A simplified fractional order PID (FOPID) controller is proposed by the suitable definition of the parameter relation with the optimized changeable coefficient. The number of the pending controller parameters is reduced, but all the proportional, integral, and derivative components are kept. The estimation model of the optimal relation coefficient between the controller parameters is established, according to which the optimal FOPID controller parameters can be calculated analytically. A case study is provided, focusing on the practical application of the simplified FOPID controller to a permanent magnet synchronous motor (PMSM) speed servo. The dynamic performance of the simplified FOPID control system is tested by motor speed control simulation and experiments. Comparisons are performed between the control systems using the proposed method and those using some other existing methods. According to the simulation and experimental results, the simplified FOPID control system achieves the optimal dynamic performance. Therefore, the validity of the proposed controller structure and tuning method is demonstrated.

中文翻译：

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简化的分数阶PID控制器的优化调整：以PMSM速度伺服为例

通过对参数关系的适当定义和优化的可变系数，提出了一种简化的分数阶PID（FOPID）控制器。待定控制器参数的数量减少了，但是所有比例，积分和微分分量都保留了下来。建立控制器参数之间最佳关系系数的估计模型，根据该模型可以解析计算出最优的FOPID控制器参数。提供了一个案例研究，重点是简化的FOPID控制器在永磁同步电动机（PMSM）速度伺服器中的实际应用。通过电机速度控制仿真和实验测试了简化的FOPID控制系统的动态性能。使用所提出的方法与使用其他一些现有方法的控制系统之间进行了比较。根据仿真和实验结果，简化的FOPID控制系统实现了最佳的动态性能。因此，证明了所提出的控制器结构和调整方法的有效性。