On robust synchronization of nonlinear systems with application to grid integration of renewable energy sources

Abstract Many systems in the natural and physical world often work in unison with similar other systems. This process of simultaneous operation is known as synchronization. In the past few decades, owing to this phenomenon’s importance, extensive research efforts have been made. However, many of the existing results consider the systems are identical and/or linear time-invariant, while practical systems are often nonlinear and nonidentical for various reasons. This observation motivated several recent studies on the synchronization of nonidentical (i.e., heterogeneous) nonlinear systems. This paper summarizes some recent results on the synchronization of heterogeneous nonlinear systems, as developed in the thesis (Ahmed 2016). First, the results on the synchronization of a particular class of robustly stable nonlinear systems are presented. Then, these results are applied to an example model known as Brockett oscillator. Finally, using the Brockett oscillator as a common dynamics, output oscillatory synchronization results are given for heterogeneous nonlinear systems of relative degree 2 or higher. An application example of Brockett oscillator for power-grid synchronization is also presented. Some outlooks are provided regarding future research directions.

[1]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[2]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[3]  Denis Efimov,et al.  Robust Global Synchronization of Brockett Oscillators , 2019, IEEE Transactions on Control of Network Systems.

[4]  Frank L. Lewis,et al.  Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback , 2011, IEEE Transactions on Automatic Control.

[5]  Denis Efimov,et al.  On the robust synchronization of Brockett oscillators , 2016 .

[6]  Eduardo D. Sontag,et al.  Input to state stability and allied system properties , 2011 .

[7]  Manuel Mazo,et al.  Simple synchronization protocols for heterogeneous networks: beyond passivity (extended version) , 2017, ArXiv.

[8]  Hafiz Ahmed,et al.  Modeling and synchronization of biological rhythms: from cells to oyster behavior. (Modélisation et synchronisation: des rythmes cellulaires au comportement de l'huître) , 2016 .

[9]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[10]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[11]  Hafiz Ahmed,et al.  Fast Estimation of Phase and Frequency for Single-Phase Grid Signal , 2019, IEEE Transactions on Industrial Electronics.

[12]  L. Fridman,et al.  Higher‐order sliding‐mode observer for state estimation and input reconstruction in nonlinear systems , 2008 .

[13]  Mihir Sen,et al.  Review of Synchronization in Mechanical Systems , 2019, Nonlinear Structural Dynamics and Damping.

[14]  Feng Qian,et al.  Synchronization in complex networks and its application - A survey of recent advances and challenges , 2014, Annu. Rev. Control..

[15]  Masayuki Fujita,et al.  Passivity-Based Control and Estimation in Networked Robotics , 2015 .

[16]  Hafiz Ahmed,et al.  Modeling and Tuning of Circular Limit Cycle Oscillator FLL With Preloop Filter , 2019, IEEE Transactions on Industrial Electronics.

[17]  David Angeli,et al.  The ISS approach to the stability and robustness properties of nonautonomous systems with decomposable invariant sets: An overview , 2016, Eur. J. Control.

[18]  Ebrahim Babaei,et al.  Super Twisting Sliding-Mode Control of DVR With Frequency-Adaptive Brockett Oscillator , 2021, IEEE Transactions on Industrial Electronics.

[19]  Emilia Fridman,et al.  Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays , 2015, J. Frankl. Inst..

[20]  Denis Efimov,et al.  Experimental study of the robust global synchronization of Brockett oscillators , 2017 .

[21]  Rafael Martínez-Guerra,et al.  Chaotic Synchronization and Secure Communication via Sliding-Mode Observer , 2008, Int. J. Bifurc. Chaos.

[22]  Frede Blaabjerg,et al.  Overview of Control and Grid Synchronization for Distributed Power Generation Systems , 2006, IEEE Transactions on Industrial Electronics.

[23]  P. Holmes,et al.  Structurally stable heteroclinic cycles , 1988, Mathematical Proceedings of the Cambridge Philosophical Society.

[24]  Romain Postoyan,et al.  Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics , 2020, Annu. Rev. Control..

[25]  Isaac Skog,et al.  Time Synchronization Errors in Loosely Coupled GPS-Aided Inertial Navigation Systems , 2011, IEEE Transactions on Intelligent Transportation Systems.

[26]  Denis V. Efimov,et al.  Robust Synchronization for Multistable Systems , 2016, IEEE Transactions on Automatic Control.

[27]  David Angeli,et al.  Characterizations of Input-to-State Stability for Systems With Multiple Invariant Sets , 2015, IEEE Transactions on Automatic Control.

[28]  Leonid Fridman,et al.  Output global oscillatory synchronisation of heterogeneous systems , 2019, Int. J. Control.

[29]  M. Karimi-Ghartemani,et al.  Addressing DC Component in PLL and Notch Filter Algorithms , 2012, IEEE Transactions on Power Electronics.

[30]  Lorenzo Marconi,et al.  Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory , 2013, 52nd IEEE Conference on Decision and Control.

[31]  Frank L. Lewis,et al.  Optimal Synchronization of Heterogeneous Nonlinear Systems With Unknown Dynamics , 2018, IEEE Transactions on Automatic Control.

[32]  Shigeru Kondo,et al.  Noise-resistant and synchronized oscillation of the segmentation clock , 2006, Nature.

[33]  Frank L. Lewis,et al.  Synchronization of nonlinear heterogeneous cooperative systems using input-output feedback linearization , 2014, Autom..

[34]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[35]  Xavier Guillaud,et al.  Current limiting algorithms and transient stability analysis of grid-forming VSCs , 2020 .

[36]  R. Potrie,et al.  Local and global aspects of almost global stability , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[37]  Mohamed Benbouzid,et al.  Enhanced Frequency Adaptive Demodulation Technique for Grid-Connected Converters , 2020, IEEE Transactions on Industrial Electronics.

[38]  Michael Shub,et al.  FILTRATIONS, DECOMPOSITIONS, AND EXPLOSIONS. , 1975 .

[39]  Mohamed Benbouzid,et al.  Robust Gradient Estimator for Unknown Frequency Estimation in Noisy Environment: Application to Grid-Synchronization , 2020, IEEE Access.

[40]  Rodolphe Sepulchre,et al.  Consensus on nonlinear spaces , 2010, Annu. Rev. Control..

[41]  Mohamed Benbouzid,et al.  Multiple Nonlinear Harmonic Oscillator-Based Frequency Estimation for Distorted Grid Voltage , 2020, IEEE Transactions on Instrumentation and Measurement.

[42]  Hafiz Ahmed,et al.  Frequency-Locked Loop-Based Estimation of Single-Phase Grid Voltage Parameters , 2019, IEEE Transactions on Industrial Electronics.

[43]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[44]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[45]  David Angeli,et al.  On Input-to-State Stability with respect to decomposable invariant sets , 2013, 52nd IEEE Conference on Decision and Control.