Design of Fuzzy Double-hysteresis-loop DTC System for New Type TFPM

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Communications in Control Science and Engineering (CCSE) Volume 3, 2015

Design of Fuzzy Double-hysteresis-loop DTC System for New Type TFPM Xiaoqing Yuan*1, Zongyang Yu2 College of Mechanical Engineering, Northwestern Polytechnical University, P.O.Box:403, Xi’an, China 710072

1,2 *1

yuan@nwpu.edu.cn; 2815989042@qq.com

Abstract Transverse flux permanent-magnet motor has the advantages of high torque density. However, because of its own structural defects, the traditional direct torque control has the problem of torque fluctuations, especially at low speed, so it is not available for the control system of TFPM. Analyzing the motors mathematical model, we can conclude superiority of zero vector. So in this paper we take the place of traditional flux and torque hysteresis controller with new double hysteresis loop controller respectively. And then we use fuzzy logic method to improve the controller’s performance. We build system simulation models to compare three methods’ advantages. The research results show that the new fuzzy double hysteresis loop control system has a high precision and a better speed respond characteristic. And at the same time it reduces system torque fluctuations and improves the low speed performance.

Keywords Transverse Flux Permanent-Magnet Motor; Zero Vector; Double Hysteresis Loop; Fuzzy Logic

Introduction Transverse Flux Permanent-Magnet Motor (TFPM) is a kind of motor of which the main flux magnetic circuit is distributed in three-dimensional space. And it is characterized by low speed and high torque density (Shi et al., 2013), which has a strong adaptability in low speed direct drive. The structure and control system design of the TFPM is becoming the hot spots in the present research.

Direct Torque Control (DTC) is a kind of motor control theory which can be applied to the weak magnetic speed regulation. Its control idea is novel, with efficient control performance and simple system structure. But there are also some technical defects, for example: the torque pulsation fluctuates seriously, the performance of low speed is poor (Zhang et al., 2011; Xia et al., 2014). The traditional DTC system is no longer suitable for TFPM because of the characteristics of low speed and large torque. A new kind of double six-phase TFPM is proposed with analyzing its mathematical model and working principle. And the improved DTC system which is more suitable for the new type TFPM is designed. In this paper, the theory that zero vector can effectively reduce the torque ripple and improve the performance of the system is put forward after analyzing. A new zero vector combining scheme is proposed, which is based on double hysteresis control of the stator flux and torque, replacing the original single hysteresis loop. On this basis, fuzzy logic is combined with double hysteresis loop. And at last it forms a new fuzzy double hysteresis control system which can be used for TFPM specially. The simulation results show that the fuzzy double hysteresis control system has good response characteristics, high control precision and strong robustness. It can effectively improve performance of the control system of double six-phase TFPM. Motor Model Design and Zero Vector Analysis Structure and Operational Principle for TFPM In this paper, a new type of double six-phase TFPM mechanism is presented. The new motor has multi-phase composite structure. It can be divided into two modules with twelve phases in all. Each module is composed of two stator units and a rotor disk unit. And each stator unit is equipped with three-phase winding which has a phase difference of 120 degree. The two modules should be staggered with a certain mechanical angle for assembly. A 3D model of one module is shown in Fig. 1 (Su, 2014).

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FIG.1 3D MODEL OF ONE MODULE

When the stator winding is energized, the two teeth of the stator can be equivalent to two poles with opposite polarity. The magnetic field produced by the teeth will attract or repel the rotor disc, which makes the rotor rotate.

Each permanent magnet patch on the disk is opposite on polarity to the adjacent one in radial or circumferential.

So when the rotor turns a polar distance, the current direction can make a change correspondingly to make the motor rotate continuously.

Analysis of Zero Vector in TFPM For double six-phase TFPM, the mathematical model can be equivalent to the coupling of two double three-phase TFPM. Therefore, ignoring the core saturation, hysteresis losses and eddy-current losses of the motor, this paper will analyze mathematical model of one module under ideal conditions.

