In an induction machine, the rotor flux is established entirely through electromagnetic coupling. This single-sided excitation makes its control significantly more challenging. This chapter extends the four-coil primitive machine model from Chapter 4 to the induction motor, treating both stator and rotor as orthogonal two-phase windings, and systematically derives the flux linkage, voltage, and torque equations in three coordinate frames: stationary, rotor-fixed, and field synchronous. The chapter focuses on “rotor field orientation” vector control equations, aligning the MT synchronous frame with the rotor flux vector and imposing the constraint that the T-axis flux component is zero. It reveals the physical mechanism by which the motional EMF drives the torque-producing T-axis rotor current while the transformer EMF governs the field-exciting M-axis current—this decoupling is the foundation of vector control. Under rotor field orientation, dynamic equations for flux linkage and torque are derived, and fundamental vector control topics such as MTPA, current limit circle, voltage limit ellipse, field weakening, and MTPV are discussed in detail. The analysis is conducted in both the current and voltage planes, providing complementary perspectives on the three operating regions—constant torque, constant power, and constant voltage—across the entire speed range.