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Polynomial Method for PLL Controller Optimization†
Institute of Civil Aviation, National Cheng-Kung University, No.1 University Road, Tainan 701, Taiwan
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
MediaTek Inc., No.1 Dusing Road. 1, Hsinchu Science Park, Hsinchu 30078, Taiwan
† Based on “Nonlinear Phase-Locked Loop Design using Semidefinite Programming”, by Ta-Chung Wang, Tsung-Yu Chiou and Sanjay Lall, which was presented at the 16th IEEE Mediterranean Conference on Control and Automation. ©2008 IEEE.
* Author to whom correspondence should be addressed.
Received: 12 May 2011; in revised form: 15 June 2011 / Accepted: 22 June 2011 / Published: 27 June 2011
Abstract: The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach.
Keywords: non-linear systems; phase-locked loop; optimization
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MDPI and ACS Style
Wang, T.-C.; Lall, S.; Chiou, T.-Y. Polynomial Method for PLL Controller Optimization. Sensors 2011, 11, 6575-6592.
Wang T-C, Lall S, Chiou T-Y. Polynomial Method for PLL Controller Optimization. Sensors. 2011; 11(7):6575-6592.
Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu. 2011. "Polynomial Method for PLL Controller Optimization." Sensors 11, no. 7: 6575-6592.