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This work presents an improved Direct Torque Control (DTC) method for a 5phase interior permanent magnet synchronous motor (5PIPMSM) based on space vector modulation (SVM) and fuzzy logic (FL). In this proposed DTC control, we replaced the traditional proportionalintegral (PI) by the FL controller. The main goal is to improve system performance by minimizing the ripple of the stator flux and the torque ripples. The proposed control technique applied on the 5PIPMSM is verified by Matlab/Simulink software followed by an analyzed and compared to verify the effectiveness of the proposed method. Many improvements have been made to the stator flux ripples, torque ripples, rise time and the robustness to disturbance.
direct torque control, stator flux ripple, fuzzy logic controller, multiphase interior permanent magnet synchronous motor, torque ripple, space vector modulation
Multiphase machines (MPMs) have useful properties compared to a traditional threephase system [1]. Among them, for the same power rating, the phase currents are much smaller in MPMs and characterized by an inherent fault tolerance that can be improved [2, 3]. As for the application areas, they are many and varied, such as automobiles and the wind energy conversion system [4, 5].
Direct torque control (DTC) is the most important method used nowadays. The DTC strategy was first proposed for the induction motor (IM) in 1985 by Takahashi et al. [6]. The basic idea of this technique is a direct command of the stator flux and torque of IM without any pulse width modulation (PWM) strategy and proportionalintegral (PI) controllers. However, this method is a simple structure compared to the fieldoriented control (FOC) strategy. In this method, the switching table is used to control the inverter. On the other hand, the DTC method has many advantages, the fast dynamic response, lower parameter dependency, and reliability. But, the principal drawbacks, is the stator flux and torque ripples [7, 8].
A DTC control scheme was proposed to control permanent synchrone motor (PMSM) [9]. A DTC technique was designed to regulate the torque of the doubly fed induction machine (DFIM) [10]. The authors [11] propose a DTC strategy based on the neural controller. In this proposed DTC control, the switching table is replaced by artificial neural networks (ANNs) controller. The DTC control is proposed to command the IM drive using a fivelevel neutral point clamped (NPC) inverter [12]. This proposed technique minimized the total harmonic distortion (THD) of voltage and torque ripple compared to classical DTC strategy. The DTC method was proposed based on space vector modulation (SVM) to command IM drive by using two PI controllers [13].
DTC control scheme was proposed based on second order sliding mode control (SOSMC) to command the DFIGbased wind power [14]. The switching table of DTC control is replaced by the fuzzy logic controller (FLC) [15]. This proposed strategy is simple scheme and minimize the ripples in torque and stator flux. The authors propose a fourlevel DTC strategy with the ANN controller by using neural PI controller of speed [16]. The switching table of DTC is replaced by ANN controller and PI controller of speed by using fuzzy controller [17].
