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On-Line Controller for Fuel Consumption on Spilt-Type Hybrid Electric Vehicle*
Preprints, 8th IFAC International Symposium on Preprints, 8th IFAC International on Advances in Automotive Control Symposium Preprints, 8th IFAC International International Symposium on on Preprints, 8th IFAC Symposium Advances in2016. Automotive Control June 19-23, Norrköping, Sweden Available online at www.sciencedirect.com Advances Automotive Control Advances in2016. Automotive Control June 19-23,in Norrköping, Sweden June 19-23, 19-23, 2016. 2016. Norrköping, Norrköping, Sweden Sweden June
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On-Line Controller for On-Line Controller for On-Line Controller for on Spilt-Type Hybrid on Spilt-Type Hybrid on Spilt-Type Hybrid ∗
Fuel Consumption Fuel Consumption Fuel Consumption Electric Vehicle Electric Vehicle Electric Vehicle ∗∗
Hiroki Koguchi ∗ Koichi Hidaka ∗∗ Hiroki Koguchi ∗ Koichi Hidaka ∗∗ Hiroki Koguchi ∗ Koichi Koichi Hidaka Hidaka ∗∗ Hiroki Koguchi ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗∗ ∗ Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗∗ NIDEC Corporation, Kawasaki, Kanagawa, Japan. TokyoELESYS Denki University, Adachi, Tokyo, Japan, (e-mail: ∗∗ [email protected]) ∗∗ Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper proposes a controller used by an extremum seeking (ES) algorithm with Abstract: This paper proposes controller used vehicle by an extremum seeking (ES) algorithm with semi-optimal controller gains for a hybrid electric (HEV) system. The semi-optimization Abstract: This paper a used by seeking (ES) algorithm Abstract: This paper proposes proposes aaa controller controller used vehicle by an an extremum extremum seeking (ES) algorithm with with semi-optimal controller gains for hybrid electric (HEV) system. The semi-optimization gains connectcontroller at each gains output ofa sampleelectric controllers that are system. given byThe benchmark problem semi-optimal controller gains for a hybrid electric vehicle (HEV) system. The semi-optimization semi-optimal for hybrid vehicle (HEV) semi-optimization gains connect at each output of sample controllers that are given by benchmark problem in advance. These gainsoutput are decided according to thethat approximate on fuel economy gains connect at of controllers are by problem gains connect at each each of sample sample controllers that are given given convex by benchmark benchmark problem in advance. These gainsoutput are target decided according to the approximate convex on fuel economy ∗ function via each gains. The engine speed of EM1 controller, ω , is perturbed with the in advance. These gains are decided according to the approximate convex on fuel economy ∗ in advance. These gainsThe are target decided according to the approximate convex on fuel economy function via each gains. engine speed of EM1 controller, ω , is perturbed with the ∗ ES algorithm based on fuel economy and State of Charge (SOC). Furthermore, the proposed ∗ , is perturbed function via each gains. The target engine speed of EM1 controller, ω with function via each gains. Theeconomy target engine speedofofCharge EM1 controller, ω , is perturbed with the the ES algorithm based on fuel and State (SOC). Furthermore, the proposed algorithm switches depending SOCof restraining the decline of The ES algorithm based controller on fuel fuel economy economy andon State of for Charge (SOC).of Furthermore, theSOC. proposed ES algorithm based on and State Charge (SOC). Furthermore, the proposed algorithm switches controller depending on SOC for restraining of the decline of SOC. The sample controllers four units, and each unit controller controls driving of algorithm switches controller depending on for of SOC. algorithm switches have controller depending on SOC SOC for restraining restraining of the the decline decline of HEV. SOC. The sample controllers have four the units, andFor each unit controller controls drivingcontroller, HEV. The sample controllers can drive HEV. showing the validity of our proposed fuel have four units, and each unit controller controls the driving of HEV. sample controllers can havedrive four the units, andFor each unit controller controls the drivingcontroller, of HEV. The The HEV. showing the validity of our proposed fuel economies of the proposed controller and sample controller are compared by simulator for this sample controllers can drive the HEV. For showing the validity of our proposed controller, fuel sample controllers can drivecontroller the HEV.and Forsample showing the validity of our proposed controller, fuel economies of the proposed controller are compared by simulator for this benchmark. While the fuel controller economy achieved by controller the sampleare controller is by 41.44 mpg, the final economies of the proposed controller and sample controller are compared by simulator for this economies of the proposed and sample compared simulator for this benchmark. While the fuel economy achieved by the sample controller is 41.44 mpg, the final fuel economyWhile on the method is almost 59.29 mpg,controller and the is final SOC is 64.45 %. benchmark. the fuel achieved by sample 41.44 mpg, the benchmark. While theproposed fuel economy economy achieved by the the sample is 