标题： 基于缩放相对图的非线性带宽和博德图 显示英文标题

标题： Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs

摘要： 尺度相对图（SRGs）提供了一种新颖的图形化频域方法来分析非线性系统。本文中，我们利用SRG在特定输入空间上的限制来计算增量稳定的非线性系统的频率相关增益界限。这导致了Bode图的非线性（NL）推广，在其中正弦、谐波和次谐波输入被单独考虑。当应用于非线性（NL）环路传递函数和灵敏度的分析时，我们定义了开环和闭环带宽的概念，这些概念与线性时不变（LTI）系统的定义相兼容。我们通过分析一个具有寄生非线性的直流电机来展示我们方法的强大，并在仿真中验证了我们的结果。 显示英文摘要

摘要： Scaled Relative Graphs (SRGs) provide a novel graphical frequency domain method for the analysis of nonlinear systems. In this paper, we use the restriction of the SRG to particular input spaces to compute frequency-dependent gain bounds for incrementally stable nonlinear systems. This leads to a nonlinear (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 LTI definitions. We illustrate the power of our method on the analysis of a DC motor with a parasitic nonlinearity, verifying our results in simulations.