The direct flux and torque control of speed sensorless fivephase interior permanent magnet synchronous motor (5PIPMSM) based on adaptive sliding mode control (ASMC) is presented [18]. A new fault tolerant drives for a 5PIPMSM to achieve the MTPA operation (maximum torque per ampere) under opencircuit faults [19]. On the other hand, the 5PIPMSM is an MPM and reduces the electromagnetic torque compared to the classical PMSM. The DTC strategy of 5PIPMSM based on adaptive inputoutput feedback linearization (AIOFL) is presented [20]. A SOSMC technique was proposed to control the two 5PIPMSM drives [21]. FLC technique and sliding mode control (SMC) control are combined to regulate the torque and speed of 5PIPMSM [22]. The author proposes a comparison between classical DTC and DTC with SVM technique for fivephase induction motor [23].
In this work, we propose a new DTC method based on the FLC technique named DTCSVMFuzzy. The original contribution is the application of the intelligent control in the DTC method by using SVM technique and simulation investigation of this new method. The main advantages of the DTCSVMFuzzy method are the simplicity of implementation and minimizing the ripple of the stator flux and the torque ripples compared to a traditional DTC system and DTCSVM with PI controller of the 5PIPMSM.
The principle of DTC method is presented in detail in the papers [618]. To learn DTC strategy, we review some of the equations of 5phase IPMSM. The electromagnetic torque is written in terms of current and stator flux as [24]:
${{T}_{e}}=\frac{5}{2}P({{\Phi }_{\alpha }}{{i}_{\beta }}{{\Phi }_{\beta }}{{i}_{\alpha }})$ (1)
The switching states of the inverter are determined by flux and torque errors, as shown in Eq. (2):
$\left\{ \begin{align} & \Delta {{T}_{e}}={{T}_{e}}^{*}{{T}_{e}} \\ & \Delta {{\Phi }_{s}}={{\Phi }_{s}}^{*}{{\Phi }_{s}} \\ \end{align} \right.$ (2)
where,
T_{e}^{* }: Reference torque.
Φ_{s}^{* }: Reference flux.
Using the quantities of Concordia, the amplitude of the stator flux is expressed by:
${{\Phi }_{s}}=\sqrt{{{\Phi }_{\alpha }}^{2}+{{\Phi }_{\beta }}^{2}}$ (3)
And position of the stator flux:
${{\theta }_{s}}={{\tan }^{1}}\frac{{{\Phi }_{\beta }}}{{{\Phi }_{\alpha }}}$ (4)
The DTCST control scheme contains three control loops: the control loop for the electromagnetic torque in which the hysteresis comparator, as well as the control loop for the magnitude of the flux has a hysteresis comparator, while the speed control loop for the motor has a PI regulator. In addition, the classic DTC is a simple control scheme and easy to implement compared to vector control. However, this strategy gives more ripples in stator flux and electromagnetic torque, due to the variable switching frequency.
Listwan and Pieńkowski [23] proposed a new switching table for classical DTC of the fivephase IPMSM drives; this proposed switching table is given in Table 1. On the other hand, the modeling of a 5phase IPMSM is expressed in a rotary frame dqxy as [25, 26]:
The state equation of stator voltage:
$\left\{ \begin{align} & v_{ds}^{{}}={{R}_{s}}i_{ds}^{{}}+\frac{d}{dt}\Phi _{ds}^{{}}{{w}_{r}}\Phi _{qs}^{{}} \\ & v_{qs}^{{}}={{R}_{s}}i_{qs}^{{}}+\frac{d}{dt}\Phi _{qs}^{{}}+{{w}_{r}}{{\Phi }_{ds}} \\ & v_{xs}^{{}}={{R}_{s}}i_{xs}^{{}}+\frac{d}{dt}\Phi _{xs}^{{}} \\ & v_{ys}^{{}}={{R}_{s}}i_{ys}^{{}}+\frac{d}{dt}\Phi _{ys}^{{}} \\ & v_{0s}^{{}}={{R}_{s}}i_{0s}^{{}}+\frac{d}{dt}\Phi _{s0}^{{}} \\ \end{align} \right.$ (5)
Table 1. Switching table for conventional DTC
dɸ 
+1 
0 

