Method of estimating a rotor position of synchronous motor, method of controlling synchronous motor with no position sensor and a controller of synchronous motor

In a method of accurately estimating the rotor position of a synchronous motor having saliency from observable quantities, a control system for adjusting an output frequency ( omega 1) of an inverter (13) on the basis of a value of axis shift ( DELTA ) of the synchronous motor (2) to operate the motor (2) synchronously with the output frequency ( omega 1) is provided with an induced voltage estimating/axis shift operating unit (61). Currents (Idc, Iqc) resulting from conversion of detection currents (iu, iw) on a control axis, voltage commands (Vdc*, Vqc*) to be inputted to an inverse converter (44) and a speed command ( omega r*) are inputted to the operating unit (61) to estimate an induced voltage of the motor 2 and determine the axis shift ( DELTA ) from a phase of the estimated induced voltage. By using an electrical constant Lq of inductance, a voltage drop across the inductance is determined by the product of a motor speed command ( omega r*) and magnitude of motor current. The voltage drop is a virtual quantity that does not depend on the motor rotor position. A vector of the virtual quantity is so introduced as not to change a phase of the original induced voltage.