Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

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 opt...

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Bibliographic Details
Published in:International journal of robust and nonlinear control Vol. 29; no. 15; pp. 5195 - 5212
Main Authors: Zhang, Shuo, Liu, Lu, Cui, Xinshu
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.10.2019
Subjects:
Algorithms
Computer simulation
Control algorithms
Control stability
Control systems design
Control theory
Controllers
Crossovers
Delay
delay system
FOPID control
fractional‐order
positive stability region (PSR)
Proportional integral derivative
robust analysis
Robust control
Stability analysis
Transient performance
ISSN:1049-8923, 1099-1239
Online Access:Get full text
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Summary: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 kp, ki, kd 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.
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4667