A fuzzy fractional-order PID control algorithm for a general type industrial temperature control system is proposed in this paper. In order to improve the production quality and controlled model accuracy, a fractional-order elementary system is used to describe the temperature control process. The gain coefficients of the proposed fractional-order PID controller is updated online based on a set of fractional-order fuzzy rules which are defined by Mittag–Leffler functions and follow fat-tailed distributions. Therefore, the proposed controller parameters could be auto-tuned according to model uncertainties, noise disturbance, random delay, and etc. Examples of the studied temperature control systems are shown to verify the effectiveness of the proposed controller. The superiority of fractional calculus is fully explored in the presented control methodology. The controlled temperature profile with the proposed algorithm could realize more satisfactory dynamic performance, better robustness respect to environment changes caused by internal and external disturbance.

提出了一种适用于通用型工业温度控制系统的模糊分数阶PID控制算法。为了提高生产质量和控制模型精度，采用分数阶初等系统来描述温度控制过程。所提出的分数阶 PID 控制器的增益系数基于一组分数阶模糊规则在线更新，这些规则由 Mittag-Leffler 函数定义并遵循肥尾分布。因此，所提出的控制器参数可以根据模型的不确定性、噪声干扰、随机延迟等进行自动调整。所研究的温度控制系统的例子显示了所提出的控制器的有效性。在所提出的控制方法中充分探索了分数阶微积分的优越性。使用所提出的算法控制的温度曲线可以实现更令人满意的动态性能，对内部和外部干扰引起的环境变化具有更好的鲁棒性。