for a switch-on time of the voltage vector 。 Each of the six possible active voltage vectors has a component radially and a component tangentially to the stator flux linkage vector。 From (4) thus follows that the radial component of a voltage vector changes the amplitude of the stator flux linkage while the tangential component changes the rotation speed of the stator flux vector and consequently the load angle。

This way the stator flux linkage and the torque can be simultaneously controlled with a VSI。 The instantaneous error between the reference and estimated values of stator flux linkage and torque are minimized by applying the most appropriate voltage vector。 Thus a controller minimizing the error is needed, together with an estimation of the stator flux linkage and torque。

In the overview of section III different types of controllers are discussed。make an estimation of the stator flux linkage (3) can be used。 Yet, unlike IMs, in PMSMs the initial value of the stator flux vector  differs from zero and depends on the rotor position。 As a result the initial rotor position has to be measured or estimated。

III。 POSSIBLE IMPLEMENTATIONS

number of different implementations are proposed in the literature。 One of the first papers to mention direct torque control for PMSMs is [2]。 However the propose dscheme cannot be considered as a true DTC scheme as it is in fact a current control scheme。 As pointed out in [4], a DTC scheme can be used to control, besides the electromagnetic torque of course, the direct-axis current or reactive power instead of the stator flux linkage。 In the following these schemes are not considered, as such all the considered schemes are of the type direct torque and flux control (DTFC)。 In [5] an excellent overview of DTC techniques is given, but the focus is on DTC for induction machines。

In this section an attempt to summarize the different known implementations of DTC for PMSMs is given。 The schemes are pided according to voltage vector selection, but are also different in terms of (initial) stator flux estimation and the use of position sensors。 Some of the discussed schemes namely require the rotor position ,thus losing the advantage of inherent motion-sensor less control。

Switching-table DTC

1) Basic Switching-table DTC: A classical DTC scheme has a hysteresis comparator for the stator flux linkage and a quantisizer for the torque。 A typical scheme is shown in Fig。2, the quantities and denote reference values and the optional encoder is shown as a dashed line。 The instantaneous error for the stator flux linkage  thus has two possible values (1 and −1), whereas the instantaneous torque error has three (−1, 0 and 1)。 Furthermore the  plane is pided in six sections。 The errors and , together with the section number containing the stator flux vector serve as input for a switching table。 The output of the switching table is one of the eight possible voltage vectors。 Such a scheme is implemented in [6] for SPMSMs, with the same switching table as used in [1] for induction machines。 Furthermore a first order filter is proposed as quasi-integrator to solve the problem of initial flux estimation。 As the steady-state output of a first order filter is independent of the initial conditions the quasi-integrator will indeed yield good results, but not at start up of the drive。

Switching-table DTC is also implemented in [3], but no zero voltage vectors are used to control the motor。 This essentially reduces the quantisizer for the torque error to a normal hysteresis comparator。 The flux estimation is based on (3) and the initial flux position is assumed to be known。 The method is applicable to IPMSMs and SPMSMs。

In [7] and [8] this scheme with reduced switching table is applied for IPMSMs and the initial rotor position is known from a low resolution encoder。 It is shown that by varying the stator flux linkage reference either maximum torque per ampere (MTPA) or field weakening operation of the drive is possible。 Recent papers have further reported on the use of these reference-flux-generating methods。 In [9] a maximum torque per flux (MTPF) scheme is discussed, based on switching table DTC。 A method to optimize efficiency under switching table DTC of PMSMs is given in [10], where the stator flux linkage is selected to yield maxi mu efficiency。 In all of these reference-flux-generating methods off-line calculations are needed to determine the look-up tables for the reference stator flux。