DocumentCode :
642974
Title :
On a perturbed phase-locked loop system: A simple physical model
Author :
Gawalwad, Balaji G. ; Sharma, Sanjeev Narayan
Author_Institution :
Electr. Eng. Dept., S.V. Nat. Inst. of Technol., Surat, India
fYear :
2013
fDate :
28-30 Aug. 2013
Firstpage :
430
Lastpage :
436
Abstract :
The stochastic Phase-Locked Loop (PLL) system, a non-linear dynamic circuit, is an appealing and non-trivial case in the general theory of dynamical systems. In this paper, the stochastically-influenced PLL system is the subject of investigation in lieu of the noise-free case. Significantly, Stochastic Differential Equation (SDE) descriptions refine estimation algorithms, stability conditions and control laws of dynamical systems in contrast to classical descriptions. More precisely, the stochastic version of the PLL system of this paper accounts non-linearity as well as the noise contribution at the output of the multiplier and noise in the resistor of a low pass filter. Subsequently, the PLL stochastic differential equation of this paper is recast by utilizing the Itô stochastic interpretation in contrast to the white noise interpretation. Importantly, the Itô interpretation is a formal stochastic interpretation, on the other hand, the white noise is an informal interpretation. The noise analysis of the PLL system is accomplished using the Kolmogorov forward and backward equations for the Markov process. As a result of this, we arrive at a set of two estimation evolution equations for the stochastic problem of concern here. This paper will be of interest to research communities in systems and control looking for noise analysis of dynamical systems in formal stochastic interpretations.
Keywords :
Markov processes; circuit stability; differential equations; nonlinear dynamical systems; phase locked loops; stochastic systems; white noise; Itô stochastic interpretation; Kolmogorov forward-backward equations; Markov process; SDE description refine estimation algorithms; control laws; dynamical systems; estimation evolution equations; formal stochastic interpretation; informal interpretation; low pass filter; multiplier; noise analysis; nonlinear dynamic circuit; perturbed phase-locked loop system; resistor; simple physical model; stability conditions; stochastic differential equation; stochastic phase-locked loop system; stochastically-influenced PLL system; white noise interpretation; Equations; Estimation; Mathematical model; Noise; Phase locked loops; Stochastic processes; Trajectory; Brownian motion; Itô differential rule; Kolmogorov backward equation; Kolmogorov forward equation; Stochastic Differential Equations;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Applications (CCA), 2013 IEEE International Conference on
Conference_Location :
Hyderabad
ISSN :
1085-1992
Type :
conf
DOI :
10.1109/CCA.2013.6662787
Filename :
6662787
Link To Document :
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