In this paper, a simulation model for 7phase BLDC motor drives for an Autonomous Underwater Vehicles (AUV) is proposed. A 7phase BLDC motor is designed and the electrical characteristics are analyzed using FEA program and the power electronics drives for the 7phase BLDC motor are theoretically analyzed and the actual implementation has been accomplished using Matlab Simulink. PI controller and fuzzy controller are compared for verifying the validity of the proposed model and the informative results are described in detail. Especially A fuzzy controller is used to characterize 7phase BLDC motor, drive systems under normal and fault operating conditions.
1. Introduction
The electric motor is equipped into an Autonomous Underwater Vehicle (AUV) as the torpedo propulsion system and it requires high power for short time and high power density with respect of size and weight due to onboard spatial limitation. Among of various types of electric motors, brushless dc (BLDC) motors is regarded as a good candidate for the propulsion system of an AUV due to their high efficiency, high power density, high torque, easy to control, and lower maintenance.
Until now, DC motors have been mainly adopted and tested for this purpose. However, with the requirement of high fault tolerance for military applications, in recent multiphase BLDC motors have been seriously investigated and, a German newest torpedo adopted 7phase BLDC motor producing 300kW power
[1]
.
A BLDC motor with higher number of phase has several advantages, compared with the conventional 3phase one such that it can reduce torque ripple and stator current per phase without increasing voltage and also can increase torqueperampere ratio for the same volume, reliability, and power density. In special, for the military application, a motor can be still operated under the malfunction, such as failure condition of one of motor phases, so that it can insure survivability for the system.
Fig. 1
shows the prototype of 7phase BLDC motor for a smallsized AUV. At the initial stage of development of the 7phase BLDC motor drive system, one needs a strong simulation program in order to examine the overall electrical and mechanical characteristics of 7phase BLDC motors for AUV and to test the control algorithms for the drive systems. Specially, the behavior of military machine in health state and under fault condition must be considered in the initial design state of the machine including the each component.
Prototype of 7phase BLDC motor for a smallsized AUV
However, one can only refer literatures in the area of 3 phase BLDC motor drives and unfortunately has some trouble to get enough literatures for 7phase BLDC motor drives
[2

4]
. Therefore, the aim of this modeling and analysis is to foresee the electrical and mechanical characteristics of 7phase BLDC motors for AUV and the change of motor performance due to the different faults of the motor drive.
Also different control strategies have been considered for improving the performance of BLDC motors for application in AUV. The PI, the PID controller and the hysteresis current control have been the most widely used control techniques for controlling a BLDC motor. However, the main drawback is the linear nature of classical PID controller that lacks robustness when facing an operation scenario, where parameter variations and disturbances are added to the nominal model
[5]
.
In order to obtain an acceptable dynamic response over the whole operation range, Fuzzy control drive system is attempted in this paper.
2. General Description of 7Phase BLDC Motor Drives
The developed 7phase BLDC motor has 4 poles and 28 slots. The developed motor has a maximum torque 0.31Nm, maximum speed 10,000rpm, R=0.474Ω, L=0.4mH, and input operating voltage 200Vdc
The BLDC motor has a permanentmagnet rotor and the stator windings are wounded such that the back electromotive force is trapezoidal. The trapezoidal back EMF implies that the mutual inductance between the stator and rotor is nonsinusoidal. Therefore, no particular advantage exists in transforming the machine equations into the wellknown twoaxis equations, which is done in the case of machines with sinusoidal back EMF’s
[6]
.
The 7phase currents are controlled to take a type of quasisquare waveform in order to synchronize with the trapezoidal back EMF to produce the constant torque. This task is performed by the speed/torque control loop in cooperation with the rotor position sensor and current controller as shown in
Fig. 2
.
Control block diagram for 7phase BLDC motor drives
3. Development of Simulation Model
In this section, the modeling process is explained and the actual implementation using Matlab Simulink is described.
