Nonlinear Bandwidth and Bode Diagrams based on Scaled Relative Graphs
By: Julius P. J. Krebbekx, Roland Tóth, Amritam Das
Potential Business Impact:
Maps how machines change signals.
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.
Similar Papers
Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability
Systems and Control
Makes machines more reliable and predictable.
Stability results for MIMO LTI systems via Scaled Relative Graphs
Systems and Control
Makes complex machines safer to control.
A Cascade of Systems and the Product of Their $θ$-Symmetric Scaled Relative Graphs
Systems and Control
Helps machines understand complex connections better.