*4.1.2. Direct Torque Control (DTC)*

Therefore, the improved FFT expression with the Blackman-Harris Window can be shown as

( 1) ( ) ( ) <sup>2</sup>

With use of the improved FFT, the high-frequency and low-frequency components can be decomposed from the load demand, for the power distribution to UC and battery, as shown

The concept of vector control was first proposed by Siemens' F. Blaschke in the early 1970s, which is also named as field-oriented control (FOC). In this method, the stator current of a three-phase AC motor is transformed into two orthogonal components [18]. One component

In a typical FOC block diagram for a permanent magnet synchronous motor (PMSM), the control system first transforms the command speed or torque into the corresponding current

generate the reference d–q axis reference voltage. The transistor switching is defined by the

For the FOC system, the most important thing is to realize the Clarke and Park transformation. It is these transformations that connect the three-phase coordinate system to the *d* −*q* axis coordinate system. The Clarke transformation converts three-phase currents to a two-axis plot

between the stationary coordinates *α* −*β* and the *d* −*q* coordinate reference frame rotated to align with the rotor flux. As the *d* axis is always in the direction of magnet flux linkage and *q*

FOC is used to control the AC synchronous and induction motors by transforming their dynamic structure into that of DC machines. Unfortunately, the scheme requires many electronic components such as sensors, amplifiers, or multipliers which increase the cost and more calculations are needed to realize the control strategy. This situation is changed due to the availability of microelectronics, with the cost of control hardware being no longer a major

*<sup>d</sup>* and *i*

\*. Then, proportional-integral (PI) controllers are used as current regulator to

*<sup>α</sup>* and *i*

*<sup>β</sup>*. And the Park transformation is

*q*.

*<sup>q</sup>* remain constant. The flux and torque

*<sup>d</sup>* and quadrature-axis current *i*

= - -+ + é ù å ë û (12)

follows based on equations (9) and (10):

14 New Applications of Electric Drives

*4.1.1. Speed/torque vector control*

in Figure 5.

command *i*

*d* \*, *i q*

consideration [19].

( ) <sup>3</sup>

*w*

0

*i*

**4.1. Overview of traction motor speed/torque control strategies**

can control the magnetic flux; the other can control the torque.

to create time-varying quadrature-current values *i*

are separately controlled by stator direct-axis current *i*

axis in the quadrature direction, the values of *i*

pulse-width modulation signal according to the stator references voltage.

=

*i i*

*<sup>a</sup> X k Xk i Xk i*

**4. Advanced motor control strategies for AFV-based electric drives**

Direct torque control (DTC) is a method that controls the torque (and thus finally the speed) of three-phase AC electric motors. The key point of this control is to select stator voltage vectors according to the differences between the references of torque and stator flux linkage and their actual values estimated on basis of the measured voltage and current of the motor [20], [21].

In a PMSM drive with DTC, the *dq* axis currents *i <sup>d</sup>* and *i q*, are obtained from the measured threephase currents, and the voltages *vd* and *vq* are calculated from the dc-link voltage, since the voltage vectors determined by the switching table are known. By integrating the stator voltages, we can calculate the stator flux linkage. Torque is calculated by a cross product of calculated stator flux linkage vector and measured motor current vector. Then the calculated flux magnitude and torque are compared with their reference values to get the flux and torque errors. If either the calculated flux or torque deviates from the reference more than the allowed tolerance, the transistors of the variable frequency drive are turned off and on to generate one certain voltage.

Without the current controller followed by a pulse-width modulation (PWM) comparator, and not using the parameters of the motor, except the stator resistance, the DTC owns the advan‐ tages of less parameter dependence and fast torque response when compared with the torque control via PWM current control. But torque and flux linkage ripples are always the main disadvantage of the DTC.
