SUMMARYThis paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust D-stability. Firstly, general result is presented to check the robust 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 D-stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID D-stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the D-stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: multi-linear interval uncertainty and mixed-type uncertainties. Numerical examples are followed to illustrate the effectiveness of the method.
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