41.44 mpg, the final final fuel economy on the proposed method is improved almost 59.29 mpg,controller and thecompared final SOC is 64.45 %. The performance of fuel economy can be by almost 43 % to the sample fuel economy on the proposed method is almost 59.29 mpg, and the final SOC is 64.45 %. fuel economy on the proposed method is improved almost 59.29 mpg, and thecompared final SOC is 64.45 %. The performance of fuel economy can be by almost 43 % to the sample controller. The performance of fuel economy can be improved by almost 43 % compared to the sample The performance of fuel economy can be improved by almost 43 % compared to the sample controller. controller. controller. © 2016, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Hybrid electricFederation Vehicle control, Control system, Model-free Controller Design, Keywords: Hybrid electric Vehicle control, Control system, Model-free Controller Design, Extremum seeking electric algorithm, Splitcontrol, hybrid Control electric powertrain Keywords: Vehicle system, Keywords: Hybrid Vehicle system, Model-free Model-free Controller Controller Design, Design, Extremum Hybrid seeking electric algorithm, Splitcontrol, hybrid Control electric powertrain Extremum seeking algorithm, Split hybrid electric powertrain Extremum seeking algorithm, Split hybrid electric powertrain 1. INTRODUCTION The control task is referred to as energy management. The 1. INTRODUCTION The control task is referred to has as energy management.(e.g., The energy management problem been investigated. 1. INTRODUCTION The control task to as management. The 1. INTRODUCTION The control task is is referred referred to has as energy energy management.(e.g., The energy management problem been investigated. (2003), Dextreit (2014), Larsson (2014)). On the other The Hybrid electric vehicles (HEVs) are gaining mar- Lin energy management problem has been investigated. (e.g., energy management problemLarsson has been investigated. (e.g., Lin (2003), Dextreit (2014), (2014)). On the other The Hybrid electric vehicles (HEVs) are gaining marthe split configuration in the(2014)). commuter vehicles, ket and accelerating propelled by a mix of hand, Lin (2003), Dextreit (2014), Larsson Larsson (2014)). On the the other The popularity Hybrid electric electric vehicles (HEVs) (HEVs) are gaining gaining mar(2003), Dextreit (2014), On other The Hybrid vehicles are marhand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by abusiness mix of Lin e.g., Toyota’s Prius, is used. The split configuration has environmental concerns, rising fuel prices, and hand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by a mix of hand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by a mix of e.g., Toyota’s Prius, is used. The split configuration configuration and has environmental The concerns, rising fuel prices, anddegrees business the both features between the parallel opportunities. typical HEV has multiple of e.g., Toyota’s Prius, is used. The split configuration has environmental The concerns, rising fuel prices, anddegrees business e.g., Toyota’s Prius, is used. The split configuration configuration and has environmental concerns, rising fuel prices, and business the both features between the parallel opportunities. typical HEV has multiple of serial configuration, and the structures are complex. Thus, freedom for delivering wheel torque, unlike conventional the both features between the parallel configuration and opportunities. The typical HEV has multiple degrees of both features between the parallelare configuration and opportunities. The typical HEV has unlike multiple degrees of the serial configuration, and the structures complex. Thus, freedom for delivering wheel torque, conventional control system ofand the the energy management is important. vehicles. Thedelivering conventional have threeconventional powertrain the serial configuration, structures are complex. complex. Thus, freedom for for wheelHEVs torque, unlike conventional serial configuration, structures are Thus, freedom wheel torque, unlike the control system(2015)). ofand the the energy management is important. vehicles. Thedelivering conventional HEVs have three powertrain (See Overington The control systems for HEV configurations, known as series, parallel, and split (series the control system of the energy management is important. vehicles. The conventional HEVs have three powertrain the control system of the energy management is important. vehicles. The conventional HEVs have three powertrain Overington The control HEV known asInseries, parallel,type, and the splitinternal (series (See system have(2015)). been proposed. (e.g.,systems Musardofor -configurations, parallel), respectively. the parallel (See Overington The systems for HEV configurations, known as asInseries, series, parallel,type, and the splitinternal (series drive (See Overington (2015)). The control control systems for(2005), HEV configurations, known parallel, and split (series drive systemMura have(2015)). been proposed. (e.g., Musardo (2005), -combustion parallel), respectively. the parallel Kim (2015), (2015)), However, these systems are for engine (ICE) and the electric machine (EM) drive system have been proposed. (e.g., Musardo (2005), --combustion parallel), respectively. In the parallel type, the