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In this article feedback linearization for control-affine nonlinear systems is extended to systems where linearization is not feasible in the complete state space by combining state feedback linearization and homotopy numerical continuation in subspaces of the phase space where feedback linearization fails. Starting from the conceptual simplicity of feedback linearization, this new method expands the scope of their applicability to irregular systems with poorly expressed relative degree. The method is illustrated on a simple SISO–system and by controlling the speed and the rotor flux linkage in a three phase induction machine.
Methods for increasing the energy efficiency of induction motors by an appropriate control strategy have been a subject of research during the last years. Several methods for loss minimization have been developed for induction motors operated in a steady state. In recent years, some solutions for the dynamic case have been given as well either using an online or offline optimization approach, implying a certain computational burden, which is undesired in practice. This paper shows that the appropriate application of steady state techniques during transients due to a changing motor torque is a suboptimal strategy with an acceptable performance for efficiency optimization given an induction machine where saturation effects of the main inductance must be considered. The optimization problem is simplified such that a simple suboptimal solution is possible and the quality of the suboptimal solution is investigated by simulations and measurements. The proposed solution is simple, easy to implement, and does not require an online optimization. In addition, the influence of magnetizing induction saturation is considered.