【正文】 n . In [14] the difference between actual and reference torque is supplied to a PI controller resulting in a desired change of loadangle . This signal, together with the measured currents and the actual and reference flux are used in a predictive controller to calculate, based on (3), the desired voltage vector in polar coordinates. The stator voltage mand is supplied to a space vector modulator. However, this method uses a motionstate sensor. A very much related scheme is proposed in [15] for IPMSMs, but without the use of a position sensor. The estimated stator flux linkage position, the load angle correction (from a PIcontroller) and the reference flux amplitude are used to calculate a reference flux vector. The error between this reference flux vector and the actual vector, both in amplitude as angle, is then corrected by applying the required voltage vector through SVM. A lower ripple and fixed switching frequency are reported to be obtained in [14], [15]. However one has tonotice that the use of a PIcontroller may deteriorate the performance of the drive as the PIcontroller is sensitive to detuning.2) Stator Flux Oriented Control: Direct stator flux linkage control for SPMSMs asproposed in [16] is related to the previous SVMDTC schemes. Again the pulse widthmodulator is used to generate an increment of stator flux linkage (both in amplitude asangle), but the torque control is open loop. The scheme controls the load angle andamplitude of the stator flux linkage. The reference value for the load angle can becalculated from the torque reference. In the proposed scheme a position sensor is used.3) Predictive Control: A predictive direct torque controller for SPMSMs is discussed in [17] and schematically shown in . By using the equations of the PMSM, the calculation of the trajectory of the torque in a given time is possible. In this way an optimum switching sequence can be calculated. In a constant switching interval a suitable voltage vector is applied for the time required to reach the border of the calculated ripple band, then the zero voltage vector is applied for the remainder of the switching interval so that the torque reaches the minimum of ripple band.In steady state this yields a constant switching frequency and a constant torqueripple. The selection of the voltage vector and switching time is based on the predictionof torque and flux at the beginning of every sampling interval. For the prediction of the torque, the time derivative of the torque dT dt is calculated as function of the stator voltages, stator currents, permanent magnet flux and rotor position. It is clear that the motor parameter dependence in this scheme is larger than in basic DTC. Nevertheless the scheme needs a position encoder to obtain the rotor position .4) Variable Structure Control: A variable structure controller (VSC) for DTC ofIPMSMs is proposed in [18] where the sliding surfaces and VSC law are derived. Thetorque and stator flux linkage errors, together with the flux ponents, rotor speed athe extended flux are used by the variable structure controller to calculate the voltagevector driving the system states to the sliding surface. By means of SVM this voltagevector is realized. A lower ripple and fixed switching frequency is obtained, but a speed encoder is used. The calculations for the VSC result in a larger dependence on motor parameters for the drive IV. STATOR FLUX LINKAGE ESTIMATIONThe basic principle of DTC is to control the torque by altering the stator flux vector in such a way that instantaneous torque and stator flux linkage errors are minimized. As such the estimation of the stator flux linkage vector is very important for a correct operation of the DTC drive. A method to estimate the stator flux linkage is to measure stator voltages and currents and equation (3). The only motor parameter needed is the stator resistance . The use of an integration however has its disadvantages: any dc offset in the measurements of voltages or currents lead to large drifts in the estimated stator flux linkage. Several pensation techniques have been reported and a short overview is given in [19]To overe this problem a programmable cascade of lowpass filters (LPF) isproposed as alternative to an integrator in [19]. Each of the lowpass filters has atransfer characteristic with T the filter time constant and the frequencyof the signal. The cascade can achieve the same phase lag and gain as a pure integrator if the time constant and gain G are programmable and adjusted to the rotor speed.Another problem for the estimation of the stator flux linkage based on the voltageequations is the stator resistance variation. Due to skin effect and temperature changes,the stator resistance can have significant variations. Using the wrong value for in (3)will give rise to large errors. A technique for tator resistance estimation is described in[19] and [20]. It is based on the relationship between the change in resistance and thechange in current, which allows a PIcontroller to determine the stator resistancecorrection. The algorithm has no need for the rotor position. Despite the dependency ofthe reference current on and , the influence of saturation on this method is not discussed.An alternative method of estimating the stator flux linkage is presented in [21].The method is based on the monitoring of the scalar product of estimated stator flux and the measured stator current. The ac part is extracted, filtered and used for the correction of the estimated stator flux linkage. Both simple LPF and adaptive filtering are methods to estimate the stator flux linkage are extended Kalman filtering(EKF) as in [22], which allows also to estimate the mechanical state of the consideredSPMSM, and observers based on sliding mode as in [23].V. INITIAL ROTOR POSITION ESTIMATIONAs mentioned earlier in section II, the initial rotor position must be known in aDTC drive as it is required for the estimation of the