internal drive systemMura have (2015)), been proposed. (e.g., Musardo (2005), parallel), respectively. Inand the the parallel type, the internal Kim (2015), However, these systems are for engine (ICE) electric machine (EM) series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled to the drive shaft of the vehicle, Kim (2015), Mura (2015)), (2015)), However, these systems are are for combustion engine (ICE) to and the electric machine (EM) Kim (2015), Mura However, these systems for combustion engine (ICE) and the electric machine (EM) series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled the drive shaft of the vehicle, neers of Japan) and SICE (The Society of InstrumentEngiand and the wheel power is the sum of the individual power. series HEV. Therefore, JSAE (Society of Automotive are mechanically coupled to the drive shaft of the vehicle, series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled to the drive shaft of the vehicle, neers of Japan) and SICE (Thethree Society of Instrument and and the wheeltopology power iscan the reduce sum of drivetrain the individual power. Control Engineers) provided benchmark problems The parallel losses, and neers of and (The Society of and and the the wheeltopology power is iscan the reduce sum of of drivetrain the individual individual power. neers of Japan) Japan) and SICE SICE (Thethree Society of Instrument Instrument and and wheel power the sum the power. Control Engineers) provided benchmark problems The parallel losses, and in 2011, and the one of the benchmark problems is given lead to a lower average ICE operating efficiency. The parControl Engineers) provided three benchmark problems The parallel topology can reduce drivetrain losses, and Engineers) provided three benchmark problems The parallel topology can reduce drivetrain losses, and Control in 2011, and the one of the benchmark problems is given lead to a lower average ICE operating efficiency. The par“Fuel and economy optimization of the commuter allel structure ICE in 2011, and the one one of the the benchmark benchmark problems is isvehicle given lead to to lower limits average ICEoperating, operatinghowever. efficiency.The Theseries par- as in 2011, the of problems given lead aa lower average ICE operating efficiency. The paras “Fuel economy optimization of the(2012)). commuter vehicle allel structure limits ICE operating, however. The series using hybrid powertrain”. (See Yasui The hybrid powertrain is characterized by directly uncoupled between as “Fuel economy optimization of the commuter vehicle allel structure limits ICE operating, however. The series as “Fuel economy optimization of the commuter vehicle allel structure limits ICE operating, however. The series using hybrid powertrain”. (See Yasui (2012)). The hybrid powertrain is characterized by directly uncoupled between using the split the ICE and EM. This powertrain can operate the ICE powertrain using hybrid (See Yasui The hybrid powertrain is characterized characterized by directly directly uncoupled between hybridis powertrain”. (Seeconfiguration. Yasui (2012)). (2012)).The The control hybrid powertrain is by uncoupled between powertrain ispowertrain”. using the split configuration. The control the ICE and EM. This powertrain can operate the ICE using designs for the benchmark problem have been proposed, speed and torque regardless of the vehicle speed. Thus, powertrain is using the split configuration. The control the ICE and EM. This powertrain can operate the ICE is using the split configuration. The control the ICE and EM. regardless This powertrain can operate theThus, ICE powertrain designs for the benchmark problem have been proposed, speed and torque of the vehicle speed. are as modelproblem free types and model based the topology can operate theof optimal conditions designs for known the benchmark benchmark problem have been proposed, speed and torque torque regardless ofICE theat vehicle speed. Thus, which designs for the have been proposed, speed and regardless the speed. Thus, which are known as model free(2014)). types and model based the topology can operate thethe ICE atvehicle optimal conditions types. (e.g., Yu (2013), Ahmad Model-based conthat minimize emissions and combined loss of the ICE which are known as model free types and model the topology topology can operateand thethe ICE at optimal conditions which are known as model free(2014)). types and model based based the can operate the ICE at optimal conditions types. (e.g., Yu (2013), Ahmad Model-based conthat minimize emissions combined loss of the ICE trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large types. (e.g., Yu (2013), Ahmad (2014)). Model-based conthat minimize emissions and the combined loss of the ICE (e.g., Yufor(2013), Ahmad (2014)). Model-based conthat minimize emissions and the combined loss ofthe thelarge ICE types. trol is useful the energy management for HEV. The and generator. (See Egardt (2014)). However, present proposed model-based controllers have not be able size battery is needed. The split topology is a mixture trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large present proposed model-based controllers have not be able size battery is needed. The split topology is a mixture to obtain more than 25 km/Lcontrollers of the fuel economy