TORQUE SMOOTHING OF A FAULT TOLERANT SEGMENTAL STATOR SWITCHED RELUCTANCE MOTOR TORQUE SMOOTHING OF A FAULT TOLERANT SEGMENTAL STATOR SWITCHED RELUCTANCE MOTOR

become more competitive for variable speed drives used in automotive and industrial applications. One of the most promising approaches to reduce the torque ripples of a SRM is the use of a direct instantaneous torque controller. In the paper the effectiveness of this type of control will be proved for a fault tolerant segmental stator SRM. By advanced simulation techniques the working principle of the direct instantaneous torque controlled drive system is illustrated, and its performances are demonstrated.


Introduction
Beside high electrical and mechanical performances the fault tolerance is the main issue for electrical machines used in diverse safety-critical applications, as aerospace, automotive, military, medical, etc.).
The switched reluctance motor (SRM) due to its robust and simple construction and to the magnetic independence of its phases is inherently one of the most fault tolerant motors on the market [1]. Combining the fault tolerance increasing solutions cited in the literature [2], [3] and [4] with an innovative modular construction of its stator a novel SRM was developed, which is very reliable and quickly repairable. Its performances were improved by minimizing its torque ripples by estimating and controlling the developed instantaneous torque.

The segmental stator SRM
The stator of the proposed segmental stator SRM is built up of independent modules. Each one has an E-type iron core and a coil wound on its yoke. The modules corresponding to a phase are placed diametrically opposed in the stator. Between the neighboring modules a non-magnetic spacer is placed to assure the adequate shift of the modules and a good magnetic separation (see Fig. 1).
The four-phase variant has 8 stator modules. The entire segmental stator construction is tightened by 16 rods, 2 passing through each module. The stator is placed between two end shields. The conventional SRM rotor has 14 poles and it is built of laminations. The construction of the segmental stator SRM is given in Fig. 2.  segmental stator SRM in study. Hence, one phase of the machine is compound of two coils from diametrically opposed modules, connected in series or in parallel. Due to the specific construction there is no mutual coupling between adjacent coils [6]. The drawback of this solution is that a more complex power converter is required, having as many converter legs as channels [9] and [10].
The adopted modular stator topology allows for an easy and quite low cost manufacturing, and assures the possibility of a fast replacement of a damaged module in case of a coil failure [5].
The main rated specifications of the sample segmental stator SRM taken into study are: • power: 350 W; • current: 6 A; • average torque: 5 Nm.

The direct instantaneous torque control
One of the main disadvantages of the SRMs, and also of the particular segmental stator SRM in study, is their high torque ripple. These can generate significant undesired vibrations and noises.
In the literature several methods of SRM torque smoothening methods are cited [11] and [12] and [13]. These all require complex control [14] and [15], accurate torque and rotor position measurement [16], and complex current regulation techniques [17]. Current profiling [18] and [19] and torque sharing [20] and [21], methods are just two solutions that can be used for minimizing the SRM torque ripples.
A common conclusion can be drawn upon studying these methods, namely that as the complexity of the control strategy is increased, the losses in the SRM are also higher [22]. Therefore, a novel method was applied, the direct instantaneous torque control (DITC) [23], [24] and [25]. This has to be used where the losses have to be as low as possible, the system response has to be fast and accurate, and the generated torque must be very smooth [26].
The main advantage of the DITC is the lack of minor current loops, and of the precise tuning requirements of the PI or PID controllers. The torque is controlled directly by using a specific digital hysteresis controller. On the other hand, as the phase currents are not controlled, overheating of the power switches can occur. At high speeds, and when the currents are very high, the falling to nil of the current could be not enough fast and negative torques could be generated by a phase.
The instantaneous torque developed by the SRM needs to be known at each time step. Its precise measurement is difficult and expensive. A more effective approach is the estimation of the torque. In the literature basically four methods are cited for torque estimation. These methods are based on look-up tables, interpolation, analytical approach and artificial neural networks The flux lines in the motor obtained by means of finite elements analysis (FEA) for unaligned and aligned positions are shown in Fig. 3 [5].
As it can be seen, the magnetic flux is closed between the two poles of a single module hence they are not passing through the central part of the rotor. Therefore, due to the shorter flux paths the losses in the machine are less than in a classical 4-phase SRM. Also due to this novel design the forces are better balanced in the machine [6].
One of the common fault tolerance increasing solutions is the division of the phases into individual coils, called channels [4], [7] and [8]. This way a fault of a channel will not influence the operation of the other channels of the same phase or of other phases. This solution was used also in the case of the 3. after the end of the commutation period the torque will be again controlled within the outer hysteresis band. Upon the actual value of the torque relatively to the two hysteresis bands the voltages of the phases are commutated by soft chopping between three values: +V dc , 0, and -V dc .
To simulate the DITC system an advance SRM model was built up. The simple, voltage equations based mathematical models [1] cannot be applied here, because of the necessity to integrate also the converter model and the DITC strategy. Therefore a more complex, FEA results based model was applied. For the sample SRM two look-up tables were built up upon the previously obtained FEA results [5], [33] and [34]. They contain the magnetic flux and the torque, respectively, versus the phase current and the rotor position. Upon the values from the two look-up tables two 3D static characteristics for one phase of the segmental stator SRM were plotted (see Fig. 6). The static characteristics of the magnetic flux are required only by the simulation program while that of the total torque both by the control strategy implementation and the DITC system model.   [27], [28] and [29]. For the DITC method, the look-up table approach seems to be the best solution [23], [30] and [31].
For estimating the torque from the measured current and rotor position the static torque versus current and angular position is required. The values of this characteristic are stored in a 2D look-up table which can be obtained via measurements or FEA of the SRM [30] and [31]. Knowing at each time step the actual current and the rotor position, the torque of the SRM can be found by a simple looking in the table. It should be mentioned that separate look-up tables have to be computed for each SRM variant. The simplified block scheme of the DITC system of a SRM under study is given in Fig. 4 [13]. Fig. 4 The block scheme of the DITC system of a SRM [13]

