ABSTRACT
This chapter reviews the theory of Hopf bifurcations and bifurcation is detected with standard tangent approximation analysis. It describes simulations that corroborate the theoretical predictions and a complementary analysis of bifurcation detection via harmonic balance. The chapter shows that self-sustained oscillations in indirect field-oriented control for induction motors may be due to the appearance of a Hopf bifurcation. Field-oriented control (FOC) is the standard for high dynamic performance induction motor drives due to its high reliability. Historically, this remarkable controller was derived as a result of physical intuition and a deep understanding of the machine operation, with little concern about a rigorous analytical study of its stability and performance. The conditions for the emergence of a Hopf bifurcation only predict when an oscillation appears. The Hopf bifurcation is the most interesting phenomenon regarding oscillations from the practical point of view.
