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

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.