The DITC of the modular SRM
The block diagram of the proposed DITC is given in Fig. 5 Fig. 5 The block scheme of the DITC [32] The firing angles compared with the actual rotor position only indicate the conduction zones of the SRM. The main control tasks are performed by the torque hysteresis controller and the generator of switching logic signals. The torque controller uses two different hysteresis bands, one larger than the other. The control strategy follows the following rules: 1. while a single motor phase is active, the torque is controlled inside the main (the wider outer) hysteresis band; 2. during the phase commutation the torque control is performed as follows: • for the formerly conducting phase the thinner hysteresis band is imposed; • for the next phase the larger outer hysteresis band is prescribed; 12.45%) are much smaller than those obtained in the case of a classical controlled modular SRM (near 30% [6]). Fig. 9 Results of simulation: the total, the imposed and the phase torques developed by the segmental stator SRM Fig. 10 Zoom of the results given in Fig. 9 showing the two hysteresis bands and the two phase voltages, currents and torques during a commutation The model of the DITC system controlled modular SRM was built up in the MATLAB ® /Simulink ® environment [34]. The main window of the simulation program is given in Fig. 7.

Fig. 7 The main window of the simulation program
The blocks modeling the hysteresis torque controller, the four-phase power converter, the modular SRM and the firing angle computation unit all can be easily distinguished in the modularly built up model.
The Hysteresis torque controller subsystem is using three Relay type blocks, as shown in Fig. 8. The maximum achievable frequency of the current controllers is 20 kHz.

Fig. 8 The Hysteresis torque controller subsystem
The H-bridges of power converter were modeled by using blocks from the SimPowerSystems library of Simulink ® , as IGBT/ Diode, etc. [35].
The model of the motor is based mainly on the two 2D look-up tables, built up upon the static characteristics given in Fig. 6.
The simulations were performed under diverse conditions. Here some significant results obtained for the reference torque and speed of 4.5 N•m and 400 r/min are given.
In Fig. 9 the total torque, the imposed one and those developed by the four phases of the segmental stator SRM are given. As it can be seen the developed total torque is very close to the imposed 4.5 N•m reference value. The torque ripples (of In such high demanding systems also the relatively great torque ripples of the SRMs could be an important drawback. Therefore a simple, but yet effective control approach was taken into study: the DITC technique. The principles of this strategy are detailed in the paper.
The control method has several advantages, as smooth torque generation, direct compensation of the inherent torque ripple during phase commutation, good steady state torque control accuracy, simplification of sets of control variables and reduction of tuning control variables. All these are emphasized in the paper by advanced simulations performed via a MATLAB ® / Simulink ® model of the machine. The model was developed by using the static magnetic flux and torque characteristics versus current and rotor position, fetched from the FEA of the machine. The converter model was built up by using blocks from the SimPowerSystems library of Simulink ® .
The presented results prove the effectiveness of the proposed control method, and hopefully will help the specialists working in this field to deepen their understanding in advanced control of the SRMs.
Future works will include the fault tolerance study of the segmental stator SRM with the proposed DITC. The control strategy will be implemented on an advanced DSpace system for the laboratory model of the SRM. A real-time turn ON and OFF angle optimization will be also investigated, which hopefully will more smooth the torque. This way, the DITC method will be applicable on the entire speed range of the machine, even with the possibility to work at speeds above the rated one. In Fig. 10 a zoom of the results from Fig. 8 during a commutation are given. It can be clearly observed how the instantaneous torque is kept within one of the two (inner and outer) hysteresis bands, upon the developed control strategy. Also the way as the dc voltage is soft chopped between three values (+V dc , 0, and -V dc ) can be followed.

Acknowledgment
Before approximately 0.023 s, while only phase 3 is in conduction, the torque is controlled inside the main (the outer) hysteresis band. During the phase commutation when usually the torque drops, the torque control is more severe since it is partially performed upon the thinner inner hysteresis band. For the period of commutation also the higher frequency of the voltage soft chopping is clearly visible. After the commutation took place, the torque is kept again within the outer inner hysteresis band.
During the commutation, due to the higher commutation frequency imposed, also the losses in the motor are higher. This is the reason for which the torque is controlled inside the inner hysteresis band only during the phase commutation, the most critical period for a low torque ripple.

Conclusions
The paper deals with the control of a fault tolerant SRM having a segmental stator specially designed for safety-critical applications.
The modular construction of the SRM simplifies both its manufacturing and repairing. The independent stator segments can be manufactured separately, and the entire stator can be easily assembled. The SRM can be quickly repaired if winding faults occur, without removing it from the load.
The fault tolerance of this SRM was proven in several previous papers [5] and [6]. Therefore, it can be used in diverse safety-critical applications in the fields of advanced automation systems, automotive, medical, aerospace, military, etc. [36], [37] and [38].