Fig. 3
shows the overall block diagram of the developed model for 7phase BLDC motor drives. As shown in
Fig. 3
, the proposed model consists of five functional blocks: back EMF block, phase current block, current control block, PWM inverter block and speed/torque control block
[2]
.
Overall block diagram of the developed model for 7phase BLDC motor drives
 3.1 Back EMF block
The back EMF is a function of rotor position and has the amplitude
E
=
K_{e}·ω_{r}
(
K_{e}
is the back EMF constant and
ω_{r}
is rotor speed). In this paper the modeling of the back EMF is performed under the assumption that all seven phases have identical back EMF waveforms. Based on the rotor position, the numerical expression of back EMF on the case of the phase A can be obtained as Eq. (1) and it is implemented as shown in
Fig. 4
. Also, the actual back EMF waveform is obtained from the FEA data to examine the actual torque ripple and the detailed information will be explained in “Section 4. Simulation Results.”
Implementation of back EMF according to rotor positions
 3.2 Phase current and PWM inverter block
The idea is to understand how 7phase sources are connected under the assumption of floating neutral point.
Fig. 5
shows the proposed electrical representation of a 7phase BLDC motor drive.
Electrical representation of 7phase BLDC motor drives.
The circuit equation of the 7phase BLDC motor drive including neutral voltage can be represented as
where,
phase voltages [
V
]=[
ν_{ao} ν_{bo} ν_{co} ν_{do} ν_{eo} ν_{fo} ν_{go}
]
^{T}
,
line resistance
R = R_{a} = R_{b} = R_{c} = R_{d} = R_{e} = R_{f} = R_{g},
winding resistances
phase currents [
I
]=[
i_{a} i_{b} i_{c} i_{d} i_{e} i_{f} i_{g}
]
^{T}
,
inductance of phase
i
related to phase
j
back EMF [E]=[
e_{a} e_{b} e_{c} e_{d} e_{e} e_{f} e_{g}
]
^{T}
,
neutral voltages [
v_{no}
]=[ν
_{no}
ν
_{no}
ν
_{no}
ν
_{no}
ν
_{no}
ν
_{no}
ν
_{no}
]
^{T}
.
For a balanced wyeconnected BLDC motor, the 7phase currents always meet the following equation:
Therefore, the neutral voltage
ν_{no}
can be simplified as
Substituting (4) into (2) gives
where,
Each selfinductance and mutual inductance can be defined as follows:
Therefore, Eq. (5) can be rewritten as Eq. (10).
where,
Each phase voltages can be derived as Eq. (11) using switching function SF
_{1_a,b,c,d,e,f,g}
obtained from current control block. Based on the derived switching function, one can generate pole voltages (V
_{ao}
, V
_{bo}
, V
_{co}
, V
_{do}
, V
_{eo}
, V
_{fo}
, V
_{go}
) by multiplying the half of dclink voltage and phase voltages and linetoline voltage can be easily obtained as following equations. The voltage generation process can be expressed as Eqs. (11) and (12) and it can be implemented as shown in
Fig. 6
.
Implementation of phase voltages
As noted from Eqs. (11) and (12), it is important to select the proper pattern for switching functions for the entire simulation program according to the pwm algorithms. In case of Sinusoidal PWM (SPWM), the switching functions can be obtained by comparing triangular and sinusoidal control signals. In case of BLDC motor drives, the switching functions can be obtained from hysteresis current control algorithm, which will be explained in the next Section.
 3.3 Current control block
The current control strategies of the BLDC motor drive are typically grouped into pulse with modulation technique and hysteresis technique. In this paper, bipolar hysteresis current control is used for obtaining the fast dynamic response during the transient states.
In order to express the exact phenomena of current dynamics, the phase current needs to be modeled into four modes as show in
Fig. 7
, such as
I_{a}
<
lower
lim
it
(
LL
) (mode [1]),
I_{a}
>
upper
lim
it
(
UL
) (mode [2]),
LL
<
I_{a}
<
UL
and
> 0 (mode [3]), and
LL
<
I_{a}
<
UL
and
< 0 (mode [4]).
