标题： 基于相位裕度和 crossover 频率约束的 IAE 最优 PID 调谐 显示英文标题

标题： IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints

摘要： 本文提出了一种新颖的PID调节方法PMwc-Tune，该方法独特地结合了频域鲁棒性约束与时域性能优化（通过约束非线性规划实现）。 关键贡献在于一个统一的公式，该公式同时满足相位裕度和交叉频率要求（通过非线性等式约束），并最小化闭环响应的积分绝对误差（IAE）。 该算法采用序列二次规划（SQP）解决此约束优化问题，在保证数值容差内满足规格的同时优化瞬态性能。 基准系统的数值验证表明，与MATLAB的pidtune相比，相位裕度和交叉频率误差小于1%，并且IAE减少了4.6%。 开源实现提供了方法论透明性和实际设计灵活性，从而能够严格平衡频域鲁棒性和时域性能的PID控制器。 显示英文摘要

摘要： 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.