Comparative Study of Time Delay Estimation Based Optimal 1st and 2nd Order Sliding Mode for Current Regulation of Six-Phase Induction Machines

In this work, a time delay estimation based optimal conventional and second order sliding mode stator currents controller are proposed and compared for a six-phase induction machine fed by voltage source power converters. In a first step, the speed is regulated in an outer loop using a proportional-integral controller. Then, in a second step, the stator currents are controlled in an inner loop using the proposed methods. On one hand, the first method is a combination of time delay estimation with optimal first order sliding mode with exponential reaching law. On the other hand, the second method is a combination of time delay estimation with optimal super-twisting control. Based on Lyapunov theory, the stability of the stator currents closed-loop error dynamics is demonstrated and sufficient conditions of stability are determinate. As a case example, numerical simulations have been conducted on an asymmetrical six-phase induction machine to demonstrate the good features of the developed nonlinear controllers.