Analysis and design of nonlinear systems in the frequency domain / / Yunpeng Zhu

• Record Nr.: UNINA9910484062803321
• Autore: Zhu Yunpeng
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-70833-0
• Descrizione fisica: 1 online resource (xxi, 164 pages) : illustrations
• Collana: Springer Theses, Recognizing Outstanding Ph.D. Research
• Disciplina: 003.75
• Soggetti: Nonlinear systems - Mathematical models; Volterra equations; Sistemes no lineals; Models matemàtics; Equacions de Volterra; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Supervisor's Foreword -- Preface -- Acknowledgements -- Contents -- Contributors -- Abbreviations -- 1 Introduction -- 1.1 Background -- 1.1.1 Modelling of Nonlinear Systems -- 1.1.2 Frequency Domain Analysis and Design of Nonlinear Systems -- 1.1.3 LS Methods in Nonlinear System Analyses -- 1.1.4 Convergence Issues with the Frequency Analysis of Nonlinear Systems -- 1.2 Aim, Objectives and Contributions -- 1.3 Thesis Layout -- References -- 2 Nonlinear Systems and the Frequency Domain Representations -- 2.1 Introduction -- 2.2 Polynomial Models of Nonlinear Systems -- 2.2.1 The NDE Model of Nonlinear Systems -- 2.2.2 The Polynomial NARX Model of Nonlinear Systems -- 2.2.3 The NARX-M-for-D of Nonlinear Systems -- 2.3 The Frequency Domain Representations of Nonlinear Systems -- 2.3.1 The Volterra Series Representation -- 2.3.2 The Generalised Frequency Response Functions (GFRFs) of Nonlinear Systems -- 2.3.3 The Nonlinear Output Frequency Response Functions (NOFRFs) of Nonlinear Systems -- 2.3.4 The Output Frequency Response Function (OFRF) of Nonlinear Systems -- 2.4 Conclusions -- ; References -- 3 Generalized Associated Linear Equations (GALEs) with Applications to Nonlinear System Analyses -- 3.1 Introduction -- 3.2 The Associated Linear Equations (ALEs) of Nonlinear Systems -- 3.2.1 The ALEs of Duffing Equations -- 3.2.2 The ALEs of the NARX Model -- 3.3 The Generalized Associated Linear Equations (GALEs) -- 3.3.1 The Concept of the GALEs -- 3.3.2 Determination of the GALEs -- 3.4 System Analyses Using the GALEs -- 3.4.1 Evaluation of the Output Response of Nonlinear Systems -- 3.4.2 Evaluation of the NOFRFs of Nonlinear Systems -- 3.4.3 Evaluation of the OFRF of Nonlinear Systems -- 3.5 Application of the GALEs to Nonlinear System Modelling, Fault Diagnosis, and Design.; 3.5.1 Application to the Identification of the NDE Model of a Nonlinear System -- 3.5.2 Application to the NOFRFs Based Fault Diagnosis -- 3.5.3 Application to the OFRFs Based Design of Nonlinear Energy Harvester Systems -- 3.6 Conclusions -- References -- 4 The Convergence of the Volterra Series Representation of Nonlinear Systems -- 4.1 Introduction -- 4.2 The NARX Model in the Frequency Domain: Nonlinear Output Characteristic Spectra (NOCS) Model -- 4.3 The Generalized Output Bound Characteristic Function (GOBCF) Based Convergence Analysis -- 4.3.1 A Sufficient Condition of the Convergence -- 4.3.2 The Determination of the GOBCF -- 4.3.3 Convergence Analysis of the Volterra Series Representation of Nonlinear Systems -- 4.3.4 The Procedure for the New Convergence Analysis -- 4.4 Case Studies -- 4.4.1 Case 1-Unplugged Van der Pol Equation -- 4.4.2 Case 2-Duffing Oscillator with Cubic Damping -- 4.5 Conclusions -- References -- 5 The Effects of Both Linear and Nonlinear Characteristic Parameters on the Output Response of Nonlinear Systems -- 5.1 Introduction -- 5.2 The OFRF Based Design of NARX-M-for-D -- 5.2.1 The OFRF of the NARX-M-for-D -- 5.2.2 The Determination of the OFRF of NARX-M-for-D -- 5.2.3 The OFRF Based Design of Nonlinear Systems -- 5.3 The Associated Output Frequency Response Function (AOFRF) -- 5.3.1 Explicit Relationships Between the GFRFs and the Parameters of the NARX Model -- 5.3.2 Two Special Cases -- 5.3.3 The Concept of the Associated Output Frequency Response Function (AOFRF) -- 5.3.4 The AOFRF in Terms of the System Linear and Nonlinear Characteristic Parameters -- 5.3.5 The AOFRF Based Representation of the Output Frequency Response of Nonlinear Systems -- 5.4 Case Studies -- 5.4.1 Case Study 1-The OFRF Based Design of the Vibration Isolation System.; 5.4.2 Case Study 2-The AOFRF Based Representation of the Output Spectrum of a Duffing Nonlinear System -- 5.5 Conclusions -- References -- 6 Nonlinear Damping Based Semi-active Building Isolation System -- 6.1 Introduction -- 6.2 Semi-active Damping System for the Sosokan Building -- 6.2.1 The Sosokan Building and Its Model Representation -- 6.2.2 Semi-active Damping System for the Sosokan Building -- 6.3 Nonlinear Damping Based Semi-active Building Vibration Isolation -- 6.4 Simulation Studies -- 6.4.1 Objectives of Nonlinear Damping Design -- 6.4.2 Effects of Nonlinear Damping Coefficient -- 6.4.3 Effects of Ground Excitation Magnitude -- 6.4.4 Isolation Performance on Higher Floors -- 6.4.5 Isolation Performance in Terms of the Roof Drift -- 6.4.6 Isolation Performance in Terms of Harmonics and a Comparison with the Performance Under LQG Control -- 6.5 Experimental Validation -- 6.6 Conclusions -- References -- 7 Conclusions -- 7.1 Main Contributions of the Present Research -- 7.2 Future Works -- Appendix A Sampling Frequency Independence -- Appendix B Proof of Lemma 5.1.