Sensorless AC Electric Motor Control pp 79-119 | Cite as

# Observer Design for AC Motors

## Abstract

Assuming that for AC electrical machines, the only measurable variables are the currents and the voltages, the mathematical models of the synchronous and induction motors are used to study their respective observability property. If this property is satisfied and under some necessary conditions introduced later, observers are designed to estimate the non-measurable variables of the electric machines. First, some definitions and an introduction to the Nonlinear Observers design are developed. Next, a classification in terms of the convergence rate of two classes of observers is studied: (1) Observers with an asymptotic convergence. (2) Observers with a finite-time convergence. Furthermore, as for nonlinear systems there are no canonical forms, several observer structures are introduced to be next applied to AC machines. From the mathematical model of the PMSM, rewritten in the form of two interconnected subsystems, an adaptive interconnected observer can be designed to estimate the rotor speed, rotor position, and load torque. Some assumptions are considered in order to ensure its asymptotic convergence of the observer. Because the stator resistance depends on the temperature which introduces a variation with respect to its nominal value, then in order to determine its real value, an adaptive interconnected observer is designed to estimate the stator resistance and simultaneously the rotor speed, rotor position, and non-measured load torque. Sufficient conditions are obtained to ensure the asymptotic convergence. Then, a super-twisting observer for a class of nonlinear systems is considered. The advantages of this observer are robustness with respect to parametric uncertainties and finite-time convergence which allows to guarantee that the separation principle can be satisfied when a controller is next applied. Similarly, from the IMPSM mathematical model, an adaptive interconnected observer is designed to estimate the rotor position, rotor speed, load torque, and stator resistance. Finally, for the induction motor, an adaptive interconnected observer is designed to simultaneously estimate the rotor speed, the fluxes, and the load torque. To guarantee the robustness property, an extension of the above observer under parametric uncertainties is developed and, by using practical stability concepts, the practical stability of the estimation error is ensured.