systems Article A New Strategy-Based PID Controller Optimized by Genetic Algorithm for DTC of the Doubly Fed Induction Motor Said Mahfoud 1 , Aziz Derouich 1 , Najib EL Ouanjli 1, *, Mohammed EL Mahfoud 2 and Mohammed Taoussi 1   Citation: Mahfoud, S.; Derouich, A.; EL Ouanjli, N.; EL Mahfoud, M.; Taoussi, M. A New Strategy-Based PID Controller Optimized by Genetic Algorithm for DTC of the Doubly Fed Induction Motor. Systems 2021, 9, 37. https://doi.org/10.3390/systems9020037 Academic Editor: Vladimír Bureš Received: 9 May 2021 Accepted: 21 May 2021 Published: 24 May 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Industrial Technologies and ServicesLaboratory, Higher School of Technology, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco; said.mahfoud@usmba.ac.ma (S.M.); aziz.deraouich@usmba.ac.ma (A.D.); Mohammed.touassi@usmba.ac.ma (M.T.) 2 Laboratory of Systems Integration and Advanced, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez 30003, Morocco; mohammed.elmahfoud@usmba.ac.ma * Correspondence: NAJIB.elaounjli@usmba.ac.ma Abstract: Proportional Integral Derivative (PID) is the most popular controller used in automatic systems, because of its robustness, ability to adapt the behaviors of the system, making them converge toward its optimum. These advantages are valid only in the case of the linear systems, as they present poor robustness in nonlinear systems. For that reason, many solutions are adopted to improve the PID robustness of the nonlinear systems. The optimization algorithm presents an efficient solution to generate the optimums PID gains adapting to the system’s nonlinearity. The regulation speed in the Direct Torque Control (DTC) is carried out by the PID controller, which caused many inconveniences in terms of speed (overshoot and rejection time), fluxes, and torque ripples. For that, this work describes a new approach for DTC of the Doubly Fed Induction Motor (DFIM) powered by two voltage inverters, using a PID controller for the regulation speed, based on a Genetic Algorithm (GA), which has been proposed for adjustment and optimizing the parameters of the PID controller, using a weighted combination of objective functions. To overcome the disadvantages cited at the beginning, the new hybrid approach GA-DTC has the efficiency to adapt to the system’s nonlinearity. This proposed strategy has been validated and implemented on Matlab/Simulink, which is attributed to many improvements in DFIM performances, such as limiting speed overshoot, reducing response time and the rate of Total Harmonic Distortion (THD) of the stator and rotor currents, and minimizing the rejection time of speed and amplitude of the torque and flux ripples. Keywords: DFIM; GA-DTC; PID; THD; objective functions 1. Introduction In the mid-1980s, the development of new signal processing techniques led to the real- ization of much more advanced control structures. The most recent steps in this direction are grouped under the term DTC, which has been proposed by Takahashi, Noguchi [1,2], and Depenbrock [3]. However, the advantages attributed to the DTC technique (dynamics, robustness, less sensitivity to parametric variation, ease of implementation, high perfor- mance), are counterbalanced by the use of the hysteresis comparator; in principle, the comparator leads to variable frequency operation, and on the other hand, the finite fre- quency sampling results in a pseudo-random overshoot of the hysteresis band [4], Thus, operation at low speed and in particular, with variations in motor resistance, affects the behavior of the motor [5]. These factors make it difficult to predict the harmonic content of the various output signals [6]. In addition, the application of the classic DTC to the DFIM induces torque oscillations that can stimulate mechanical resonances as they cause vibrations and audible noise, contributing to the early aging of the machine [7]. Recently, many researchers have suggested solutions to improve the performance of classic DTC based on artificial intelligence, such as neural networks, fuzzy logic, and Systems 2021, 9, 37. https://doi.org/10.3390/systems9020037 https://www.mdpi.com/journal/systems