yet. topology and the features of both topologies have. The present proposed model-based have not be able size battery is needed. The split topology is a mixture present proposed model-based controllers have not be able size battery isthe needed. Theofsplit is have. a mixture to obtain more than On 25 km/L of the fuelthe economy yet. topology and features bothtopology topologies The (e.g., Iyama (2015)). the other hand, model-free ICE, EM, and generator (GEN) are coupled with the to obtain more than 25 km/L of the fuel economy yet. topology and thegenerator features (GEN) of both both are topologies have. The to obtain more than On 25 km/L of the fuelthe economy yet. topology and the features of topologies have. The (e.g., Iyama (2015)). the other hand, model-free ICE, EM, and coupled with the control approaches are effective and useful for the energy planetary gear. The both EM and generator drive the (e.g., Iyama (2015)). On the other hand, the model-free ICE, EM, and generator (GEN) are coupled with Iyama (2015)). On the other hand, the model-free ICE, EM, gear. and generator (GEN) aregenerator coupled drive with the (e.g., control approaches are effective and useful for the energy planetary The both EM and controlare of effective the commuter vehicle. model vehicle. a strategy for agenerator control system to management control approaches are effective and useful useful for The the energy energy planetaryThere gear.needs The both both EM and and drive the the control approaches and for the planetary gear. The EM drive management control of weakness the commuter vehicle. The model vehicle. There needs a power strategy for agenerator control system to free controls have the on the changes of drivadjust between the two sources, the ICE and EM in management control of the commuter vehicle. The vehicle.between There needs needs strategy for aathe control system to management control of weakness the commuter vehicle. Theofmodel model vehicle. There aa power strategy for control system to free controls have the on the changes drivadjust the two sources, ICE and EM in ing conditions. The EV controller based ES algorithm, the parallel configuration, and the engine-generator unit free controls have the weakness on the changes of adjust between the two power sources, the ICE and EM in controls have weakness on based the changes of drivdrivadjust between the two power sources, the ICE and EM in free ing conditions. ThetheEV controller ES algorithm, the parallel configuration, and the engine-generator unit which is a model-free and on-line controller, has been and the electric storage system in theengine-generator series configuration. conditions. The controller based ES the parallel parallel configuration, and in thethe engine-generator unit ing ing conditions. The EV EVand controller based ES algorithm, algorithm, the configuration, and the unit which is a model-free on-line controller, has been and the electric storage system series configuration. described by Yasui (2012). However, Yasui (2012) does which is a abymodel-free model-free and However, on-line controller, controller, has been been and the electric storagebysystem system in the the series configuration. which is and on-line has and the electric storage in series configuration. This work is supported JSAE and IDAJ Co., Ltd., Japan. described Yasui (2012). Yasui (2012) does This work is supported by JSAE and IDAJ Co., Ltd., Japan. described by Yasui (2012). However, Yasui (2012) described by Yasui (2012). However, Yasui (2012) does does
This This work work is is supported supported by by JSAE JSAE and and IDAJ IDAJ Co., Co., Ltd., Ltd., Japan. Japan. Copyright © 2016 IFAC 252 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 252 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 252 Copyright © 2016 IFAC 252Control. 10.1016/j.ifacol.2016.08.037
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not investigate the fuel economy of the driving for a total time, but only was tested to the fuel economy for 1500 sec. Furthermore Yasui (2012) does not investigate the performance via the cost function of Fc and SOC. In this paper, the controller using ES with semi-optimization gains is proposed. Our proposed method joins the six gains in sample controllers that are given by benchmark problem in advance. The target engine speed of EM1 controller, ω ∗ , is perturbed with the ES algorithm based on fuel economy. Furthermore, the proposed algorithm switches controller depending on SOC since restraining of the decline of SOC. We simulate the two ES algorithms and two kinds of controller gain vector, test each on the fuel economy and SOC. By comparing these results and the sample controller, the proposed algorithm can improve the fuel economy of HEV by almost 43% to the sample controller. This paper is organized as follows. Section 2 addresses the outline of the benchmark problem and the subject HEV structure. The same optimal controller gains decision process and the proposed hybrid electric powertrain controller using ES with the semi-optimal gains are described in Section 3. The simulation setup and results are presented and discussed in Section 4. In Section 5, we introduce the key idea of our proposed controller and discuss the effectiveness on this algorithm. Conclusions are drawn in Section 6.
