Fractional Order Control System And New Type Controllers Design

Fractional order calculus is a new field in mathematic study fields, which is an expansion of traditional integral calculus theory. So far, a great of achievement has been attained in the study of fractional order calculus theory, which provides a new theory foundation for the application of fractional ordercalculus in other subjects.Based on the previous investigation foundation, this paper has done somework from the point of actual engineering. These study is as follows:(1) Several solution methods have been generalized and compared via simulation from the point of characteristics both in good and bad sides and applicability. Espcecially, two direct discretization methods for fractional-order differentiator s~v are introduced and further comparision is given in the simulation.(2) The connections and differences between fractional calculous and integral calculous are sumed up and the influence of fractional PI~λD~μcontroller parameters on the performance of close-loop systems is analyzed in detail. At last, the robustness of PI~λD~μcontroller is demonstrated in the simulation. (3) On the basis of the single variable RTD-A controller, the fractional order RTD-A controller is deduced through formula transformation. The four parameters of fractional order RTD-A controller are designed for robustness, set-point tracking and disturbance rejection and overall aggressiveness, separately. Simulation results verfy the satisfaction of the fractional order RTD-A controller.