Neural Computing and Applications

, Volume 29, Issue 10, pp 795–804 | Cite as

Fractional-order PID controller tuning using continuous state transition algorithm

  • Fengxue Zhang
  • Chunhua Yang
  • Xiaojun Zhou
  • Weihua Gui
Original Article


Theoretical and applied studies of fractional-order PI\(^{\lambda }\)D\(^{\mu }\) (FOPID) controller in many scientific and engineering fields have shown many advantages compared to the classical PID control. However, the adjustment of FOPID controller becomes more complicated due to two additional parameters. In this study, the FOPID controller adjustment problem is transformed into a nonconvex optimization problem, and then a new metaheuristic method, named state transition algorithm (STA), is introduced to select the optimal FOPID controller parameters. In the meanwhile, the influence of objective criterion and sample size on the performance of FOPID controller design is analyzed. The dominance of the proposed method, especially for tuning FOPID controller parameters, is attested by several simulation cases and the comparisons of STA with other stochastic global optimization algorithms over the same problems.


Fractional-order control PI\(^{\lambda }\)D\(^{\mu }\) State transition algorithm Objective criterion Sample size 



Authors thank the National Natural Science Foundation of China (Grant Nos. 61503416, 61533020, 61533021, 61590921) and Key Exploration Project (Grant No. 7131253) for the funding support.

Compliance with ethical standards

Conflict of interest

We declare that there is no conflict of interest.


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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Fengxue Zhang
    • 1
  • Chunhua Yang
    • 1
  • Xiaojun Zhou
    • 1
  • Weihua Gui
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina

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