Tuning the Proportional Integral Derivative, or PID, controller in cyber-physical systems is a major challenge as it requires advanced mathematical skills. Several authors in the literature have shown that optimization algorithms are efficient for auto-adjust PID controller constants, especially when there is no mathematical modeling. However, the literature lacks works that show the efficiency of the Variable Neighborhood Search (VNS) algorithm to auto-adjust the PID. In this work, we investigate the efficiency of the Variable Neighborhood Algorithm to fine-tune a PID controller of a real cyber physical-system: a birotor flying drone. The approach consists of applying a numerical neighborhood structure to optimize the three constants of the PID, according to a proposed fitness function. Experiments reveal the feasibility of fine-tuning the PID controller and the birotor balancing with the Variable Neighborhood Algorithm with reduced time. We compared the VNS-approach against one based on genetic algorithms, and on average, the VNS-approach achieves better results with lower computational and memory costs. Results suggest that the approach may be used in real or commercial systems, helping to fine-tune the controller to new environment changes or even last-minute project modifications.

中文翻译：

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PID 控制器的 VNS 算法：硬件在环方法


调整网络物理系统中的比例积分微分 (PID) 控制器是一项重大挑战，因为它需要先进的数学技能。文献中的几位作者已经表明，优化算法对于自动调整 PID 控制器常数非常有效，尤其是在没有数学建模的情况下。然而，文献中缺乏展示可变邻域搜索（VNS）算法自动调整 PID 的效率的研究。在这项工作中，我们研究了可变邻域算法对真实网络物理系统（双旋翼飞行无人机）的 PI​​D 控制器进行微调的效率。该方法包括根据提出的适应度函数应用数值邻域结构来优化 PID 的三个常数。实验揭示了使用变邻域算法在减少时间的情况下微调 PID 控制器和双转子平衡的可行性。我们将 VNS 方法与基于遗传算法的方法进行了比较，平均而言，VNS 方法以较低的计算和内存成本实现了更好的结果。结果表明，该方法可用于实际或商业系统，有助于微调控制器以适应新的环境变化，甚至是最后一刻的项目修改。