Detailed current modes to model its dynamics
In Matlab Simulink, in order to express modes [3] and [4], the memory block is used along with rotor position (
θ_{r}
) as shown in
Fig. 8
and finally the entire current dynamics can be realized using Eq. (13).
Hysteresis current control block for phase A
In this model the switching function SF
_{1}
is used to generate the inverter phase voltages. Therefore, each phase current can be obtained by
where,
[
SF_{1}
]=[
SF_{1_a}
SF_{1_b}
SF_{1_c}
SF_{1_d}
SF_{1_e}
SF_{1_f}
SF_{1_g}
]
^{T}
 3.4 Speed/Torque control block
The electromagnetic torque is expressed as
And the equation of motion is expressed as
where,
T_{L}
is load torque,
J
is inertia, and
B
is damping.
Neglecting the damping factor, speed and torque characteristics of the BLDC motor can be explained as
Using PI controller, the speed and torque control can be implemented as shown in
Fig. 9
.
Speed and torque control block for 7phase BLDC motor drives
4. Simulation Result
A 7phase BLDC motor drive with proposed model has been simulated with the following specifications: 7phase, 4 poles, rated torque of 0.15Nm, rated speed of 10,000 rpm, V
_{dc}
=200V, R=0.474Ω, L=394uH, K
_{t}
=0.2226, J = 0.00132 kgm
^{2}
, M
_{1}
= 21.87uH, M
_{2}
= 130uH, M
_{3}
= 78.73uH.
Fig. 10
shows the back EMF computed according to the previously discussed procedure using Eq. (1) at 3,500 rpm. The rotor position is varied from 0 to 2π per electric cycle 2π /7 and the back EMF has amplitude of 19.5V.
Back EMF waveforms at 3,500 rpm
Figs. 11
and
12
show the generated phase current, dynamic responses of speed and current command waveforms by the PI controller at 3,500 rpm. The phase current has amplitude of 1.8A and is well synchronized with the trapezoidal back EMF. Also to demonstrate the speed dynamic response of the PI controller algorithm, the speed response characteristic is shown in
Fig. 2
along with the reference speed change.
Phase current waveforms by a PI controller (3,500 [rpm]).
Speed response and current command by the PI controller (3,500[rpm]).
Figs. 13
and
14
show the generated phase current, dynamic responses of speed and current command waveforms by the fuzzy controller at 3,500 rpm. The phase current has amplitude of 1.8A and is well synchronized with the trapezoidal back EMF. Also to demonstrate the speed dynamic response of the Fuzzy controller algorithm, the speed response characteristic is shown in
Fig.14
along with the reference speed change. In comparison with PI controller, the speed response characteristic of Fuzzy controller is shown the no difference.
Phase current waveforms by a Fuzzy controller (3,500[rpm]).
Speed response and current command by the Fuzzy controller (3,500[rpm]).
In order to examine the feasibility on phase fault tolerance characteristics of the developed simulation program, one of phase is forcibly shorted, phases A and B phase are opened at the same time and the overall characteristics are examined and the results of overall characteristics are examined as shown
Fig. 15
and
Fig. 16
.
Current command waveforms at 3,500[rpm] in case of phase fault (opened) conditions.
Speed response waveforms at 3,500[rpm] in case of phase fault (opened) conditions.
After the fault occurrence one notice the increase of the average value of the healthy phasecurrent, due to the reaction of the superimposed speed loop; the appearance of fluctuations in the rotor speed depends to the incoming torque ripple. Nevertheless the operation is maintained at preset speed and load conditions.
Comparing with the fault condition, as one can expect, the fault condition of phases A and B makes the drive system be deteriorated with respect of speed response in special.
From the simulation results of
Figs. 15
to
16
, it is certified that the developed simulation program can effectively examine the dynamic characteristics at fault condition as well as at healthy condition of 7phase BLDC motor drives for AUV.