Taking the horizontal axis and vertical axis as the benchmark, we can build the double two-phase stationary coordinate system, and then transfer it to double two-phase rotating coordinate system d-q. Then the voltage equation in rotating coordinate system is shown as follows:  ud  R s + pLd u  =   q   -Ld ω e

-Lq ω e  id  0     + ωe Ψ f   R s + pLq   i q  1

(1)

The stator flux equation is shown as follows:  Ψ sd  Ld Ψ  =  0  sq  

0  id  1 + Ψf      Lq   i q  0 

(2)

Torque equation is shown as follows: Te = n p (Ψ f i q - Ld id i q + Lq id i q )

(3)

where Ψsd and Ψsq are the components of stator flux on d-q axis respectively. Ld and Lq are equivalent inductance of the stator winding on d-q axis. np is the number of motor pole pair, angular velocity of stator flux is ωe.

According to the formula (1) ~ (3), there is another form of expression about electromagnetic torque in rotating coordinates after a minimum time ∆t.

Te ' =

3n p Ψ s '

(

)

 2Ψ f Lq sinθ′ + Ψ s ' Ld - Lq sin2θ′  4Ld Lq 

(4)

By formula (4), the changes of torque consist of two parts mainly, stator flux increment and angle variation. Thus we can infer that reducing the changing rate of two parameters can certainly reduce the torque ripple, so that the torque change tends to be stable. The equation of flux vector’s increment is shown as follows: Ψ s ' = Ψ s 2 + U s 2 Δt 2

(5)

where Us is the loading voltage vector. It can be acknowledged that the stator flux increment is minimum whose value is zero when the zero vector is selected. And power angle variation consists of the variation of stator flux

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Communications in Control Science and Engineering (CCSE) Volume 3, 2015

angle and rotor flux linkage angle, ∆θ=∆θs-∆θf. The stator flux angle increment is influenced by voltage, rotor flux linkage angle increment by mechanical components. Within the time ∆t, mechanical transient time is much larger than the electrical transient time. Therefore, the stator flux will change faster which is the main factor of the power angle variation(Wang, 2010; Zhu et al., 2006). When loading zero voltage vector, ∆θs is zero and the power angle variation is the minimum. Through the analysis above, it can be known that the zero voltage vector has a good effect on torque ripple minimization.

Double Hysteresis Control Design Smooth torque can be obtained by adding the appropriate zero vector to the original vector control unit from the conclusion that the torque ripple can be reduced by zero vector. Double hysteresis comparator is designed to improve the original voltage vector switching table, which constitutes a new direct torque control system. And the system block diagram is shown in Fig. 2. ω +

Te *

Saturated nonlinear control

Torque controller -

ω*

Double hysteresis comparator

+

Te

*

-

Six phase inverter

TFPM

θs

ψS* +

Improved swithing table

θ

Angle position of stator flux linkage ua、ub、ia、ib

ψS

Torque and flux calculation

-

Position sensor

dθ / dt FIG.2 BLOCK DIAGRAM OF DOUBLE HYSTERESIS DTC

For the traditional DTC system, when the electromagnetic torque is larger than the given torque, the hysteresis controller outputs -1, indicating that it is necessary to reduce the torque. The reverse vector is loaded, which will generate more torque ripple than the forward vector, however(Zhang et al., 2006). So the improved scheme adopts zero vector instead of the reverse vector. If the forward vector and the zero vector are used only, the motor cannot achieve the reverse function, and also the torque’s changing rate is too slow to meet some corresponding requirements. When the torque value is beyond the second level of the given torque, the controller outputs -2, indicating that it is necessary to reduce the torque rapidly. Then the reverse vector works to realize the function of brake and reverse.

The design principle of double hysteresis controller for stator flux linkage is the same as the controller for torque.

