PID Tuning with Neutrosophic Similarity Measure

In this paper, a method for adjusting the proportional-integral-derivative (PID) coefficients based on the neutrosophic similarity measure is proposed. First, rough PID coefficients were determined by the Ziegler–Nichols method, and the upper and lower limit values for the search range of the PID coefficients were determined. At each step of the search range, we applied a unit step function to the system and obtained the transient response characteristics. The obtained values were converted into a neutrosophic set (real set) by using defined membership functions. Then, the optimal PID coefficients were obtained using the similarity ratio between the real and ideal (target) neutrosophic sets. In calculating the similarity ratio, the Hamming, Euclidean, Set-theoretic, Jaccard, and Dice approaches were applied, and the results were compared. Finally, the proposed method was tested on two transfer functions, and it was demonstrated that the proposed method can be used to adjust PID coefficients.