5. Experimental Result
A schematic diagram of the proposed drive system of 7 phase BLDC motor, which corresponds to the experimental system is designed, developed and presented in
Fig. 15
.
The experimental setup consists of four major components.
They are IGBT power inverter, 7phase BLDC motor with loading arrangement, speed, phase voltage and phase current sensing circuits, and TMS320VC33150 DSP. The BLDC motor is an electronically commutated motor.
The builtin hall sensors generate seven signals according to the rotor position. These signals are decoded to identify the rotor position and energize the appropriate windings by switching the appropriate switches in the IGBT power inverter. Experimental results of 7phase BLDC motor speed control with Fuzzy control will be compared with the results of BLDC motor speed control only with PI control.
Block diagram of experimental system.
The experimental results obtained for Fuzzy controllerbased BLDC motor drive under different operating conditions such as step change in reference speed, and with load disturbance are shown in
Fig. 19
,
Figs. 21
and
Fig. 23
in comparison with PI controller.
Current waveforms of phase A and B by the Fuzzy controller. (2ms, 2A/div., 3,500rpm)
Speed response by the Fuzzy controller with load at threestep speeds. (5s, 1A/div.)
Speed response by the Fuzzy controller with no load at increasing and decreasing speeds. (5s/div., 0→2,500→5,000→2,500→0 rpm)
Figs. 18

19
show the phase current waveforms when the 7phase motor operated at the steady state mode by each controller (Fuzzy, PI) respectively.
Current waveforms of phase A and B by the PI controller. (2ms, 2A/div., 3,500rpm)
In another test, step changing has exerted in motor command speed as shown in
Figs. 20
~
21
. Speed command changing has been in case: increasing speed command 3500, 7,000, 10,000rpm respectively with speed controller. In step increasing speed, first motor command speed is 3,500rpm. Reference speed is changed to 7,000 rpm and another increasing speed, primary motor speed is 10,000 rpm which is increased to 10,000 rpm. Rising time in each case(PI controller, Fuzzy controller) is nearly 2.5~3sec. But there are some overshoot and steady state error in responses at the sudden change speed mode with PI controller. Also we know that there is no overshoot in response at 10,000rpm with Fuzzy controller and steady state error is dispensable as shown in
Fig. 21
. Therefore we have achieved the high speed control of BLDC motor to yield excellent performance with Fuzzy controller.
Speed response by the PI controller with load at threestep speed. (5s, 1A/div.)
Also to demonstrate the speed dynamic response with no load, speed response waveforms at increasing and decreasing speed reference by each controller (Fuzzy, PI) respectively as shown in
Figs. 22

23
. When speed reference 0→2,500→5,000rpm changed, 7phase BLDC motor operated at the steady state mode by each controller (Fuzzy, PI).
Speed response by the PI controller with no load at increasing and decreasing speeds. (5s/div., 0 →2,500→5,000→2,500→0 rpm)
But in case of using PI controller, it is found that speed response characteristics are unstable in comparison Fuzzy controller at the 2500rpm mode, 5,000rpm mode. On the other hand when speed reference 5,000→ 2,500→0rpm changed, it is noted that speed response characteristics of 7phase BLDC motor by each controller (Fuzzy, PI) are same results.
The variation of load current and speed response due to change in load applied to the 7phase BLDC motor is shown in
Fig. 24

27
. Firstly to examine the performance of the 7phase BLDC motor with each controller algorithm, it is loaded, the rated torque demand in this case is 0.2Nm and the motor speed is 15,000 rpm at the
Fig. 24
~
25
. It is certified that Fuzzy controller algorithm is successfully controlled with a small speed ripple compared with PI controller when load applied and speed changed
Speed response and load application test of the PI controller (10s/div., 15,000rpm, 0.2Nm)
Speed response and load application test of the Fuzzy controller (10s/div., 15,000rpm, 0.2Nm)
Load application test of the PI controller (1s, 1V, 2A/div., 7,000rpm, 0.1Nm)
Load application test of the Fuzzy controller. (1s, 1V, 2A/div., 7,000rpm, 0.1Nm)
Next, the torque developed by the 7phase BLDC motor at 7,000rpm is 0.1Nm load applied to 7phase BLDC motor at the
Fig. 26
~
27
. It is found that speed response of PI controller is unstable when there is a sudden increase in load. But speed response of Fuzzy controller is very stable when increase in load.
