Analysis and Design of Reset Control Systems via Base Linear Scaled Graphs
This work simplifies stability analysis for reset control systems, benefiting control engineers by reducing complex nonlinear checks to linear verifications, though it is incremental as it builds on existing scaled graph theory.
The paper tackled the analysis and design of reset control systems by proving that the scaled graph of a reset system is bounded by that of its base linear system, leading to stability conditions based on linear time-invariant properties and enabling a systematic design approach, including for time-regularized systems.
In this letter, we prove that under mild conditions, the scaled graph of a reset control system is bounded by the scaled graph of its underlying base linear system, i.e., the system without resets. Building on this new insight, we establish that the negative feedback interconnection of a linear time-invariant plant and a reset controller is stable, if the scaled graphs of the underlying base linear components are strictly separated. This result simplifies reset system analysis, as stability conditions reduce to verifying properties of linear time-invariant systems. We exploit this result to develop a systematic approach for reset control system design. Our framework also accommodates reset systems with time-regularization, which were not addressed in the context of scaled graphs before.