倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

奨励金№1492

マルチモーター電気自動車のグローカル（グローバル／ローカル）
エネルギー管理グエン
東京大学

ビン特任助教ミン

Glocal (Global/Local) Energy Management forMulti-motor Electric Vehicles
Nguyen Binh Minh,
The University of Tokyo, Assistant Professor

本研究は、マルチモーター型の電気自動車を想定し、グローバルなエネルギー最小化とローカルなトラクション制御を同時に満たすために、グローバルエネルギーマネジメントのための新しいフレームワークを提案する。
電気自動車をマルチエージェントシステムとして扱い、階層分散制御構成を設計する。受動性制御と外乱オブザー
バの実用的な手法を用いて、制御性能を向上させ、システム設計への負担を軽減する。提案するフレームワークの有効性は、いくつかの電気自動車プロトタイプによって評価が行われた。
Considering the multi-motor electric vehicles, this study is to propose an energy management framework to tosimultaneously achieve the global objective of minimizing energy consumption, and the local objective of improving
the safe traction at each local driving wheel. To this end, this study treats the electric vehicles as multi-agent systems
and establish the hierarchically decentralized control configuration. The practical approaches of passivity control anddisturbance observer are utilized to improve the performance while reducing the design burden. The effectivenessof the framework has evaluated using several electric vehicle prototypes.

1．研究内容surfaces.

1.1. Research achievement

Second, due to the nonlinearity and complexity

1.1.1. Problem statementof vehicle dynamics, a practical approach to system

An electric vehicle (EV) is a system thatstabilization is still a challenge. Although someexchanges the energy between the sources and thestability analysis methods were proposed, theymotors. In recent years, both sides have beenrequire the linearization of the vehicle dynamics,

developed as multi-agent system, which

and the stability condition relies on the time-encouraged the study on energy management

varying torque distribution ratios. To alleviate thesystem (EMSs). Focusing on the EMS of the motor

computational burden, this study aims to seek aside, we recognized several unsolved issues.

design condition that is free from the torqueFirst, almost the exiting methods do not have thedistribution ratios and the linearization process.

capability of wheel slip prevention. The wheel-slip

Third, it is necessar y to formulate the motor

phenomenon results in significant energy loss,

input power as a function of both torqueespecially when the EV operates on the low frictiondistribution ratios and motor flux currents. This

倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

objective function has not been considered bylayer, the aggregated motor speed is controlled byalmost all the existing methods.

a disturbance obser ver (DOB) based controller.
Based on passivity theory, a design procedure that

1.1.2. Summary of the proposal

sufficiently guarantees L2 stability of the overall

To deal with the aforementioned issues, thisstudy focuses on the multi-motor EV prototype inwhich each wheel is driven by a permanent magnet

system is established.
The main contributions of this study can besummarized as follows (see [1], [2]):synchronous motor (PMSM) (Fig. 1). A double-(i) This study presents a new configuration forlayer EMS is proposed to minimize energy

combining EMS with anti-slip control. The

consumption and guarantees safe longitudinal

proposed configuration has only one DOB-based

motion. The system has the hierarchicallycontroller that controls the aggregated motor

decentralized configuration (Fig. 2). The inner-layer

speed. Thanks to this configuration, the DOB

distributes the torques and flux currents bycontrol signal does not inter vene the energy

minimizing the motor input power. The inner-layer

optimization problem. Hence, energy optimization

also provides an aggregated speed of the motors

and slip prevention algorithms can be designed

using the torque distribution ratios. In the outer-independently.
(ii) This study presents a convenient andpractical approach to stabilizing the overall system.
Notably, the stability condition does not rely on
torque distribution ratios, which are time-varying
variables used to minimize the motor input power.
Furthermore, there is no need to linearize the EVdynamics.
(iii) This study formulates the summation ofmotor output powers with copper losses and ironFig. 1. Model of the multi-motor EV.

losses as a function of torque distribution ratios
Outer - layerTall

 rCw ( s )Speed Controllerslip control in the outer-layer.

