IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints

Abstract: This paper presents PMwc-Tune, a novel PID tuning method that uniquely combines frequency-domain robustness constraints with time-domain performance optimization through constrained nonlinear programming. The key contribution is a unified formulation that simultaneously enforces phase margin and crossover frequency requirements (via nonlinear equality constraints) while minimizing the Integral Absolute Error (IAE) of the closed-loop response. The algorithm employs Sequential Quadratic Programming (SQP) to solve this constrained optimization problem, guaranteeing specification attainment within numerical tolerances while optimizing transient performance. Numerical validation on benchmark systems demonstrates precise convergence to design targets (phase margin and crossover frequency errors <1%) with a 4.6% IAE reduction compared to MATLAB's pidtune. The open-source implementation provides both methodological transparency and practical design flexibility, enabling PID controllers that rigorously balance frequency-domain robustness and time-domain performance.