Based on the design of the double hysteresis controller of the torque and flux, advantages of the zero vector are absorbed to improve the performance of the control system. The electromagnetic torque and stator flux double hysteresis comparator schematic diagram are shown in Fig. 3, 4. ψ t

2 1

1 -|ΔTe|'

|Te|* -|Te|

-|ΔTe|

- |Δ Te|

-|∆ψ s|

|ψ s| * -|ψ s| |∆ψ s| |∆ψ s|'

-1

-2

FIG.3 DOUBLE HYSTERESIS FOR TORQUE

FIG.4 DOUBLE HYSTERESIS FOR FLUX

On the basis of double hysteresis controller(Wang et al., 2011), the voltage vector switching table is improved with

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a new method of inserting zero vector being proposed, which is shown in Table 1.

TABLE 1 IMPROVED SWITCHING TABLE

Φ =1

Φ =0

Φ =2

Φ, τ, m τ=1 τ=0 τ = -1 τ = -2 τ=1 τ=0 τ = -1 τ = -2 τ=1 τ=0 τ = -1 τ = -2

1 2 7 7 6 3 0 0 5 2 1 1 6

2 3 0 0 1 4 7 7 6 3 2 2 1

3 4 7 7 2 5 0 0 1 4 3 3 2

4 5 0 0 3 6 7 7 2 5 4 4 3

5 6 7 7 4 1 0 0 3 6 5 5 4

6 1 0 0 5 2 7 7 4 1 6 6 5

In the selected area of the table, 0~7 is represented by the voltage vector of u0~u7, where u0 and u7 represent two zero vector voltage, u1~u6 are the six voltage space vectors as the traditional DTC system.

Simulation model of double hysteresis controller in Matlab/Simulink simulation software is shown in Fig. 5.

FIG.5 SIMULATION MODEL OF DOUBLE HYSTERESIS CONTROL

Fuzzy Double Hystersis Control Design Fuzzy control is composed of three parts, which are fuzzification of the input, fuzzy rule and the defuzzification of the output. The core idea is to obscure the changeable input parameters, which imitate artificial intelligence judgment, getting the output results with universal application. And at last defuzzifying the outputs to obtain the accurate variable. The data processed by the fuzzy logic make the system have strong robustness(Pourghasemi et al., 2012; Zou et al., 2014).

Fuzzification of the Input and Defuzzification of the Output For the combination of double hysteresis controller and fuzzy logic, the input variables which need to be fuzzified include torque error ET, stator flux error EF and stator flux angle θS. In order to reflect the method of double hysteresis control, stator flux error EF is divided into three fuzzy intervals, referring to Fig.4. NB (-∞, 0.01) , ZO (0.01, 0.02) and PB (0.01, +∞) , these three sections were used instead of the interval of the output value 0, 1 and 2 of the original flux double hysteresis controller. Similarly, torque error ET is divided into four fuzzy intervals referring to Fig.3, NB (-∞, -1) , NS (-2, 0) , ZO (-1, 1) and PB (1, +∞) , these four sections respectively replace the original torque double hysteresis controller output value which is - 2, - 1, 0, and 1. The stator flux angle θS is divided into 12 sections, as shown in Fig.6.

Fuzzy module output is space voltage vector, (0, 1, 2, 3, 4, 5, 6), corresponding to the choice of seven voltage vectors u0~u6. Considering control rules and module output, the point plot is selected as the 181, and the rule of

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Communications in Control Science and Engineering (CCSE) Volume 3, 2015

defuzzification is selected as the average maximum membership method (Mom), which uses the data with maximum degree of membership value as a result, to make sure that all the output value can be corresponding to the switching voltage vector.

FIG.6 FUZZIFICATION OF THE STATOR FLUX ANGLE

Design of Fuzzy Rules Fuzzy controller’s inference type is ‘Mamdani’, with ‘And Method’ selected as ‘Min’, ‘Implication Method’ as ‘Min’, ‘Aggregation Method’ as ‘Max’, ‘Defuzzification Method’ as ‘Mom’.

Considering the input of ET, EF, and θS, 144 corresponding rules were designed, which have the rotation for angle variable. For all the odd angle area, the table of (-30°, 30°) is the example and the rules in the table of (0°, 60°) are the examples for all the even angle area as shown in Table 2.

