This article discusses the design of a hybrid fuzzy variable structure control algorithm combined with genetic algorithm (GA) optimization technique to improve the adaptive proportional‐integral‐derivative (PID) continuous second‐order sliding mode control approach (APID2SMC), recently published in our previous article in the literature. In this article, first, as an improved extension to APID2SMC published recently in the literature, an adaptive proportional‐integral‐derivative fuzzy sliding mode scheme (APIDFSMC) is presented in which a fuzzy logic controller is added. Second, a GA‐based adaptive PID fuzzy sliding mode control approach (APIDFSMC‐GA) is introduced to obtain the optimal control parameters of the fuzzy controller in APIDFSMC. The proposed control algorithms are derived based on Lyapunov stability criterion. Simulations results show that the proposed approaches provide robustness for trajectory tracking performance under the occurrence of uncertainties. These simulation results, compared with the results of conventional sliding mode controller, APID2SMC, and standalone classical PID controller, indicate that the proposed control methods yield superior and favorable tracking control performance over the other conventional controllers.

中文翻译：

---

不确定系统的优化模糊连续滑模控制器与自适应比例积分微分控制相结合

本文讨论了一种结合遗传算法（GA）优化技术的混合模糊变结构控制算法的设计，以改进自适应比例-积分-微分（PID）连续二阶滑模控制方法（APID2SMC），该方法最近在我们的出版物中发布了文献中的前一篇文章。在本文中，首先，作为对最近在文献中发表的APID2SMC的改进扩展，提出了一种自适应比例积分微分模糊滑模方案（APIDFSMC），其中添加了模糊逻辑控制器。其次，引入了基于遗传算法的自适应PID模糊滑模控制方法（APIDFSMC‐GA），以获得APIDFSMC中模糊控制器的最优控制参数。提出的控制算法是基于Lyapunov稳定性准则导出的。仿真结果表明，所提出的方法为不确定性情况下的轨迹跟踪性能提供了鲁棒性。与常规滑模控制器，APID2SMC和独立经典PID控制器的结果相比，这些仿真结果表明，所提出的控制方法比其他常规控制器具有更好的跟踪性能。