Application of a sensorless control based on sliding mode in permanent magnet synchronous machine using an angular error extraction

In this paper, a sensorless control strategy for permanent magnet synchronous motor (PMSM) is proposed. The main contribution of this work is the extraction of the angular error $(\theta-\hat{\theta})$ of the PMSM, from the measurable currents $i_{\alpha}$ and $i_{\beta}$. Then, thanks to the robustness in the presence of disturbances, and to the convergence in finite time of the control and observation strategies based on sliding mode techniques; first, an observer is designed by using the extraction of $(\theta-\hat{\theta})$ in order to estimate rotor position, speed and disturbance of PMSM under a wide speed range. After that, the estimates of the observer are implemented in a super-twisting controller to track a desired speed reference and a current-i
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reference. Moreover, the gains of the observer and controller are parameterized in terms of only one parameter in order to reduce tuning time. In addition, based on a Lyapunov approach, a convergence analysis of the observer and a stability analysis for the closed-loop system are introduced. Finally, the proposed observer-control scheme has been validated experimentally in an PMSM in order to show its effectiveness.