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.

翻译：旋转驱动的精确调节是自主机器人学的基础，然而实际的PID环路因离散时间执行、执行器饱和以及微小延迟和测量不完善而偏离连续时间理论。我们提出了一种面向饱和离散时间关节控制的实现感知分析与整定工作流程。我们（i）利用朱里判据推导了欧拉和精确零阶保持（ZOH）离散化下的PI稳定性区域，（ii）评估了在饱和主导工况下的一种离散反算抗饱和实现，以及（iii）提出了一种混合认证贝叶斯优化工作流程，该流程在优化一个对超调和饱和占空比施加软惩罚的鲁棒IAE目标的同时，筛选解析不稳定的候选增益和行为不安全的瞬态过程。基线扫描（$τ=1.0$~s, $Δt=0.01$~s, $u\in[-10,10]$）量化了P/PI/PID的上升/稳定趋势。在一个模拟不确定性、延迟、噪声、量化和更严格饱和的随机模型族下，面向鲁棒性的整定将IAE中位数从$0.843$提升至$0.430$，同时保持超调中位数低于$2\%$。在纯仿真整定中，认证筛选在完整的鲁棒性评估前，拒绝了边界内随机采样增益的$11.6\%$，从而提高了采样效率。