Modelling of linear motor end-effects for saliency based sensorless control

In linear motors, the open structure of the armature produces the so called end-effect. The end-effect introduces non-idealities in the motor magnetic model in dq-synchronous coordinates that require a specific modelling with respect to the well known models of rotating (cylindrical) machines. In particular, for saliency based sensorless control, the end-effect introduces an error in the estimated position that must be taken into account and properly compensated. This paper introduces a general mathematical modeling of the end-effect that can be applied to all linear machines. Based on such model, modified position observers are proposed for sensorless control using pulsating or rotating voltage vectors. Experimental results are presented to verify the feasibility of the proposed method, with reference to the case of a linear tubular permanent magnet motor.