PID controllers are widely used in control systems because of their simplicity and effectiveness. Although advanced optimization techniques such as Bayesian Optimization and Differential Evolution have been applied to address the challenges of automatic tuning of PID controllers, the influence of initial system states on convergence and the balance between exploration and exploitation remains underexplored. Moreover, experimenting the influence directly on real cyber-physical systems such as mobile robots is crucial for deriving realistic insights. In the present paper, a novel framework is introduced to evaluate the impact of systematically varying these factors on the PID auto-tuning processes that utilize Bayesian Optimization and Differential Evolution. Testing was conducted on two distinct PID-controlled robotic platforms, an omnidirectional robot and a differential drive mobile robot, to assess the effects on convergence rate, settling time, rise time, and overshoot percentage. As a result, the experimental outcomes yield evidence on the effects of the systematic variations, thereby providing an empirical basis for future research studies in the field.

翻译：PID控制器因其结构简单且控制有效，在控制系统中得到广泛应用。尽管已有贝叶斯优化和差分进化等先进优化技术被应用于解决PID控制器自动整定的挑战，但初始系统状态对收敛的影响以及探索与利用之间的平衡仍未得到充分研究。此外，直接在移动机器人等真实信息物理系统上实验这些因素的影响，对于获得实际认知至关重要。本文提出了一种新颖的框架，用于评估系统性地改变这些因素对采用贝叶斯优化和差分进化的PID自整定过程的影响。研究在两个不同的PID控制机器人平台上进行了测试——一个全向机器人和一个差速驱动移动机器人，以评估其对收敛速度、调节时间、上升时间和超调百分比的影响。实验结果为这些系统性变化的影响提供了证据，从而为该领域未来的研究提供了实证基础。