Design of fractional order proportional integral controller using stability and robustness criteria in time delay system

Abstract

In this paper, a tuning procedure of the parameters of fractional order proportional integral controller is presented for time delay system with arbitrary order. On the basis of obtaining stable solution space by utilizing some stability-domain boundaries which include real-root boundary and σ-stability boundary, the optimal solution can be achieved by applying specific frequency-domain specifications which include gain crossing frequency, phase margin, and robustness constraint. Using the same synthesis by traversing phase angle and phase margin in a given interval, the complete solution space of gain crossing frequency can be obtained and visualized, which is equivalent to demonstrate the complete solution space of optimal parameters of fractional order proportional integral controllers. As a comparison, the tuning procedure of the parameters of integral order proportional integral derivative controller is also discussed. At last, the proposed algorithm is validated by numerical simulation and experimental illustrations. The results show the robustness and advantage of the proposed fractional order proportional integral controller over other controllers.

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