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An identity state observer for the permanent-magnet synchronous motor is derived which reconstructs the electrical and mechanical states of the motor from current and voltage measurements. The observer operates in the rotor frame and estimates direct and quadrature stator currents, rotor velocity, and rotor position. Since the rotor position is estimated, the rotor reference frame is approximated using the latest rotor position estimate. The motor dynamics and the transformation into the estimated rotor frame are nonlinear, and thus the observer and observer error dynamics are nonlinear. Therefore, stability is analyzed using a linearized error model. Simulations including realistic measurement disturbances are used to investigate the global stability and accuracy of the observer.>
Jones et al. (Sun,) studied this question.