Stabilizing fractional-order PI and PD controllers: an integer-order implemented system approach

作者：Rahimian M A; Tavazoei M S^*

来源：Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering, 2010, 224(I8): 893-903.

DOI：10.1243/09596518JSCE1043

• fractional-order control
• fractional-order PI controller
• fractional-order PD controller
• stability region

This paper proposes a scheme for computing the stable regions from which the parameters of fractional-order proportional integral (PI) and proportional derivative (PD) controllers can be selected. In particular, a previously investigated method for plotting the stability regions of PI(lambda) and PD(mu) controllers is extended to their integer-order approximations. Next, the two stability regions are compared and their overlapping sections, referred to as the implementable stability region, are derived. In order for the final closed-loop system to be stable, the designer must choose the controller parameters from the overlapping section of the two stability regions. Simulation results for two example systems are provided to illustrate the effectiveness of the proposed method. The authors believe that the devised scheme can facilitate the design procedure for fractional-order PI and PD controllers.

• 出版日期2010-12