Sensorless speed control of induction motors

We consider field-oriented speed control of induction motors without rotor position sensors. We augment the traditional approach with flux and speed observers and derive a sixth-order nonlinear model that describes the motor in field-oriented coordinates. The model takes into consideration the error in flux estimation. The flux regulation problem is a simple one and we follow the traditional approach of using PI controllers. For the speed regulation problem, we simplify the model by assuming that flux regulation takes place relatively fast and by using a (high-gain) PI controller to regulate the q-axis current to its command. This results in a third-order nonlinear model in which the speed and two flux estimation errors are the state variables, the q-axis current is the control input and a speed estimate (provided by the high-gain observer) is the measured output. This nonlinear model is the main contribution of this paper because it enables us to perform rigorous analysis of the closed-loop system under different controllers. In the current paper, we limit our analysis to the design of PI controllers via linearization. The linearized model is used to study when a PI controller can stabilize the nonlinear third-order model at the desired equilibrium point. 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.