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This paper presents a novel method for optimal tunning of a Fractional Order Proportional-Integral-Derivative (FOPID) controller for an Automatic Voltage Regulator (AVR) system. The presented method is based on the Yellow Saddle Goatfish Algorithm (YSGA), which is improved with Chaotic Logistic Maps. Additionally, a novel objective function for the optimization of the FOPID parameters is proposed. The performance of the obtained FOPID controller is verified by comparison with various FOPID controllers tuned by other metaheuristic algorithms. A comparative analysis is performed in terms of step response, frequency response, root locus, robustness test, and disturbance rejection ability. Results of the simulations undoubtedly show that the FOPID controller tuned with the proposed Chaotic Yellow Saddle Goatfish Algorithm (C-YSGA) outperforms FOPID controllers tuned by other algorithms, in all of the previously mentioned performance tests.

Summary This paper deals with the investigation into mathematical modeling of induction machine speed‐time and time‐speed dependencies during no‐load direct start‐up. Namely, a precise analytical formula for induction machine speed calculation during no‐load direct start‐up is given and solved in the form of the Lambert W function. The results obtained by using developed analytical solution are compared with corresponding results obtained by using methods based on numerical time‐domain computation (NTDC) that have been realized in two different program packages. Furthermore, the results obtained by using developed analytical solution are compared with corresponding experimental results. The findings showed good agreement between the obtained results. All developed MATLAB programs for speed‐time and time‐speed curve determination are given in the paper. The Mathematica program developed for solving the Lambert W equation is also provided.

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