IAE Optimized PID Tuning via Second Order Step Response Target Matching

Abstract: This paper presents SOSTIAE (Second-Order System Target IAE), a novel PID tuning method that combines IAE minimization with explicit transient response shaping for practical control applications. The algorithm generates optimal PID parameters by matching the closed-loop response to a target second-order system with user-defined settling time (Ts) and percent overshoot (PO), while maintaining the conventional IAE performance metric. Comparative evaluations on first to third-order systems demonstrate that SOSTIAE consistently outperforms MATLAB's proprietary pidtune function, achieving 47-67% lower overshoot and up to 26% better IAE performance for higher-order plants. The constrained optimization framework ensures physically realizable controllers by enforcing non-negative PID gains and stability criteria, addressing known limitations of unconstrained IAE methods. Results indicate that SOSTIAE provides engineers with a systematic alternative for PID tuning when transient specifications and practical implementation constraints are critical.