New Features of P3$\delta$ software: Partial Pole Placement via Delay Action

TL;DR

This paper introduces P3δ, a Python software tool that simplifies the design of stabilizing delayed feedback controllers using advanced properties of quasipolynomial zeros, with new features and an online version.

Contribution

The paper presents new features of P3δ software, including the admissible region visualization and an online version, enhancing the design of delay-based stabilizing feedback laws.

Findings

Detailed admissible region for root assignment

Implementation of online version of P3δ

Enhanced user interface for feedback design

Abstract

This paper presents the software Partial Pole Placement via Delay Action, or P3$\delta$ for short. P3$\delta$ is a Python software with a friendly user interface for the design of parametric stabilizing feedback laws with time-delays, thanks to two properties of the distribution of quasipolynomials' zeros, called multiplicity-induced-dominancy and coexisting real roots-induced-dominancy. After recalling recent theoretical results on these properties and their use for the feedback stabilization of control systems operating under time delays, the paper presents the main features of the current version of P3$\delta$. We detail, in particular, the assignable admissible region (the set of allowable dominant roots and the corresponding delay), which helps the user in the choice of input information, allowing a reliable stabilizing delayed feedback. We also present the newly set online version of P3$\delta$.