针对执行器饱和的机器人关节控制，提出可验证的离散PID参数优化方法。
Constraint-Aware Discrete-Time PID Gain Optimization for Robotic Joint Control Under Actuator Saturation
- 基于Jury准则分析离散化下的PI稳定性区域，考虑实际执行误差。
- 在饱和主导场景下验证反风冲算法效果，降低超调和饱和占比。
- 结合贝叶斯优化与安全筛选，提升参数搜索效率与鲁棒性。
精确调节旋转驱动是自主机器人基础，但实际中由于离散执行、执行器饱和及微小延迟与测量误差，离散时间PID回路偏离连续理论。本文提出一种面向实现的分析与调参流程：(i) 使用Jury准则推导欧拉与精确零阶保持（ZOH）离散化下的PI稳定域；(ii) 在饱和主导条件下评估离散反风冲抗饱和实现；(iii) 提出混合认证贝叶斯优化流程，在优化鲁棒积分绝对误差（IAE）目标的同时，对超调和饱和占空比施加软惩罚，并剔除解析不稳定的候选参数。基准扫描（τ=1.0秒，Δt=0.01秒，u∈[-10,10]）量化了P/PI/PID的上升与稳定趋势。在模拟不确定性、延迟、噪声、量化与更紧饱和的随机模型族下，面向鲁棒性的调参使中位数IAE从0.843降至0.430，中位超调低于2%。仅仿真调参时，认证筛选在完整鲁棒评估前剔除11.6%越界参数，显著提升采样效率。
原文摘要 · Abstract (English)
The precise regulation of rotary actuation is fundamental in autonomous robotics, yet practical PID loops deviate from continuous-time theory due to discrete-time execution, actuator saturation, and small delays and measurement imperfections. We present an implementation-aware analysis and tuning workflow for saturated discrete-time joint control. We (i) derive PI stability regions under Euler and exact zero-order-hold (ZOH) discretizations using the Jury criterion, (ii) evaluate a discrete back-calculation anti-windup realization under saturation-dominant regimes, and (iii) propose a hybrid-certified Bayesian optimization workflow that screens analytically unstable candidates and behaviorally unsafe transients while optimizing a robust IAE objective with soft penalties on overshoot and saturation duty. Baseline sweeps ($τ=1.0$~s, $Δt=0.01$~s, $u\in[-10,10]$) quantify rise/settle trends for P/PI/PID. Under a randomized model family emulating uncertainty, delay, noise, quantization, and tighter saturation, robustness-oriented tuning improves median IAE from $0.843$ to $0.430$ while keeping median overshoot below $2\%$. In simulation-only tuning, the certification screen rejects $11.6\%$ of randomly sampled gains within bounds before full robust evaluation, improving sample efficiency.
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