dT 
+1 
0 
1 
+1 
0 
1 
S_{1} 
24 
0 
17 
14 
31 
7 
S_{2} 
28 
31 
25 
6 
0 
3 
S_{3} 
12 
0 
24 
7 
31 
19 
S_{4} 
14 
31 
28 
3 
0 
17 
S_{5} 
6 
0 
12 
19 
31 
25 
S_{6} 
7 
31 
14 
17 
0 
24 
S_{7} 
3 
0 
6 
25 
31 
28 
S_{8} 
19 
31 
7 
24 
0 
12 
S_{9} 
17 
0 
3 
28 
31 
14 
S_{10} 
25 
31 
19 
12 
0 
6 
Flux linkages equation as follows:
$\left\{ \begin{align} & \Phi _{ds}^{{}}={{L}_{d}}i_{ds}^{{}}+{{\varphi }_{f}} \\ & \Phi _{qs}^{{}}={{L}_{q}}i_{qs}^{{}} \\ & \Phi _{xs}^{{}}={{L}_{ls}}i_{xs}^{{}} \\ & \Phi _{ys}^{{}}={{L}_{ls}}i_{ys}^{{}} \\ & \Phi _{s0}^{{}}={{L}_{ls}}i_{0s}^{{}} \\ \end{align} \right.$ (6)
The electromagnetic torque is expressed as follow:
${{T}_{e}}=\frac{5}{2}P(({{L}_{d}}{{L}_{q}}){{i}_{ds}}{{i}_{qs}}+{{\varphi }_{f}}{{i}_{qs}})$ (7)
The fundamental equation of dynamics is:
${{J}_{m}}\frac{d{{w}_{r}}}{dt}={{p}_{{}}}{{T}_{e}}{{p}_{{}}}{{T}_{r}}{{f}_{m}}{{w}_{r}}$ (8)
To improve classic DTC performance of the fivephase IPMSM, we propose using a new DTC control scheme with SVM technique. However, the DTCSVM method is a simple scheme and reduces stator flux ripple and electromagnetic torque ripple compared to the classic DTC and vector control.
A 5phase vector provides a total of thirtytwo spatial vectors, of which thirty are active vectors and two are zero vectors. The 30 vectors extend over 360 degrees in a twodimensional plane, forming a decagon with ten sectors of 36 degrees each. The 5phase SVM can be applied using a two or four vector method. The active switching vectors are divided in to three groups; large, medium and small switching vectors. The active switching vectors are divided in to 3 groups: small, large and medium switching vectors. Figure 1 (a) and Figure 1 (b) illustrate the active vectors for αβ frame and xy frame, respectively [27, 28].
(a)
(b)
Figure 1. The voltage space vectors and the switching states of the fivephase inverter in: (a) αβ frame, (b) xy frame
The expression for switching time (ST) using the fourvector method is given as follows:
$V_{s}^{*}{{T}_{s}}=V_{al}^{{}}T_{al}^{{}}+V_{bl}^{{}}T_{bl}^{{}}+V_{am}^{{}}T_{am}^{{}}+V_{bm}^{{}}T_{bm}^{{}}$ (9)
$\left\{ \begin{align} & \left V_{al}^{{}} \right=\left V_{bl}^{{}} \right=\left V_{l}^{{}} \right=\frac{2}{5}{{V}_{dc}}2\cos \left( \frac{\pi }{5} \right) \\ & \left V_{am}^{{}} \right=\left V_{bm}^{{}} \right=\left V_{m}^{{}} \right=\frac{2}{5}{{V}_{dc}} \\ \end{align} \right.$ (10)
$\frac{T_{al}^{{}}}{T_{am}^{{}}}=\frac{T_{bl}^{{}}}{T_{bm}^{{}}}=\frac{\left V_{l}^{{}} \right}{\left V_{m}^{{}} \right}=\tau =1.618$ (11)
We find the equation for the ST by solving equation (9), (10) and (11). These are as follows:
$\left\{ \begin{align} & T_{am}^{{}}=\frac{\left 0.2764{{V}_{ref}} \right\sin \left( k\pi /5\theta \right)}{\left {{V}_{m}} \right\sin \left( \pi /5 \right)}T_{s}^{{}} \\ & T_{al}^{{}}=\frac{\left 0.7236{{V}_{ref}} \right\sin \left( k\pi /5\theta \right)}{\left {{V}_{l}} \right\sin \left( \pi /5 \right)}T_{s}^{{}} \\ & T_{bm}^{{}}=\frac{\left 0.2764{{V}_{ref}} \right\sin \left( \theta \left( k1 \right)\pi /5 \right)}{\left {{V}_{m}} \right\sin \left( \pi /5 \right)}T_{s}^{{}} \\ & T_{bl}^{{}}=\frac{\left 0.2764{{V}_{ref}} \right\sin \left( \theta \left( k1 \right)\pi /5 \right)}{\left {{V}_{l}} \right\sin \left( \pi /5 \right)}T_{s}^{{}} \\ & T_{0}^{{}}=T_{s}^{{}}\left( T_{am}^{{}}+T_{al}^{{}}+T_{bm}^{{}}+T_{bl}^{{}} \right) \\ \end{align} \right.$ (12)
where, T_{s} switching period; T_{am}, T_{bm} the ST of medium voltage vectors; T_{0} the ST of zero voltage vectors; T_{al}, T_{bl} the ST of long voltage vectors; θ the angle of position of reference voltage vector; V_{ref} reference voltage vector; k number of sector.
To optimize the performance of the DTC strategy and the application of a fixed switching frequency, the hysteresis comparator in a DTC traditional is compensated by PI stator flux and torque comparators. The switching table is also replaced by an SVM Technique, as shown in Figure 2.
Figure 2. Diagram of DTCSVM control applied for fivephase IPMSM
Figure 5 represents the technique of the direct torque fuzzy controller (DTFC). The traditional PI controllers for torque and flux have been replaced by two FLC. The T_{e}^{*} and Φ_{s}^{*} are compared with the values obtained in the T_{e} and Φ_{s} estimator. The errors are sent to the DTFC control system. The membership function (MF) of the combined input and output variables is generally determined by a common universe of discourse. The FLC is based on the following elements: a fuzzification interface, an inference mechanism, a bases rule and a defuzzification interface [29, 30].
The ifthen rules to FLC for speed control will be 25 rules. Figure 3 (a), (b) and (c) shows MFs of input variables E_{w}, dE_{w} and output variable respectively (traditional triangular shapes). The MFs is divided into 5 fuzzy. Table 2 shows the 25 fuzzy control rules.
Figure 3. Speed regulator variables membership: (a) E_{w}, (b) dE_{w}, (c) output
Table 2. FLC rule base for speed control

