Knowledge of the direction of the flux space vector is an indispensable prerequisite for the dynamic control of a polyphase machine. In the case of a synchronous machine, the direction of the flux space vector has a fixed relationship to the rotor position. That is the reason why position transducers, which measure the position of the rotor relative to the stator and transmit it to the closed-loop control in the converter, are frequently used for controlling the machine. This method is also usable for an asynchronous machine, in that, apart from the measured rotor position, the slip angle is modeled additionally within the closed-loop control and added to the rotor position. Thus, the direction of the flux space vector relative to the stator is known in such a case as well.
A disadvantage of this procedure is the required use of a position transducer because it causes additional expense both for the position transducer, the wiring and the required evaluation in the converter.
In order to be able to dispense with the position transducer, it is therefore necessary to determine the position of the flux space vector from the electrical variables, which are available to the converter anyway.
It is known that the rotor flux vector is able to be determined from the stator voltage and the stator current, in the following mannerΨR=∫(uS−RS·iS)·dt−LS·iS 
That is to say, the time integral of the induced voltage must be calculated. Toward this end, the time integral of the voltage applied at the stator clamps of the motor minus the Ohmic voltage drop at the stator winding must be generated, and the flux component LS·iS caused by the stator current must subsequently be deducted from the calculated integral.
In this context it is problematic that the integral to be generated constitutes an open integration, in which even very small offsets in the acquisition of the variables to be integrated lead to drift of the integration result, so that the modeling of the flux space vector becomes increasingly false over time.
To avoid this problem, from the publication “Hybrid Rotor Position Observer for Wide Speed-Range Sensorless PM Motor Drives Including Zero Speed”, IEEE Transactions on Industrial Electronics, vol. 53, No. 2, April 2006 by C. Silva et al., a flux vector monitoring model is known, which uses feedback to reduce or suppress the drift of the integration element, to which the result of the integration, i.e., the rotor flux space vector, is fed back via a P-element. This prevents drift of the integrator content. However, this method has the disadvantage that, at decreasing rotational speed, the model value of the flux space vector determined in this manner increasingly deviates from the actual flux space vector of the motor. Therefore, the method can only be used in a limited range, i.e., above a given limit frequency. This minimally usable limit frequency depends on the choice of the amplification factor of the feedback, which, however, may not be selected arbitrarily small because the required suppression of drift would otherwise no longer be ensured. The feedback of the integration result, which is required for an effective suppression of the drift, produces a falsification of the monitored flux space vector even when the offsets of the measuring signals themselves vanish.
From the publication:    1. Silva, C; Araya, R.: “Sensorless Vector Control of Induction Machine with Low Speed Capability using MRAS with Drive and Inverter Nonlinearities Compensation” in EUROCON, 2007, The International Conference on “Computer as a Tool”, 9-12 Sep. 2008, Pages: 1922-1928in FIG. 1 in the “flux estimator” box, it is that the amount is generated from the integration result, and that it is compared to the specified nominal value. That is to say, the difference of the two values is calculated in the process. This is a scalar quantity, that is to say, no incremental vector. This scalar differential value is then used to generate a vector whose direction is selected such that it matches the direction of the integration result, i.e., the model value to be formed, the amount of this vector being defined by the above scalar differential value. Then, this vector is used as feedback quantity to back up the model value. The correction of the model value thus always takes place only in the radial direction, that is to say, in a manner that modifies only the amount, but does not correct the angle. Thus, it is obvious that the feedback quantity has no real physical flux space vector of the motor or a differential flux space vector for correcting the model value of the flux space vector, because the direction of the differential flux space vector is determined from the drifting integration result itself and thus is virtually never correct. In the case of the vanishing drift of the integration element, it is true that the fed-back quantity vanishes as well. But if drift is present, the feedback quantity does not stand perpendicular on the motor voltage space vector. As a consequence, the feedback quantity is not parallel to the physical, actual flux space vector of the motor.
USPTO Backgrounds
USPTO Backgrounds