Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis. (17th July 2019)

• Record Type: Journal Article
• Authors: Zhang, Shuo; Liu, Lu; Cui, Xinshu
• Other Names: Quevedo Daniel E. guestEditor.; Chatterjee Debasish guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 15(2019)
• Page Start: 5195
• Page End: 5212
• Publication Date: 2019-07-17
• Subjects: delay system -- FOPID control -- fractional‐order -- positive stability region (PSR) -- robust analysis; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4667
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k p, k i, k d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.