Sensorless AC Electric Motor Control pp 45-78 | Cite as

# Observability Property of AC Machines

## Abstract

In many cases the implementation of control algorithms requires the knowledge of all the components of the state vector. However, because of the high cost of sensors, the reduction of the physical space inside or around the motor, the weight, or the increase of the system complexity, it is often necessary to limit the number of sensors. A similar situation arises when a sensor breaks down. A solution to avoid these difficulties is to eliminate the sensors by replacing them with soft sensors, which are well known as observers in control theory. The soft sensor can also be used to increase the reliability by redundancy with respect to hardware sensors. However, before designing an observer, it is necessary to verify if the system satisfies the observability property. Several techniques and tools have been developed to study whether a nonlinear system is observable or not. Generally, the observability property of a nonlinear system can depend on the inputs. An analysis of the inputs applied to the system is then required to verify if there exist some input that renders the system unobservable. It is clear that in this case the observer may not work correctly. Usually, these inputs are used to control the system, so they are necessary. It is possible to deal with this problem by introducing a class of inputs for which it is conceivable to construct an observer. These inputs are called persistent inputs: inputs with a sufficient quantity of information, so that the observability property is retained. Regarding AC machines, an intrinsic characteristic is that the observability property of the machines is, in most cases, lost at low speed. This phenomenon limits the implementation or degrades the performance of the control algorithms. Then, from the mathematical model of AC machines, a study of the observability property has to be made. If this property is satisfied from the only available measurements, i.e., currents and voltages, the next step is to check if a nonlinear observer can be designed to estimate the nonmeasurable variables, in order to be able to implement the control algorithms.