OPI k i 

TakT

ωmEV

diag Gi1k†aQ( s)1.1.3. Main resultThis study shows that, although the EV systemGVMTdk i d ,idiag Gi1 m

cost function allows instantaneous efficiency
optimization in the inner-layer, together with anti-

Inner - layerand motor flux-current. The minimization of thisPn1 ( s )DOBFig. 2. Block diagram of the glocal energy manage­
ment system.

in Fig. 1 (with N motors) is a nonlinear complex
system, it possesses an important property: thepassivity from the motor torque to the motor
speed. Consequently, we show that the following
design procedure sufficiently guarantees the L2

倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

stability of the EMS in Fig. 2.
Design procedure of the double-layer EMS:
Stage 1-Inner-layer: Design the algorithm tominimize the summation of the input power Pm,iwith the copper loss Pcu,i and iron loss Pfe,i.
NNmin   Pm,i  Pcu,i  P fe ,i  s.t. ki 1, 0  ki  1

ki ,I od ,i  i 1 i 1

where {ki} is the torque distribution ratio and Iod,iis the motor flux current.
Stage 2-Outer-layer: Select the transfer functions
Pn(s), Q(s), and Cw(s) such that:Fig. 3. Three-wheel electric vehicle.

F(s) is stable; Ceql(s) is passive; Cw(s) and Cequ(s)are output strictly passive

four periods in which the road friction changes

from a high value to an exceptionally low value.
F( s )Q( s )1, Cequ( s ) F( s )Cw( s ), F( s )Pn( s )s ) distribution strategies are evaluated (see1The
 Q(fourF( s )Q( s )1Table 1). The strategy S#-A (# = {1, 2, 4}) maintains
, Cequ( s ) F( s )Cw( s ), F( s )Pn( s )
1  Q( s )the motor flux current at zero value. The strategy
where Ceql ( s )In [1], we showed that the optimal values of theS#-B (# = {1, 2, 4}) optimizes the motor flux current

torque distribution ratios and the motor flux

by the method proposed by Morimoto et al. [*],

currents can be calculated analytically. Thisand the strategy S3 utilizes the proposed algorithm.

reduces the computational burden and enable real-By maintaining zero flux-currents, the energy

time implementation of the proposed EMS.

consumptions of the vehicle with S1-A, S2-A, andS4-A are 1193, 1165, and 1186 (Wh), respectively.

1.1.4. Evaluation of the proposal

By updating the flux-currents to minimize theTo demonstrate the effectiveness of the double-power loss, the energy consumption of the vehicle

layer EMS, this study used the 3-wheel-EV shownwith S1-B, S2-B, and S3-B are 1018, 987.3, andin Fig. 3. This EV is driven by a 13 kW PMSM

996.9 (Wh), respectively. By simultaneously

connected to the rear wheel through 2 pulleys anddistributing the torques and flux-currents tobelt. Two 4 kW axial PMSMs are directly connected

minimize the input power, S3 is the best in term of

to the front wheels.

energy consumption. Utilizing S3, the vehicle

Various tests were conducted to evaluate theconsumed only 969.6 (Wh). In comparison with theproposed method. For instance, the New European

worst strategy of S1-A, energy consumption isDriving Cycle (NEDC) test was used to analyze thereduced 18.7％ by S3. The battery state of charges

per formance of the double-layer EMS with(SOCs) in accordance with the aforementioned

different torque and flux-current distribution

strategies are illustrated in Fig. 4(d). Transparently,strategies (Fig. 4). The NEDCʼs speed pattern andthe SOC curves of S1-A, S2-A and S3-A are always

the change of road friction are shown in Figs. 4(a)in the lower positions in comparison with the SOCand (b), respectively. During the NEDC, there are

curves of S1-B, S2-B, and S4-B. Until the end of the倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

Fig. 4. Comparison of different torque and flux-current distribution strategies.

倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

Table 1. Distribution strategies for comparison.
Strategy S1Almost front drive

Strategy S2
Equal torque distribution

S1-A

S1-B

S2-A

S2-B

k1,2 = 0.45
k3 = 0.05
Id,i = 0k1,2 = 0.45
k3 = 0.05
Id,i = opt

k1,2 = 1/3
k3 = 1/3
Id,i = 0k1,2 = 1/3
k3 = 1/3
Id,i = opt

Strategy S3
The proposed OP (23){ki,Id,i} is obtained by theproposed optimization
algorithm.

Strategy S4
Almost rear drive
S4-A

S4-B

k1,2=0.05
k3 = 0.90
Id,i = 0

k1,2 = 0.05
k3 = 0.90
Id,i = opt

Fig. 5. Optimal torque distribution ratios and motor flux-currents given by strategy S3.

