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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| Veröffentlicht in: | International journal of robust and nonlinear control Jg. 29; H. 15; S. 5195 - 5212 |
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| Sprache: | Englisch |
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Bognor Regis
Wiley Subscription Services, Inc
01.10.2019
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| ISSN: | 1049-8923, 1099-1239 |
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| 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 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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| AbstractList | 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. 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. 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. |
| Author | Zhang, Shuo Liu, Lu Cui, Xinshu |
| Author_xml | – sequence: 1 givenname: Shuo orcidid: 0000-0002-2824-618X surname: Zhang fullname: Zhang, Shuo organization: Northwestern Polytechnical University – sequence: 2 givenname: Lu orcidid: 0000-0003-3179-1004 surname: Liu fullname: Liu, Lu email: liulu12201220@nwpu.edu.cn organization: Northwestern Polytechnical University – sequence: 3 givenname: Xinshu surname: Cui fullname: Cui, Xinshu organization: Northeastern University |
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In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive... In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region... |
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| SubjectTerms | 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 |
| Title | Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis |
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