Mechanical Coordinates Observer in Stator Reference Frame for Surface Mounted Permanent Magnet Synchronous Motors

Abstract

An angular velocity and angular position observer for surface mounted permanent magnet synchronous motors has been proposed. A model in the stator reference frame, namely, the equation of dynamics of currents and flux linkages, was used as the basic model. Based on these equations, a full-order observer was designed. In order to analyze the stability and design the velocity estimation law, a transition to error dynamics was performed and new state variables were introduced. In accordance with the stability analysis using the second Lyapunov method, it was proved that the proposed observer is locally exponentially stable and guarantees an exponential estimate of the unknown variables, namely, the angular velocity and position. During the observer design, the assumption was made that the speed is constant, or changes slowly, but the observer can be tuned so that the effect of the impermanence of speed on its estimation is negligible. The position is determined on the basis of the estimated flux linkage values. The paper presents the simulation results when the observer works in the open- and close-loop. In the open-loop mode observer doesn’t influence control system operation. In the close-loop mode the observer is used to estimate the mechanical coordinates, which are then used in the vector control system and coordinates transformations instead of the measured ones. Transients have shown that the control system performance in sensorless mode is close to condition when mechanical coordinates are measured. Therefore, the proposed observer can be used instead of speed and position sensors to reduce the cost of electric drives based on surface mounted permanent magnets synchronous motors for slow dynamics applications that do not require low speed operation.