*Improved current control can be utilized effectively for torque control*

*Switched reluctance machines (SRM) become more and more attractive for many industrial applications due to their simple structure, high speed, high torque and low cost. One of the major disadvantages of the SRMs is the torque ripple. The torque is often controlled via an inner current loop. To achieve good torque control, accurate command tracking by the current control is required. Some methods for current control of the SRM are presented in [1-7].*

*By Joanna Bekiesch and Günter Schröder, University of Siegen*

### Digital current control

One typical control method is linear current control. With this method it is possible to obtain current with low ripple and thus small noise in the machine. The disadvantage of a linear controller is that it can react very sensitive to wrongly set parameters. Due to the oscillations of the controller in case of instability the maximum current of the inverter can be exceeded. Since the electrical time constant () varies widely with current and rotor position the parameters of the controller are difficult to adapt. Additionally a strong and dynamic disturbance (back EMF) causes poor performance of the controller. This is easily to be noticed during generator operation with small current (Figure 1).

These problems are related to the nonlinear behaviour of the machine, which can be expressed by the voltage equation for one phase:

Where is the back electromotive force (back EMF) term and is the incremental inductance. A mutual inductance term is neglected. Equation 1 shows that the respective operating condition of the nonlinear machine depends on position, current, and speed.

With a small current, the incremental inductance is not saturated and has both largest values and variation (Figure 3). Large inductance means small closed loop gain and poor dynamics of the control loop. Figure 2 shows the phase current and controller output in motor operation (at 750 rpm). The increasing ripple indicates falling incremental inductance. The controller gain is optimized for the worst case (lowest incremental inductance). The total controller output is limited to ±250V which is the rated voltage for the converter, after EMF compensation. The figures show the controller output before the final limit (Figure 5). The back EMF is a rapidly changing voltage forcing the controller to react very fast which causes control deviations.

To solve these problems a PI gain adaptation for the incremental inductance and an EMF compensation method are proposed.

### Gain Adaptation for Incremental Inductance

The incremental inductance of the SRM is non-linear and depends on the phase current and rotor position, as can be seen in Figure 3. This means that at low current, where the incremental inductance reaches high values, the controller with constant (gain of the P-part) can not fulfill the control task. Because of that the difference between reference current and the measured one is particularly noticeable in generator operation (Figure 1). Improper design can lead to either poor command tracking or oscillations. To decrease the fluctuation, the gain of the PI controller has to be a function of the incremental inductance. Figure 5 shows the complete structure of the control loop. The transfer function of the current loop to be controlled is:

Where is the sum of the small time constants: the time constant of the converterand half the ADC sampling time is the electrical time constant, which equals:

In this paper it is suggested to make the, which is proportional to the electrical time constant, therefore depending on the incremental inductance. The incremental inductance can be calculated from the equation:

The flux was measured with the direct measuring method introduced in [8]. To omit unnecessary calculations for adjustments and to reduce the calculation time, the incremental inductance values can be stored in a loop-up table. The electrical time constant is multiplied by a constant to get the controller gain.

### Back EMF Decoupling

The second problem for the current control is the influence of the back EMF. From Equation 1 it can be noticed that the EMF is a function of the position, phase current and speed. The back EMF is small at low speed and has not as significant negative impact on the controller. This influence increases at higher speed. The back EMF as a disturbance is already known from the DC machine. Compared to the DC machine, the change of this induced voltage is much quicker. Therefore the back EMF at the DC machine, contrary to the SRM, has no significant impact on the dynamic work of the controller. Figure 4 shows that the EMF is highly non-linear. Because of that, a controller without feed forward can not compensate for the quick and large changes of this induced voltage and a difference between reference current and the measured one develops.

To prevent this, the EMF compensation method is proposed. The task of this method is to minimize variable disturbances in the control loop which are related to the back EMF. This EMF compensation block contains a look-up table of the voltage levels for the feed forward control. For the application of the table, the angular position as well as current and speed are needed as input variables. At constant current and constant angular speed Equation 1 is reduced to:

If the winding resistance is known, the back EMF can be calculated and stored. For operation at arbitrary speed the compensation can be calculated as:

With the data from the table the voltage can be estimated on-line. The test results were determined with a regulation cycle time of 40ms. Figure 4 presents the measured values of the back EMF. The EMF compensation is made for each operating condition defined by current, position and speed in order to eliminate the variable disturbances to a large extent. Current control with EMF compensation and consideration of the variable time constant Figure 5 shows the block diagram of the proposed method. In addition to the PI controller, the EMF compensation is used and the gain of the PI controller has to be proportional to the incremental inductance.

Figure 6 and Figure 7 show the experimental result of the application of the EMF compensation method in the control loop. In compar- ison to the current without EMF compensation depicted in Figure 1 and 2 an improvement is to be noticed. The current now follows the desired current value accurately. The controller output is almost zero. That means that the controller only reacts on the variable disturbances which are not related to the back EMF. With this the controller’s capacity is not exceeded. The experimental results were determined for 10% of rated current and at speed 750 rpm.

**Conclusion**

The modification of the PI current control allows a minimization of the disturbances in the control loop, which are related to the saturation or back EMF and variable time constant. This article focuses on the SRM with low current, because the incremental inductance has extreme variations in that case and it has a significant negative impact on the dynamics of the controller. The experimental results show that the current controller is capable of performing highly dynamic output variations and that the closed loop gain can be kept on a constant high value which allows good dynamic behaviour in the whole operating range. This improved current control can be utilized effectively for torque control.

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