Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912577302298624 |
|---|---|
| author | Krebbekx, Julius P. J. Tóth, Roland Das, Amritam |
| author_facet | Krebbekx, Julius P. J. Tóth, Roland Das, Amritam |
| contents | Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of Nonlinear (NL) systems. In this paper, we restrict the SRG to particular input spaces to compute frequency-dependent incremental gain bounds for nonlinear systems. This leads to a NL generalization of the Bode diagram, where the sinusoidal, harmonic, and subharmonic inputs are considered separately. When applied to the analysis of the NL loop transfer and sensitivity, we define a notion of bandwidth for both the open-loop and closed-loop, compatible with the Linear Time-Invariant (LTI) definitions. We illustrate the power of our method on the analysis of a DC motor with a parasitic nonlinearity and verify our results in simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs Krebbekx, Julius P. J. Tóth, Roland Das, Amritam Systems and Control Optimization and Control Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of Nonlinear (NL) systems. In this paper, we restrict the SRG to particular input spaces to compute frequency-dependent incremental gain bounds for nonlinear systems. This leads to a NL generalization of the Bode diagram, where the sinusoidal, harmonic, and subharmonic inputs are considered separately. When applied to the analysis of the NL loop transfer and sensitivity, we define a notion of bandwidth for both the open-loop and closed-loop, compatible with the Linear Time-Invariant (LTI) definitions. We illustrate the power of our method on the analysis of a DC motor with a parasitic nonlinearity and verify our results in simulations. |
| title | Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2504.01585 |