The experimental results clearly show that Fuzzy controller based 7phase BLDC motor drive can provide an improved speed response with consistently when the system is subjected to load disturbance and step change in reference speed.
5. Conclusion
The propulsion motor for the autonomous underwater vehicle requires high torque, small size, and fault tolerance. Consequently, a multiphase permanent magnet brushless motor fits AUV electric propulsions.
In this paper, a functional simulation model for the 7 phase BLDC motor drive is studied and the actual implementation of the model is proposed. The performance and feasibilities have been examined by the simulation and experimental verification and it is expected that the proposed simulation model can be utilized for the development of AUV systems. Also since the fuzzy control system is easy to design and implement, effective in dealing with the uncertainties and parameter variations, and has better overall performance, fuzzy controllerbased 7phase BLDC motor drive system may be preferred over PI controllerbased 7phase BLDC motor drive for automation, robotics, position and velocity control systems, and industrial control applications.
BIO
SangHoon Song was born in Korea, in 1972. He received the B.S degree in Electrical Engineering from the Yeungnam Univ. in1998, and the M.S from the Sungkyunkwan Univ. Korea, in 2000. He currently studies for his Ph. D degree in Sungkyunkwan Univ. and has researched for the Korea Testing Laboratory from 2000.
YongHo Yoon received the M.S. and Ph.D. degrees in Mechatronics Engineering from Sungkyunkwan University, Korea, in 2002, 2007, respectively. From 2007 to 2011, he was with Technical Research Institute of Samsung Thales Company, Korea, as a senior researcher. Since 2011, he has been with Korea Testing Laboratory (KTL), where he is currently a senior researcher in the New & Renewable Energy Assessment Center, Machinery & System Division. His research interests are in the areas of analysis and control of SRM and BLDC motor and certification of renewable of photovoltaic Inverter.
ByoungKuk Lee (S’97M’02SM’04) received the B.S. and M.S. degrees from Hanyang University, Seoul, Korea, in 1994 and 1996, respectively, and the Ph.D. degree from Texas A&M University, College Station, TX, USA, in 2001, all in electrical engineering. From 2003 to 2005, he was a Senior Researcher at Power Electronics Group, Korea Electrotechnology Research Institute, Changwon, Korea. He joined the School of Information and Communication Engineering, Sungkyunkwan University, Suwon, Korea, in 2006. His research interests include charger for electric vehicles, hybrid renewable energy systems, dc distribution systems for home appliances, power conditioning systems for fuel cells and photovoltaic, modeling and simulation, and power electronics. Dr. Lee is a recipient of the Outstanding Scientists of the 21st Century from IBC and listed on 2008 Ed. of Who’s Who in America. He is an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and the IEEE TRANSACTIONS ON POWERELECTRONICS. He was the General Chair for the IEEE Vehicular Power and Propulsion Conference, in 2012.
ChungYuen Won was born in Korea, in 1955. He received the B.S degree in electrical engineering from the Sungkyunkwan Univ. Korea, in1978. And he received the M.S and Ph. D degree in electrical engineering from the Seoul National University, Korea, in 1980 and 1987, respectively. During 1990~1991 he had been in visiting professor, Department of electrical engineering, University of Tennessee. Since 1988 he has been with the faculty of Sungkyunkwan University, where he is a professor of School of Information and Communication Engineering. His research interests include dcdc converter for Fuel Cell, electromagnetic modeling and prediction for motor drive, control systems for rail power delivery applications areas of stability of ac machines, advanced control of electrical machines, and power electronics.
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