Comparison of the time vector method and the state-space method (Eigenvector analysis) for aircraft parameter identification

Many methods for aircraft parameter identification have been developed and are currently in use. Prior to the development of computer methods the graphical Time Vector Method (TVM) was introduced during 1950’s (ref.1,2). Basically the TVM is based on the mechanical vibration theory. When the aircraft responses have oscillatory modes they can be considered as vibrations even though the typical frequency of these may be higher than those of the mechanical vibrations. Because of the graphical approach, the TVM may produce inaccurate results. But it gives use thorough understanding of the physical system. Owing to the rapid development of computers and sophisticated parameter identification algorithms, the rather limited graphical method has fallen into disuse and the other have emerged to replace it. They are, typically, the output error methods, the equation error methods, the Kalman filter estimator, the maximum likelihood technique, and so on (ref. 3~6).

The damping angle, natural frequency, relative magnitude and phase angle of each dynamic mode are the basis of the TVM. In this respect the state-space models can provide the same information. In particular the eigenvalues and eigenvectors which involve all the response information of the system, have the same properties as the time vectors. So, the objective of this report is to shown the relationship between the TVM and the state-space method of an analysis and hence to facilitate the state-space method (eigenvector analysis) for aircraft parameter identification.