Improved structured filter design and analysis for perturbed phase-locked loops via sector and H-infinity norm constraints with convex computations

摘要

This work focuses on designing a structured filter in a phase-locked loop (PLL) system that is perturbed by nonlinear effects from the phase comparator. The filter is designed based on H-infinity control synthesis which is also optimized along with the stability condition of the nonlinear PLL model. The improvement on the design technique is introduced via relaxations of the H-infinity norm constraint on the system's frequency response and integration with the nonlinearity's sector bound. The resulting problems are then formulated into matrix inequalities where the solvability conditions are provided via convex computation approaches. Numerical results and computer simulations demonstrate that the tracking capability of the PLL can be enforced via the proposed methods which then lead to a wider lock-in range and a faster acquisition time as compared to existing techniques. (C) 2019 Elsevier Ltd. All rights reserved.