Comparative study of feedback linearization control for IM taking into account magnetic saturation effects

Abstract

• Feedback Linearization Control with Saturation Effects: designed a feedback linearization controller that explicitly accounts for the saturation effects in the core of the induction machine (IM). This ensures precise control under nonlinear conditions caused by magnetic saturation. • Feedback Linearization Control without Saturation Effects: developed a conventional feedback linearization controller, assuming a linearized machine model, to provide a baseline for evaluating the impact of saturation effects on performance. • Nonlinear Observer Design Based on Induction Machine Model with Saturation: designed a nonlinear observer tailored to the dynamic behavior of the induction machine, incorporating saturation effects. This observer enhances the estimation accuracy of key machine parameters under nonlinear operating conditions. • Luenberger Observer for Linearized Induction Machine Model: designed a Luenberger observer considering the induction machine as a linear time-invariant (LTI) system. This observer provides a simplified approach for parameter estimation and control. • Comparative Evaluation of Controllers and Observers: conducted a detailed comparative analysis of both feedback linearization controllers (with and without saturation effects) and the two observer designs. This comparison highlights the trade-offs in accuracy, complexity, and robustness in controlling induction machines under various operating conditions. This study examines how the nonlinear characteristics of the magnetic core, where the magnetic material in an induction machine (IM) exhibits a nonlinear relationship between magnetizing current and resulting flux, affect the performance of control systems. In typical IM operation, these nonlinearities lead to noticeable changes in inductance values, complicating accurate flux estimation. To address this, we develop a nonlinear observer (NLO) that explicitly incorporates the effects of the magnetic core's nonlinearity for rotor flux estimation. The observer gain is designed using a Lyapunov stability framework to ensure exponential convergence of the estimation error under varying flux conditions. This approach is compared with a conventional full-order Luenberger observer (LO) that assumes a simple, linear magnetization characteristic. Within the FOC framework, two feedback linearization strategies are evaluated. The FL sat takes into account the non-linear variations in machine inductances caused by saturation, enabling a more accurate representation of IM dynamics. However, this approach is more complex to calculate because of the nonlinear terms. The FL unsat simplifies control design by neglecting the effects of magnetic saturation, thus reducing computational requirements. Despite its simplified structure, FL unsat delivers comparable performance over the nominal speed and flux operating range. The results highlight a trade-off between dynamic modeling fidelity and control accuracy, offering valuable insights for the design of controllers and observers for IM. While FL sat is well suited to scenarios requiring high accuracy and dynamic tracking, FL unsat emerges as a pragmatic alternative for applications favoring simplicity and real-time implementation. Quantitative measurements further support these results: under constant resistances, the proposed NLO achieves an absolute integral error (IAE) of 0.0133 in rotor magnetization current tracking compared to 1.026 with LO, underlining the robustness and accuracy advantages of explicit magnetic saturation modeling.