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This paper deals with model reference adaptive system (MRAS) speed estimators based on a secondary flux for linear induction motors (LIMs). The operation of these estimators significantly depends on an adaptation mechanism. Fixed-gain PI controller is the most common adaptation mechanism that may fail to estimate the speed correctly in different conditions, such as variation in machine parameters and noisy environment. Two adaptation mechanisms are proposed to improve LIM drive system performance, particularly at very low speed. The first adaptation mechanism is based on fuzzy theory, and the second is obtained from an LIM mechanical model. Compared with a conventional PI controller, the proposed adaptation mechanisms have low sensitivity to both variations of machine parameters and noise. The optimum parameters of adaptation mechanisms are tuned using an offline method through chaotic optimization algorithm (COA) because no design criterion is given to provide these values. The efficiency of MRAS speed estimator is validated by both numerical simulation and real-time hardware-in-the-loop (HIL) implementations. Results indicate that the proposed adaptation mechanisms improve performance of MRAS speed estimator. [ABSTRACT FROM AUTHOR]