Fractional-order PID controller tuning using continuous state transition algorithm

Theoretical and applied studies of fractional-order PIλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\lambda }$$\end{document}Dμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\mu }$$\end{document} (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.