Pole-placement with minimum effort for linear multivariable systems

This dissertation is concerned with the problem of the exact pole-placement by minimum control effort using state and output feedback for linear multivariable systems. The novelty of the design lies in obtaining a direct transformation of the system matrices into a modified controllable canonical form. Two realizations are identified, and the algorithms to obtain them are derived. In both cases, the transformation matrix has some degrees of freedom by tuning a scalar or a set of scalars within the matrix. These degrees of freedom are utilized in the solution to reduce further the norm of the state feedback matrix. Then the pole-placement problem is solved by minimizing a certain functional, subject to a set of specified constraints. A non-canonical form approach to the problem is also proposed, where it was only necessary to transform the input matrix to a special form. The transformation matrix, in this method, has larger degrees of freedom which can be utilized in the solution. Moreover, a new pole-placement method based on the non-canonical approach is derived. The solution, in this method, was made possible by solving the Lyapunov matrix equation. Finally, an iterative algorithm for pole-placement by output feedback is extended so as to obtain an output feedback matrix with a small norm. The extension has been accomplished by applying the successive pole shifting method. Two schemes for the pole shifting are proposed. The first is to successively shift the poles through straight paths starting from the open loop poles and ending at the desired poles, whereas the second scheme shifts the poles according to a successive change of their characteristic polynomial coefficients.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical Engineering

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1988

Author dc:creator

• Al-Muthairi, Naser F.

Chair dc:contributor.committeechair

• Bingulac, S.

Committee members dc:contributor.committeemember

• Lindner, Douglas
• Luse, D.W.
• McCoy, Robert A.
• VanLandingham, Hugh F.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Handle dc:identifier.uri

http://hdl.handle.net/10919/49916

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/49916