Nonlinear Analysis of Correlative Tracking Systems Using Renewal Process Theory,
Abstract
Renewal process theory is used to describe the behavior of an n-th order synchronous control system in which the nonlinearity is periodic (PLL-type) or a nonperiodic (DLL-type). It is shown that the stationary pdf, the mean time between two cycle slips and the average number of cycles slipped to the right and to the left can be obtained by solving a single Fokker-Planck equation of the renewal process. The renewal process approach is compared with the so-called 'periodic extension' (PE) appraoch introduced by Lindsey. It is shown that the pdf obtained via the renewal process approach can be reduced to agree with the PE solution for a first order loop only. In the general case of an n-th order system, however, the two approaches lead to a different set of differential equations. In fact, it is shown that the approach based upon renewal process theory yields more information about the steady-state behavior of the system than does the PE solution. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1974
- Accession Number
- AD0778297
Entities
People
- Heinrich Meyr
Organizations
- University of Southern California