TABLE 2 THE EXAMPLE OF FUZZY RULES

θS EF, ET PB ZO NB

PB U2 U2 U3

(-30°, 30°) ZO NS U1 U1 U0 U0 U0 U0

NB U6 U6 U5

PB U2 U2 U4

(0°, 60°) ZO NS U2 U1 U0 U0 U0 U0

NB U6 U6 U5

Simulation Experiment and Data Analysis In this paper, a simulation experiment is carried out on the Matlab/Simulink platform. And the application of Fuzzy Logic is used to construct the fuzzy double hysteresis controller’s module, which constitutes the TFPM DTC system with the self-design motor model and other modules. The connection model of the fuzzy double hysteresis module is shown in Fig.7.

FIG.7 FUZZY DOUBLE HYSTERESIS MODULE

The parameters of the simulation experiment are: p = 12, the rated speed n = 1500r/min, the motor winding resistance Rs = 1.89Ω, rotary inertia J = 0.0267kg·m2, direct axis inductance Ld = 44.5667mH, quadrature axis inductance Lq = 46.4333mH, control period is 50μs, simulation step is 2μs.

Simulations are carried out on the software platform after building the traditional DTC system model, the double hysteresis control DTC system model (D-DTC) and the fuzzy double hysteresis control DTC model (FD-DTC) of

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TFPM. The torque ripple curves of these three systems are obtained as shown in Fig.8. The reduction of double hysteresis system’s torque ripple is significantly improved on the mean value and the amplitude value compared with the traditional one. And the fuzzy double hysteresis system is the best one.

The speed response curve of the double six-phase TFPM is analyzed, which is shown in Fig. 9. The motor will be given a load torque at the 0.4 second. It is known that the response curve of fuzzy double hysteresis control is superior to the traditional DTC system in dynamic performance.

80 FD-DTC DTC D-DTC

60

40

20

0

-20

-40 0.063

0.064

0.065

0.066

0.067

0.068

0.069

0.071

0.07

0.072

0.073

FIG.8 TORQUE RESPONSE CURVE 50 DTC FD-DTC 45

40

35

30

25

0.2

0.25

0.3

0.35

0.4

0.45

0.5

FIG.9 SPEED RESPONSE CURVE

Conclusion Starting from the analysis of the mathematical model of new type double six-phase TFPM, the theory that low speed torque ripple of DTC system can be reduced by zero vector is applied to the design of double hysteresis control, developing a new control system with fuzzy logic. Simulation experiments are carried out on the simulation platform. According to the experimental data, the fuzzy double hysteresis DTC system can reduce the torque ripple and make TFPM run more stably, improving its dynamic performance with strong robustness.

Therefore, the research of this paper has some theoretical significance and application value on solving the problem of TFPM’s low speed torque ripple and dynamic performance.

ACKNOWLEDGEMENT

The research is supported by National Natural Science Foundation of China (51105316), Natural Science Foundation of Shaanxi Province, China (2014JM7280) and fundamental research project of Northwestern

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Polytechnical University (JCY20130118).

REFERENCES

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Xiaoqing Yuan was born in Queshan, Henan province, China on January 1, 1979. He receives his Bachelor’s degree in mechanical design, manufacturing and automation, Master degree in electrical theory and new technology, Doctor degree in mechanical engineering at the school of mechanical engineering, Northwestern Polytechnical University in Xi’an, China in 2001, 2004, 2010.

He currently works as an associate professor at school of mechanical engineering, Northwestern Polytechnical University since 2004. His interests are new motor design and fault dection and diagnosis.

Zongyang Yu was born in Langfang, Hebei province, China on March 27, 1991. He receives his Bachelor’s degree in mechanical design, manufacturing and automation at the school of mechanical engineering, Northwestern Polytechnical University in Xi’an, China in 2013, he currently is a graduate student whose interest is new motor control at Northwestern Polytechnical University.

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