E_{w} 

NS 
PB 
ZE 
NB 
PS 

dE_{w} 
NB 
ZE 
PB 
PB 
ZE 
PB 
PB 
NB 
ZE 
NB 
NB 
ZE 

ZE 
ZE 
NS 
ZE 
PS 
ZE 

PS 
NS 
ZE 
NS 
NS 
ZE 

NS 
ZE 
PS 
PS 
ZE 
PS 
The fuzzy labels used in this method are positive small (PS), equal zero (ZE), positive big (PB), negative big (NB) and negative small (NS).
The same steps used for the conception of the speed controller (FLC) will be repeated for the torque and flux controller as shown in Figure 4, only we have: E_{Φ}= Φ_{s}^{ *} Φ_{s }for the first fuzzy controller of flux Φ_{s} and for the second fuzzy controller of torque E_{T}= T_{e}^{*} T_{e} for the first fuzzy controller of torque T_{e}.
We represent the input/output variables by MF, as show in Figure 4, each one divided into 3 fuzzy. Table 3 shows the 9 fuzzy control rules and bestow the change of the FLC output in terms of two inputs E_{Φ,T} and dE_{Φ,T}.
Figure 4. Torque and flux regulator variables membership: (a) E_{Φ,T}, (b) dE_{Φ,T}, (c) output
Table 3. The rule base for controlling the torque and flux

E_{Φ,T} 

P 
Z 
N 

dE_{Φ,T} 
N 
Z 
N 
N 
P 
P 
P 
Z 

Z 
P 
Z 
N 
The MFs is also assigned with three fuzzy sets: Z (zero), N (negative), P (positive).
The bloc diagram of the DTCSVM fuzzy for fivephase IPMSM is given by Figure 5.
Figure 5. Block diagram of the fivephase IPMSM with DTCSVMFuzzy
To verify the method proposed in this work, Matlab/Simulink software based simulations were performed. The parameters of the 5phase IPMSM are as follows: R_{s} = 0.7 Ω, J_{m }= 0.0025 Kg/m^{2}, f_{m }= 0.005 Nm/rad.s^{1}, L_{d }= 0.0018 H, L_{q }= 0.0042 H, P=2, ϕ_{f=}0.5 web.
Three control strategies: DTCST, DTCSVM and DTCSVMfuzzy are simulated and compared to reference tracking, sensitivity to load torque change, torque and stator flux ripples, and robustness against variations in machine parameters.
5.1 Reference tracking test
Figure 6 show the performance of the 5phase IPMSM under change in the T_{r}from 0 Nm to 10 Nm at t = 0.3s, after that, the T_{r} is reduced to 0 Nm at t = 0.6 s. The reference speed is set at 100 to 100 rad/s at t=0.9s. This figure shows that the effect of the T_{r}is very evident on the speed curve of the DTC with the PI controller, while the effects are negligible for the DTC with FLC (see Figure 10). We can see that the latter has an almost ideal speed disturbance rejection (about 2%).
Figure 7 presents the response of torque with T_{r} application. A comparison of the results obtained indicates that the DTCSVM Fuzzy method reduced torque ripple by 68% compared to traditional DTC and by 20% compared to DTCSVM (see Figure 11). These results confirm that the torque ripple in the proposed method has considerably decreased. A comparative study is provided in Table 4.
Figure 8 presents the response of the stator flux for these three methods. It is obvious that DTCSVMFuzzy method can improve steady and dynamic performances of the system and decrease flux ripple (see Figure 12). Figure 9 (a) presents the stator flux loci for traditional DTC. The stator flux locus with the DTCSVM diagram is shown in Figure 9 (b) and with the DTCSVMFuzzy diagram is shown in Figure 9 (c). In Figure 9 (c) the Lucas of stator flux is improved with very low ripple as compared with classical DTC.
Figure 6. Rotor speed response of the fivephase IPMSM controlled by classical DTC, DTCSVM and DTCSVMfuzzy
Figure 7. Torque response
Figure 8. Stator flux response
(a)
(b)
(c)
Figure 9. Stator flux circular trajectory in αβ axis: (a) Classical DTC, (b) DTCSVM, (c) DTCSVMfuzzy
(a) (b)
Figure 10. Zoom in the rotor speed response: (a) When startup, (b) When applying the load torque
Figure 11. Torque response (Zoom)
Figure 12. Stator flux (Zoom)
Table 4. Amplitude of ripples

