International Journal of Robust and Nonlinear Control (Internat. J. Robust Nonlinear Control) (20160101), 26, no.~5, 1112-1142. ISSN: 1049-8923 (print).eISSN: 1099-1239.
Subject
93 Systems theory; control -- 93C Control systems 93C80 Frequency-response methods
Summary: ``This paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust $\Cal D$-stability. Firstly, general result is presented to check the robust $\Cal D$-stability of the linear fractional order interval polynomial. Then some alternative algorithms and results are proposed to reduce the computational effort of the general result. Secondly, a general graphical tuning method together with some computational efficient algorithms are proposed to determine the complete set of FOPID controllers that provides $\Cal D$-stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID $\Cal D$-stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the $\Cal D$-stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: {\it multi-linear interval uncertainty} and {\it mixed-type uncertainties}. Numerical examples are followed to illustrate the effectiveness of the method.''