Soft Computing (2021) 25:5895–5907 https://doi.org/10.1007/s00500-021-05582-y METHODOLOGIES AND APPLICATION A new adaptive non-singleton general type-2 fuzzy control of induction motors subject to unknown time-varying dynamics and unknown load torque Akram Sedaghati 1 · Naser Pariz 2 · Mehdi Siahi 3 · Roohollah Barzamini 1 Published online: 5 February 2021 © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract In this paper, a new fault-tolerant control strategy is suggested to control the induction motors (IMs). The mathematical model of IMs is supposed to be unknown and also the main disturbances such as perturbation in the rotor resistance, and suddenly changes in the load torque are considered. A general type-2 fuzzy system using a new non-singleton fuzzification is proposed to cope with the uncertainties. The robustness and the stability of the proposed control scheme is studied on basis of the Lyapunov theorem. The simulation results show that the suggested control method has good performance in the versus of unknown dynamics of IM, time-varying disturbances, abrupt faults and measurement errors. The proposed scheme is compared with other popular control systems and other kind of fuzzy systems and singleton fizzification. Keywords Induction motor · General type-2 fuzzy systems · Lyapunov stability · Rotor resistance · Load torque 1 Introduction The induction motor (IMs) is commonly employed in indus- tries because of its reliability, less cost and maintenance free (Deng et al. 2019; Lopes et al. 2017). The dynamics of the induction motors is complicated and is disturbed by varia- tion in rotor resistance and changes in load torque and so on Guedes et al. (2019). Then the control problem of the induction motors has attained great attention in recent years. Various control methods have been applied to the control of IMs. The proposed methods are classified in three cate- gories. In the first category, some simple and ordinary control schemes have been designed for IMs. For instance, the field- oriented control approach is designed for the speed control of IMs (Kubota and Matsuse 1994). In Yu et al. (2001), the vector controller is developed for IMs. The other simple con- B Naser Pariz n-pariz@um.ac.ir 1 Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran 2 Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran 3 Faculty of Mechanics, Electrical Power and Computer, Science and Research Branch, Islamic Azad University, Tehran, Iran troller which is frequently applied on IMs is PID control method (Lim et al. 2013). Many optimization methods and algorithms have been applied to optimize the PID control for IMs such as genetic algorithm, particle swarm optimization, fuzzy systems, imperialist competitive algorithm and so on (Thangaraj et al. 2011; Ustun and Demirtas 2008; Uddin et al. 2002; Ali 2015). The next main approach for the control of IMs is the clas- sical control methods. For instance, the predictive control is developed for IMs (Zhang and Yang 2015; Zhang et al. 2016). In Lascu et al. (2016), the feedback linearzation method designed for IMs and its performance is compared with the sliding mode approach. The backstepping control technique is studied for IMs in Regaya et al. (2018), and its robust- ness against variation of rotor resistance is investigated. The immersion and invariance control strategy is studied for IMs in Sabzalian et al. (2019b), and its robustness is investigated. The other most common controller that is frequently used to control of IMs is the sliding model control (SMC) approach. Various version of sliding mode control technique has been studied for IMs such as traditional SMC, adaptive exponen- tial SMC, second-order SMC, terminal SMC, integral SMC, and so on (Xu et al. 2019; Ponce et al. 2018). The main drawback of the reviewed studies is that the dynamic model of IM is considered to be certain and known. To cope with uncertainties of the mathematical model of 123