Generalized Mathematical Model of a Linear Induction Motor

Linear motors are used in many industries such as manufacturing, defence, transportation. The growing application of a linear induction motors in industry requires in-depth research of mathematical models which can be aplied for the development systems where this motors used. The characteristics of linear motors are affected by electromagnetic processes that occur due to the opening of the magnetic circuit, as well as the “input-output” effects during the transition of the contours of the secondary element from the final zone to the active one at the approaching end of the inductor and from active to the final one at the coincident end, as a result of which the so-called, “end effects”. The opening of the magnetic circuit and the end effects lead to a change in the shape of the flow and induction in the air gap along the longitudinal axis, as a result of which additional EMFs appear in the winding coils, which causes asymmetry of the phase currents, the presence of MMF harmonics and unwanted losses. Such things like increased air gap, overlap of secondary and end effects should be considered. This paper shows existing types of linear machines and mathematical models of them, but it also derrives the mathematical model of linear induction motor. Existing types of linear machines are defined by many parametres such as motion type, current type etc. Obtained mathematical model based on equivalent substitution scheme is adaptive for frequency control. The well-known Duncan model is used to account end effects.