EIGENVECTOR GEOMETRY OF THIRD ORDER LINEAR PHASE TRAJECTORIES
Abstract
An investigation into the general nature and properties of phase trajectories of third order linear feedback control systems has been conducted. The geometry of eigenvectors, eigenplanes, and the conic surface named the eigencone was investigated with respect to system root parameters. An analysis has been made of the orientation of eigenplanes of systems with three real roots, and of complex eigenplane geometry as the damping ratio, and undamped natural frequency were varied. A method is introduced for determining system roots that will locate an eigenplane or complex eigenplane in a pre-determined location in third order error space. Analog and digital computer programs used to obtain phase trajectories of third order linear systems are presented. The effect of root location in the s-plane on phase trajectories is discussed. A thorough analysis of the effect of initial conditions on real root and complex root phase trajectories is presented along with numerous photographs of three- dimensional phase trajectory models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1962
- Accession Number
- AD0480857
Entities
People
- Darrel E. Westbrook Jr.
- Richard C. Dietz
Organizations
- Naval Postgraduate School