Traditional DTC 
DTCSVM 
DTCSVMfuzzy 
T_{e} ripples (Nm) 
6,213,6 (7,4 Nm) 
8,511,4 (2,9 Nm) 
8,911,1 (2,2 Nm) 
Φ_{s} ripples (Wb) 
0,3930,407 (0,014 Wb) 
0,3960,405 (0,009 Wb) 
0,3980,403 (0,005 Wb) 
5.2 Robustness test
To study the robustness of the proposed method, the nominal value of the stator resistance R_{s} and the inertia variation J_{m} is increased by 100%, L_{d} and L_{q} we reduce them by 50%. Simulation results are shown in Figures 1318. These variations have a clear effect on the rotor speed, torque and stator flux curves and the effect seems more important to DTCST and DTCSVM control scheme compared to DTCSVMfuzzy (see Figures 1618). A comparative study is provided in Table 5. We conclude the FLC that they are more robust to this parameter variation than a PI controller.
Figure 13. Rotor speed response of the fivephase IPMSM controlled by classical DTC, DTCSVM and DTCSVMfuzzy
Figure 14. Torque response
Figure 15. Stator flux response
(a) (b)
Figure 16. Zoom in the rotor speed response: (a) When startup, (b) When applying the load torque
Figure 17. Torque response (Zoom)
Figure 18. Stator flux (Zoom)
Table 5. Amplitude of ripples

Traditional DTC 
DTCSVM 
DTCSVMfuzzy 
T_{e} ripples (Nm) 
4,316 (11,7 Nm) 
7,911,9 (4 Nm) 
8,811,2 (2,4 Nm) 
Φ_{s} ripples (Wb) 
0,3890,411 (0,022 Wb) 
0,3920,407 (0,015 Wb) 
0,3970,404 (0,007 Wb) 
In this work, a DTFC of the 5PIPMSM based on SVM was proposed to improve the performance of the DTC technique. Simulation results achieved by the proposed method of DTCSVM with FLC confirm a considerable reduction in ripples of the stator flux, torque ripples and the robustness to the system compared to a traditional DTC system and DTCSVM with PI controller.
For future works, it will address the experimental validation of the proposed method. Next, it is interesting to extend the DTCSVM with type2 fuzzy algorithm add an observer for speed estimation.
DTC 
Direct Torque Control 
IPMSM 
Interior Permanent Magnet Synchronous Motor 
FLC 
Fuzzy Logic Controller 
PI 
ProportionalIntegral 
SVM 
Space Vector Modulation 
f_{m} 
Viscous damping 
J_{m} 
Inertia moment 
L_{d }, L_{q} 
d and q axis stator inductance 
i_{s} 
Stator currents 
R_{s} 
Stator resistance 
L_{x}, L_{y} 
x and y axis stator inductance 
p 
Number of pairs poles 
v_{s} 
Stator voltages 
Greek symbols 

θ_{r} 
Electrical angle 
T_{e} 
Electromagnetic torque 
T_{r} 
Load torque 
ϕ_{f} 
Magnetic flux 
θ_{s} 
Position of the stator flux 
Φ_{s} 
Stator flux 
1. Block diagram of the FLC
The block diagram of FL controller is shown in Figure 19.
Figure 19. Block diagram of the FL controller
2. The coefficients of the FLC stator flux, torque and speed controllers
Table 6 shows the constants values of the stator flux, torque and speed FL controller algorithm gains.
Table 6. FL controller gains
Stator flux 
Torque 
Speed 

K1 
K2 
K3 
K1 
K2 
K3 
K1 
K2 
K3 
200 
0.01 
50 
150 
0.01 
70 
70 
0.4 
170 
The Table 7 shows the parameters of fuzzy controller.
Table 7. Parameters of fuzzy controller
Fis type 
Mamdani 
And method 
Min 
Or method 
Max 
Implication 
Min 
Aggregation 
Max 
Defuzzification 
Centroid 
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