Robust region tuning method for fractional-order parameter uncertain systems based on affine algorithm

In the industrial domain, an optimal controller parameter range can significantly enhance operational efficiency. To continuously improve the accuracy of models in production processes, fractional-order systems have been increasingly adopted across various industries. Consequently, this paper proposes a controller tuning method for uncertain fractional-order systems. First, considering the coupling between system parameters, a novel approach to grouping boundary systems is introduced based on affine algorithms. This method delineates a controller stability region that effectively addresses the issue of overly conservative solution intervals inherent in traditional methods. Next, the concept of a virtual phase margin tester is incorporated to determine an efficient controller parameter range. By configuring this tester, a robustness domain for controllers meeting predefined conditions can be established, thereby serving actual production processes more effectively. The proposed method is general and rigorously proven through theoretical analysis. Finally, three simulation examples are provided to verify and analyze its effectiveness.