A Spectral-Based Tuning Criterion for PI Controllers in IPDT Systems With Unified Tracking and Disturbance Rejection Performance

TL;DR

This paper introduces a spectral-based method for tuning PI controllers in IPDT systems, achieving unified tracking and disturbance rejection with improved speed and robustness without heuristic trade-offs.

Contribution

A novel spectral-based tuning criterion for PI controllers in IPDT systems that ensures unified exponential decay and avoids heuristic parameter selection.

Findings

Faster convergence compared to classical tuning rules.

Enhanced robustness margins demonstrated in simulations.

Unique PI gain set derived without heuristic trade-offs.

Abstract

This paper proposes a spectral-based tuning method for proportional-integral (PI) controllers in integrating-plus-dead-time (IPDT) systems. The design objective is to achieve unified exponential decay for both reference tracking and disturbance rejection by minimizing the spectral abscissa of the closed-loop system. A second-order semi-discrete model accurately captures the integrator and delay dynamics while enabling efficient dominant pole extraction. These discrete-time poles are mapped to continuous time and refined using Newton-Raphson iterations on the exact transcendental characteristic equation. The method produces a unique PI gain set without requiring heuristic trade-offs or weighting parameters. Comparative simulations demonstrate that the proposed tuning achieves faster convergence and improved robustness margins compared to classical rules (Ziegler-Nichols, SIMC) and integral performance criteria (IAE, ITAE). The approach provides a transparent and computationally efficient framework for PI control in delay-dominant systems.