, the aim is to develop a new methodology for determining the best angle between closed-loop eigenvectors by optimising the minimal condition number of the closed-loop eigenvector matrix. This problem is strongly linked to sensitivity of eigenvalues to parameter uncertainty, perturbations to model parameter uncertainty. The importance of this methodology can be expressed in terms of results related to the Sensitivity of eigenvalues, Relative measures of controllability and observability and also deviations from strong stability to overshooting behaviour. Among this variety of eigenstructure assignment methods, special consideration has been paid to Geometric Theory, which introduces an alternative solution to the assignability of spectrum of controllability subspaces (cs) based on an eigenvector approach and then develops a new pole assignment algorithm based on openloop/ closed-loop spectra as a practical application of this approach. In order to tackle the problem of measuring the skewness of angles between closed-loop eigenvalues, some measures for Eigenframe skewness have been defined in general and so the necessary and efficient conditions have been derived for the angle between some subspaces in a direct sum decomposition to be maximized. This has been done via three metrics; Condition Number, Determinant of Gram Matrix and Singular Values. The thesis presents the parametrisation of closed-loop eigenframes result by the method generated in [4]. Within this thesis, a non-smooth algorithm has been developed in order to select the most orthogonal closed-loop eigenframe and so the influence of selected closed-loop spectra. Also, the parametrisation of controllability subspaces in a standard direct sum decomposition using matrix fraction description (MFD) has been derived.

Within this thesis the construction and the existence of controllability subspaces connected to (A,B)-invariant subspaces, has also been studied. In addition, an algebraic description of the total system behaviour which leads to an algebraic characterisation of the total input, state and output behaviour in an implicit formulation is given based on properties of MFD descriptions, a topic which remains open for future studies.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Science & Technology > Engineering
Doctoral Theses
School of Science & Technology > School of Science & Technology Doctoral Theses
Text - Accepted Version
Download (1MB) | Preview



Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login