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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

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Polynomial method for PLL controller optimization.

Ta-Chung Wang¹, Sanjay Lall, Tsung-Yu Chiou

¹Institute of Civil Aviation, National Cheng-Kung University, No.1 University Road, Tainan 701, Taiwan. tachung@mail.ncku.edu.tw

Sensors (Basel, Switzerland)

|December 14, 2011

Summary

This study enhances Phase-Locked Loop (PLL) systems for accurate signal tracking, even with noise. New methods using semi-definite programming and sum-of-squares improve pull-in range and controller design for robust performance.

Keywords:

non-linear systems optimization phase-locked loop

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Area of Science:

Control Systems Engineering
Signal Processing
Optimization Theory

Background:

Phase-Locked Loops (PLLs) are critical for signal extraction in communication and control.
Accurate phase estimation is vital for applications like GPS carrier tracking, demanding centimeter-level precision.
Robust PLL performance is challenged by noise and interference, necessitating advanced design techniques.

Purpose of the Study:

To develop a novel approach for enhancing Phase-Locked Loop (PLL) system performance.
To improve the pull-in range and robustness of PLLs against noise and interference.
To provide a systematic design procedure for optimizing PLL controller parameters.

Main Methods:

Utilizing semi-definite programming (SDP) and sum-of-squares (SOS) techniques.
Searching for a Lyapunov function as a certificate for the PLL's pull-in range.
Proposing a polynomial design procedure for controller parameter refinement.

Main Results:

Demonstrated effectiveness through extensive simulation results.
Validated the proposed approach with an experimental result.
Showcased improved pull-in range and controller performance.

Conclusions:

The presented approach effectively enhances PLL performance using advanced optimization techniques.
The combination of SDP, SOS, and polynomial design offers a robust method for PLL controller design.
This work contributes to achieving higher accuracy in signal tracking systems.