Using the rooted tree optimization to increase the performance of the improved backstepping control used to control the induction machine

Using backstepping control to control the operation of an induction motor often leads to unwanted torque and current fluctuations. Also, the value of total harmonic distortion (THD) of current increases if the machine parameters change. These drawbacks can be attributed to the gain values of the backstepping control approach. In this work, a synergetic-sliding mode control (SSMC) technique is used to compensate for the gains of the backstepping control. Using an SSMC controller is an effective and convenient solution. On the other hand, the rooted tree optimization (RTO) algorithm is used to calculate the parameter values of the SSMC controller to improve the performance and effectiveness of the backstepping control of the induction motor. Four SSMC-RTO controllers were used in addition to the pulse width modulation strategy to control the operation of the machine’s inverter. This proposed strategy is characterized by high performance, great robustness, and high efficiency in reducing torque ripples and reducing the value of THD of current. Also, the proposed approach improves the values of the integral of square error (ISE), integral of absolute error (IAE), integral of time multiplied square error (ITSE), and integral of time multiplied absolute error (ITAE) compared to the SSMC-BC approach. The proposed approach was implemented using MATLAB, and the performance was compared with the BC-SSMC approach. The effectiveness of the proposed approach is evaluated using several different tests. Simulation results show that the proposed SSMC-BC approach based on RTO algorithm has high performance and significantly improves current and torque quality compared to the BC-SSMC approach. The proposed approach significantly reduces the overshoot value of the flux compared to the SSMC-BC technique. The simulation results show that the proposed approach significantly outperforms the SSMC-BC technique and some related work in terms of the THD value of current, as the THD value was reduced by approximately 13.56%, 11.11%, and 34.51% compared to the SSMC-BC technique. These results make the proposed approach of interest in other industrial applications in the future.