This paper focuses on tuning parameters of fractional order PID controller (FOPID) by using neural networks (NNs). For tuning the coefficients of the controller and orders of fractional derivative and integrator, five exclusive NNs are employed. Moreover, an emulator is used to identify the plant’s behavior. Extended Kalman Filter (EKF) algorithm is used to update the weights of the controller’s NNs, and Back Propagation (BP) algorithm is used for the weight updating procedure of the emulator’s NNs. The proposed neural fractional order PID controller (NFOPID) is capable of being applied to various plants. Thus, two plants with different dynamics are examined. One is vibration damping of a Euler–Bernoulli beam, which has a fast dynamic, and the other is a time-delayed system like temperature control of a tempered glass furnace. The controller could deal appropriately with these tasks and is compared for accuracy and robustness with other controllers. The results were satisfactory for both systems.

本文重点介绍使用神经网络 (NN) 调整分数阶 PID 控制器 (FOPID) 的参数。为了调整控制器的系数以及分数阶导数和积分器的阶数，使用了五个专用 NN。此外，仿真器用于识别工厂的行为。扩展卡尔曼滤波器（EKF）算法用于更新控制器神经网络的权重，反向传播（BP）算法用于仿真器神经网络的权重更新过程。所提出的神经分数阶 PID 控制器 (NFOPID) 能够应用于各种植物。因此，检查了具有不同动态的两种植物。一个是动态快的欧拉-伯努利梁的减振，另一个是像钢化玻璃炉温控这样的延时系统。控制器可以适当地处理这些任务，并与其他控制器进行准确性和鲁棒性比较。两种系统的结果都令人满意。