Abstract
A fifth-order dynamic continuous model of a linear induction motor (LIM), without considering “end effects” and considering attraction force, was developed. The attraction force is necessary in considering the dynamic analysis of the mechanically loaded linear induction motor. To obtain the circuit parameters of the LIM, a physical system was implemented in the laboratory with a Rapid Prototype System. The model was created by modifying the traditional three-phase model of a Y-connected rotary induction motor in a d–q stationary reference frame. The discrete-time LIM model was obtained through the continuous time model solution for its application in simulations or computational solutions in order to analyze nonlinear behaviors and for use in discrete time control systems. To obtain the solution, the continuous time model was divided into a current-fed linear induction motor third-order model, where the current inputs were considered as pseudo-inputs, and a second-order subsystem that only models the currents of the primary with voltages as inputs. For the discrete time model, the current-fed model is discretized by solving a set of differential equations, and the subsystem is discretized by a first-order Taylor series. Finally, a comparison of the continuous and discrete time model behaviors was shown graphically in order to validate the discrete time model.
Highlights
The linear motor was invented and patented more than a century ago, in the beginning it was impractical due to the difficulty of having a small air gap without roughness and with low power factor efficiency
The continuous time model was divided into a current-fed linear induction motor third-order model, where the current inputs were considered as pseudo-inputs, and a second-order subsystem that only models the currents of the primary, with voltages as inputs
Discrete vs. continuous time model simulation results are shown in Figure 3, which refers to the transformation axis
Summary
The linear motor was invented and patented more than a century ago, in the beginning it was impractical due to the difficulty of having a small air gap without roughness and with low power factor efficiency. With respect to the regulation theory, there are few works related to the regulation or sliding-mode regulation of linear induction motors. All these approaches require full state measurement. There are few works on sampling LIM dynamics; it is of great significance to investigate an exact sampled-data representation of full linear induction motor dynamics (fifth-order model), and to design exact discrete-time sliding-mode controllers. Figure system implemented to obtaintotheobtain linear induction motor (LIM) model parameters [25]. Peripheral ideal no-load speed in RIMs has the same Formula (1) where τ is the pole pitch (the spatial semi-period of Without the travelling field) [30]
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