<![CDATA[In this paper, a nonlinear adaptive position controller for a permanent magnet linear synchronous motor based on a newly developed adaptive backstepping control approach is discussed and analyzed. The backstepping approach is a systematic method; it is used for non-linear systems such as the linear synchronous motor. This controller combines the notion of the Lyapunov function, which is based on the definition of a positive energy function; to ensure stability in the sense of Lyapunov, it is necessary to ensure the negativity of this function by a judicious choice of a control variable called virtual control. But this method is mainly based on the mathematical model of the permanent magnet linear synchronous machine (PMLSM) which makes this control sensitive to the variation of the parameters of the machine, to overcome this problem an adaptive control was proposed, the adaptive backstepping control approach is utilized to obtain the robustness for mismatched parameter uncertainties and disturbance load force. The overall stability of the system controller and adaptive low is shown using the Lyapunov theorem. The validity of the proposed controller is supported by computer simulation results.]]>
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