Minimization torque ripple for SRM based on flux linkage partition in DB-DTFC

. This paper proposes a novel deadbeat torque and flux control (DB-DTFC) to reduce torque ripple for switched reluctance motor (SRM). DB-DTFC combines the advantages of direct torque control (DTC) and space-vector modulation (SVM). DB-DTFC leads current vector control into DTC in order to find the equation between torque and current through deadbeat prediction theory i.e. a beat reaches a given point. In addition, the deadbeat calculation module here is similar to that of permanent magnet synchronous motor. Based on dq 0 reference frame of SRM, the most suitable dq 0 axis current of next moment corresponding to different torque errors is calculated and predicted. According to the calculated dq 0 axis current, the optimal space voltage vectors can be selected to reduce torque ripple. In order to verify the effectiveness and correctness of the proposed scheme, DB-DTFC is verified and compared with the DTC-SVM by simulation.


Introduction
As a new type of reluctance motor, switched reluctance motor (SRM) has attracted much attention because of its outstanding advantages, such as simple and robust structure, wide speed range, good reliability and high efficiency [1]. However, double salient structure and the principle of minimum reluctance lead to SRM's nonlinear strong coupling characteristic. This characteristic is an important reason for large noise and torque ripple of SRM [2].
Traditional current chopper control and angle control can not make speed regulation and torque ripple reduction compatible perfectly, then space-vector modulation (SVM) and direct torque control (DTC) are proposed. With the development of DTC, many DTC-based control method has been explored. [3] proposes direct instantaneous torque control (DITC) based on double hysteresis control. [4] proposed the direct torque and predictive flux control method based on model prediction of SRM.
Current vector control (CVC) is an important part of vector control. The traditional CVC is only closed loop control of stator current in the d-q coordinate system without torque closed loop. When the idea of CVC is introduced into DTC, the relationship between torque and current can be found. Deadbeat direct toque flux control (DB-DTFC) of induction machine (IM) [5] is proposed. DB-DTFC not only has the advantages of DTC and SVM, but also can calculate the d-q axis current through torque error, so as to the selection of optimal voltage vectors. Because of these advantages, DB-DTFC has been applied interior permanent magnet synchronous machine (IPMSM) [6] and synchronous reluctance motor [7].
Since the promotion of DB-DTFC, many scholars have made contributions on improving DB-DTFC for IPMSM. In [8] deadbeat direct current control is proposed to reduce computation load of DB-DTFC . Although there is no torque closed loop in this method, the author use the idea of maximum torque per ampere to combine the torque and current. [9] proposes the loss minimization DB-DTFC from the point of loss and proved the validity of the method. Based on DTC-SVM , reference [10] proposes an optimal deadbeat control method which combined adjacent voltage vectors with optimal voltage vectors. Although DB-DTFC is widely used and developed in other motors, the application of DB-DTFC in SRM has been greatly limited. The reasons of the restriction are uncertain torque expression and the absence of rotor flux linkage.
According to [11], the mathematical model of dq0 coordinate system makes it possible for DB-DTFC to be applied on SRM. [12] proposes a new current vector control method based on the dq0 coordinate system and emphasizes the effect of zero-phase current on the torque control. Another vector control about speed-sensorless SRM drive is also proposed based on the dq0 coordinate system [13].
Since DB-DTFC have both advantages of DTC and SVM, this paper proposes a novel DB-DTFC of SRM based on dq0 coordinate system and deadbeat prediction theory. The dq0 coordinate system is established to find the equation between dq0 axis current and torque. As for the deadbeat prediction, it is used to find the optimal current and voltage under different torque errors. Due to the difference between SRM and IPMSM, DB-DTFC of SRM is different from that of IPMSM, especially in the case of zero phase current optimization. The proposed method uses torque flux decoupling control and finds the optimal dq0 axis current. DB-DTFC is verified the validity and correctness by simulation. It is also compared with DTC-SVM for the performance of torque ripple under different conditions.
Expression (1) can also be written in matrix form as p is differential operator.
Among the matrix neglecting the mutual inductance, the self-inductance part is expressed as: where dc L and ac L are DC self-inductance and DC self-induction amplitude, respectively; r  is rotor position angle and N is phase number, 1,2,..., k N  ,. The instantaneous torque expression of SRM can be defined as: where e T is the instantaneous torque; P is magnetic pole number.

Mathematical model of rotating coordinate
According to literature [11], "rotor flux" generated by the DC current, when DC current is applied to each circuit. The rotating coordinate system is established by rotating the "rotor flux". In the synchronous rotating coordinate, current can be expressed as: where  is the electrical angle; q i and d i are the qaxis and d-axis components of a i , b i and c i , 0 i is zero-phase current.

Derivation of deadbeat control algorithms
Considering (4) as the torque expression in deadbeat control, when the speed in constant, are determined by motor parameters. They can be regarded as constants. Therefore when the sampling time is small enough, only the three-phase current needs to be adjusted to control the torque increase and decrease .
Substituting (5) into (4), a i , b i and c i can be replaced by q i , d i and 0 i to achieve the same control effect of torque as three-phase stator current. According to the decoupling control of DB-DTFC based on IPMSM [6], flux and torque can be decoupled into two independent systems. Torque is affected both q i and 0 i [12], flux is only controlled by d i . In 2 ) sin ( 2 )) 6 3 2 2 ( sin 4 sin( 4 ) sin( 4 ))] 3 3 2 ( sin 2 cos( 2 ) sin ( 2 ) The two factors q i and 0 i affecting the torque need to be set to and make sure that the values of the next moment are the smallest current values.
Due to the short sampling time, current can be discretized. In the discrete time, substituting

Analysis of simulation results
The simulation results of proposed DB-DTFC and DTC-SVM will be analyzed and compared in this part. Relying on Matlab/simulink the simluation can be established based on the three-phase 12/8-pole SRM, and the rated voltage is 520V.
In order to assess the effect of different algorithms.  Fig.6 is the waveform of 600rpm with 10N·m load torque, the optimization of RC T is not obvious as that of Fig.7 and Fig.8 with high speed loading.
(a) (b) Fig. 6. ω=650rpm, TL=10N·m ( From the torque waveform, the two method both have good control to the torque. But the more excellent control performance of DB-DTFC can be seen than that of DTC. The torque ripple becomes smaller than that of DTC-SVM.

Conclusion
To solve the problem of switched SRM torque ripple, DB-DTFC is proposed based on dq0 coordinate system. DB-DTFC is based on DTC-SVM and introduces current vector into the control system. But the flux and torque control of DB-DTFC is different from DTC-SVM. Especially, decoupling flux and torque and adopting dq0 axis currents control respectively. Using q i , 0 i control the torque and using d i controls the flux. The flux control is similar to DB-DTFC based on IPMSM. But the zero phase current is taken into account in the torque control. DB-DTFC is compared with DTC-SVM by simulation on the stable state. The better performance of DB-DTFC is reflected in the torque ripple values. The simulation results can also verify the validity and feasibility of DB-DTFC.