Towards robust controller design using μ\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}-synthesis approach for speed regulation of an uncertain wind turbine

Wind turbines are subjected to factors like fatigue, aerodynamics, structural flexibility and wind turbulence which lead to uncertain behaviour. This affects stability and deteriorates the performance of the large structured wind turbine. In order to reduce the effects of uncertainties on the system performance and its structure, a robust controller design is necessary. In this paper, it is proposed to design a μ\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}-synthesis-based robust controller to overcome the effects due to uncertainties. A ±25%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm \,25\%$$\end{document} variation in the values of the system matrix elements is considered for analysis in this paper. A 109th order of the proposed μ\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}-controller is obtained, wherein it is reduced to a 7th order controller by using the balanced truncation method. The robust stability and robust performances are satisfactorily achieved with both these controllers. Furthermore, the worst-case performance of the uncertain wind turbine is also analysed.