NEDC, the SOC curve of S3 always dominates thecomplete his thesis on［受動性理論に基づく電気highest position. These results prove the

自動車の運動制御とエネルギー最適制御の統合

ef fectiveness of the proposal. The optimal化］．He has obtained the knowledge on vehicle

distribution ratios and flux-currents obtained by S3dynamics, anti-slip control, passivity theory, and theare shown in Fig. 5.

energy model of the electric motor. He presented[*] S. Morimoto, Y. Tong, Y. Takeda, and T. Hirasa,“Loss Minimization Control of Permanent Magnet
Synchronous Motor Drives,” IEEE Transactions on
Industrial Electronics, Vol. 41, No. 5, pp. 511-517, 1994.

his results at several conferences, including the 第10 回計測自動制御学会制御部門マルチシンポジウ
ム [3].
1.2.2. Master student at the University of

1.2. Educational achievement
1.2.1. Master student at Toyota TechnologicalInstituteTokyoThe hierarchical decentralized control system inFig. 2 were utilized to the longitudinal motion

Based on this research project, we have advised

control in [1], [2], and [3]. Besides, we alsoa Master student to study and successfully

developed the lateral dynamics version and倉田奨励金研究報告書 第 52 集
2021 年度（第 53 回）助成

自然科学・工学－都市・交通：1 年助成

presented it at the 2023 IEEE International

respect to the nonlinearity and complexity of theConference on Mechatronics [4]. The outer-layer ismulti-motor EV system, data-driven, fuzzy logic andto control the yaw-rate, and the inner-layer is tointelligent control algorithms can also becontrol the wheel driving force via wheel speed

considered in the double-layer EMS framework. Wecontrol. We are considering the energy

are also looking for the practical applications of theoptimization via driving force distribution in the

proposed framework by collaborating with thefiscal year 2023.

industrial circles.

1.2.3. PhD student at University of Sherbrooke

2．発表（研究成果の発表）

Besides the multi-motor EV prototypes, we also

2.1. Research achievement

considered the EV handled by multi-steering[1] B. -M. Nguyen, J. P. F. Trovão, and M. C. Ta,system. The idea of lateral force distribution and“Double-Layer Energy Management for Multi-control via steering mechanism was presented at

Motor Electric Vehicles,” IEEE Transactions on

the 2022 IEEE Vehicle Power and Propulsion

Vehicular Technology, doi: 10.1109/TVT.2023.

Conference [5].

3244808 (2023).
[2] M. C. Ta, A.-T. Nguyen, B.-M. Nguyen, P.

1.3. Conclusions and future works

Messier, and J. P. F. Trovao, “Four-wheel

This study proposes a double-layer EMS, which

Independently Driven Formula: Experimental EV

can effectively utilize the electric energy byfor Motion Control Studies,” 2022 IEEE Energy

preventing the wheel slip and optimally distributing

Conversion Congress and Exposition (2022).

both the torque commands and the flux currents ofthe motors. Using a three-wheel vehicle model, we

2.2. Educational achievement

published the main finding of this study on the[3] 長谷川 大地、B.-M. Nguyen、川西 通裕、成IEEE Transactions on Vehicular Technology [1].

清 辰生：受動性理論に基づく電気自動車の運動制

The idea of hierarchical decentralized control with

御とエネルギー最適制御の統合化、第 10 回計測自energy optimization has also been extended to the動制御学会制御部門マルチシンポジウ（2023）.

four-wheel independent driven formula developed[4] T. Ueno, B.-M. Nguyen, and H. Fujimoto,at University of Sherbrooke [2].

“Direct Yaw Moment Control for Electric Vehicles

Three students have been supported partially bywith Variable Rate-Slip-Ratio-Limiter Based Driving

this study to conduct their own research. We also

Force Control,” IEEE International Conference onorganized several events to share the idea of thisMechatronics (2023).

study to the research circles. The most successful[5] A.-T. Nguyen, B.-M. Nguyen, T. Vo-Duy, and M.

event was the Special Session on “AdvancedC. Ta, “Steering Vector Control for Lateral ForceControl Technologies for Multi-Motor Multi-Source

Distribution of Electric Vehicles,” IEEE Vehicle

Vehicles” at the 2022 IEEE Vehicle Power andPower and Propulsion Conference (2022).

Propulsion Conference.
In the future, we will examine the EMS for
considering both motor side and source side. With