We consider field-oriented speed control of induction motors without mechanical sensors. We augment the traditional approach with a flux observer and derive a sixth-order nonlinear model that takes into consideration the error in flux estimation. A high-gain speed observer is included to estimate the speed from field-oriented currents and voltages. The observer design is independent of the feedback controller design. By high-gain-observer theory, we define a virtual speed output for the sixth-order nonlinear model, which can now be used to design a feedback controller whose performance is recovered by the speed observer when the observer gain is chosen high enough. We then focus on the traditional field oriented control (FOC) approach where the flux is regulated to a constant reference and high-gain current controllers are used. By designing a flux regulator to maintain the flux at a constant reference, and a current regulator to regulate the $q$-axis current to its command, we derive a third-order nonlinear model that captures the essence of the speed regulation problem. The model has the speed and two flux estimation errors as the state variables, the $q$ -axis current as the control input, and the virtual speed as the measured output. It enables us to perform rigorous analysis of the closed-loop system under different controllers, and under uncertainties in the rotor and stator resistances and the load torque. In this paper, we emphasize the design of feedback controllers that include integral action. The analysis reveals an important role played by the steady-state product of the flux frequency and the $q$-axis current in determining the control properties of the system. The conclusions arrived at by using the reduced-order model are collaborated by simulation --and experimental results.
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