Sensorless Control of Permanent Magnet Synchronous Machine Based on Second-Order Sliding-Mode Observer With Online Resistance Estimation

In this paper, a supertwisting algorithm based second-order sliding-mode observer (STA-SMO) with online stator resistance (<inline-formula><tex-math notation="LaTeX">$ R_{s}$</tex-math></inline-formula>) estimation for sensorless control of a nonsalient permanent magnet synchronous machine is proposed. A stator current observer is designed based on an STA to estimate the back electromotive force. A discontinuous sign function in the conventional SMO is replaced by a supertwisting function. The chattering problem, unavoidable in conventional SMO, is eliminated by reducing the amplitude of switching function of an STA-SMO. Meanwhile, a parallel online <inline-formula><tex-math notation="LaTeX"> $ R_{s}$</tex-math></inline-formula> estimation scheme is presented based on a modified SMO. Because mismatch between actual and set resistance may lead to estimation error and even system instability. The Lyapunov stability theorem is used to obtain the stable conditions of the proposed online <inline-formula><tex-math notation="LaTeX">$ R_{s}$ </tex-math></inline-formula> observer at both motoring and generating mode. With the help of online <inline-formula> <tex-math notation="LaTeX">$ R_{s}$</tex-math></inline-formula> observer, resistance uncertainties caused by temperature variation can be taken into account, which means robustness and stability of an STA-SMO can be improved. At the same time, higher position and speed estimation accuracy is obtained and operation range of sensorless control is extended. Finally, the proposed method is validated and compared with a conventional method by simulations and experiments.