Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University, Shenyang, 110036, PR China.
ISA Trans. 2018 Dec;83:25-34. doi: 10.1016/j.isatra.2018.09.004. Epub 2018 Sep 13.
This paper proposes a stabilization criterion for a fractional-order plant involving interval uncertainties in the coefficients using fractional-order PD controller with a filter. The vertex functions of the value set corresponding to the characteristic function of the closed loop system are determined by the law of Minkowski sum. The finite test frequency interval is offered to simplify the calculation of the test for the stabilization. The analytical method to test the position relationship between the origin and the value set is investigated within the finite test frequency interval. Then, the stabilization criterion with an analytical method is provided based on the zero exclusion principle. Finally, three examples are given to verify the effectiveness of this criterion.
本文提出了一种使用带有滤波器的分数阶 PD 控制器对系数中存在区间不确定性的分数阶系统进行稳定性判据的方法。通过 Minkowski 求和律确定了对应于闭环系统特征函数的值集的顶点函数。提供了有限测试频率间隔，以简化对稳定性测试的计算。在有限测试频率间隔内研究了分析方法来测试原点和值集之间的位置关系。然后，基于零排除原理，提供了一种具有分析方法的稳定性判据。最后，给出了三个示例来验证该判据的有效性。
