2) Stator Flux Oriented Control: Direct stator flux linkage control for SPMSMs as proposed in [16] is related to the previous SVM-DTC schemes。 Again the pulse width modulator is used to generate an increment of stator flux linkage (both in amplitude as angle), but the torque control is open loop。 The scheme controls the load angle and amplitude of the stator flux linkage。 The reference value for the load angle can be calculated 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 Fig。4。 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 torque ripple。 The selection of the voltage vector and switching time is based on the prediction of 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 of IPMSMs is proposed in [18] where the sliding surfaces and VSC law are derived。 The torque and stator flux linkage errors, together with the flux components, rotor speed the extended flux are used by the variable structure controller to calculate the voltage vector driving the system states to the sliding surface。 By means of SVM this voltage vector 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 performance。

IV。 STATOR FLUX LINKAGE ESTIMATION

The 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 compensation techniques have been reported and a short overview is given in [19]。

To overcome this problem a programmable cascade of low-pass filters (LPF) is proposed as alternative to an integrator in [19]。 Each of the low-pass filters has   atransfer characteristic with T the filter time constant and the  frequency of 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 voltage equations 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 ta tor resistance estimation is described in[19] and [20]。 It is based on the relationship between the change in resistance and the change in current, which allows a PI-controller to determine the stator resistance correction。 The algorithm has no need for the rotor position。 Despite the dependency of the reference current on and , the influence of saturation on this method is not discussed。