Open AccessChaos and bifurcation in time delayed third order phase-locked loop
Author(s) -
Boulos Harb,
Mohammad Al Qudah,
Ibrahim Ghareeb,
Ahmad Harb
Publication year - 2021
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v11i2.pp1431-1438
Subject(s) - control theory (sociology) , chaotic , phase locked loop , loop (graph theory) , bifurcation , representation (politics) , nonlinear system , parameter space , padé approximant , stability (learning theory) , mathematics , computer science , phase (matter) , physics , control (management) , law , statistics , quantum mechanics , combinatorics , artificial intelligence , politics , machine learning , political science
In this paper, the modern nonlinear theory is applied to a third order phase locked loop (PLL) with a feedback time delay. Due to this delay, different behaviors that are not accounted for in a conventional PLL model are identified, namely, oscillatory instability, periodic doubling and chaos. Firstly, a Pade approximation is used to model the time delay where it is utilized in deriving the state space representation of the PLL under investigation. The PLL under consideration is simulated with and without time delay. It is shown that for certain loop gain (control parameter) and time delay values, the system changes its stability and becomes chaotic. Simulations show that the PLL with time delay becomes chaotic for control parameter value less than the one without time delay, i.e, the stable region becomes narrower. Moreover, the chaotic region becomes wider as time delay increases.