ing conditions are changed according to “driving time“, “day of the week“, and “whether“. The driving cycles on Monday to Friday are measured data on commuting driving, and the data on the weekend are measured on driving for leisure. Therefore, the driving cycles on the weekend include the high-speed data. The object of the benchmark problem is the design of the controller for HEV in order to minimum the fuel economy, Fc , under keeping a driver’s satisfaction function, Sd (Tend ), more than 90%, where Tend is the total driving cycle time, and Sd (Tend ) is given as � Tend Sd (Tend ) = 100 − ΔSd (t)dt (2) 0 ⎧ ⎨ 0 , (e (t) ≤ 7.5) 0.1 , (7.5 < e (t) ≤ 15) (3) ΔSd (t) = ⎩ 1 , (15 < e (t)) e(t) = |vd (t) − vc (t)| (4) where vd (t) km/h and vc (t) km/h are the driver’s demanded vehicle speed and the vehicle speed, respectively. Fc at T is defined as Dd (T ) Fc (T ) = (5) Sf (T ) � T � T |vd (t)|dt , Sf (T ) = |sf (t)|dt (6) Dd (T ) = 0
2. OUTLINE OF BENCHMARK PROBLEM AND HEV SYSTEM The controller-plant, HEV, is equipped with split type hybrid powertrain. A driving motor, a generator, and an internal combustion engine are linked by planetary gear set. After this, the driving motor, the generator, and the internal combustion engine are expressed as EM1, EM2, and ICE, respectively. Both EM2 and ICE can drive the vehicle and EM1, and EM2 can generate the electric power and charge the battery. The DCM is the driving cycle manager and HEV and driver model is the target plant. Figure 2 outlines the power flows via ICE, EM1, and EM2 for the HEV drivetrain system, and the figure 1 illustrates the structure of split hybrid electric powertrain. This powertrain has the following 6 modes, which are as (i) an electric vehicle mode driving by EM2, (ii) ICE and EM2 driving mode, (iii) ICE assists mode by EM2, (iV) regenerative braking mode, (v) charge mode by ICE, and (vi) stop mode. The speed of EM1, ω1 , the speed of EM2, ω2 , and the speed of ICE, ωe , in the modes, (ii) and (iii), are given by ε 1 ωe = (1) ω1 + ω2 1+ε 1+ε where ε is a planetary gear ratio, and given as 0.3846. The target HEV is a medium class car with the engine displacement as 1, 339 cc, and the vehicle weight is 1, 460 kg. The maximum powers of ICE, EM1, and EM2 can generate 51 kW, 15 kW, and 25 kW, respectively. The detail conditions and setting of benchmark problem are described in Yasui (2012). The evaluation of energy management in HEV is usually investigated over the New European Driving Cycle (NEDC) in EU, the FTP-75 in the US, and the JC08 in Japan. (See Overington (2015)). However, the driving cycles in this benchmark problem are the actual driving patterns for 3 weeks shown in figure 3a, and the fuel economy is evaluated over the driving cycle. The driv253
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Dd (T ) : Driving distance at T sf (t) : Fuel economy rate per second L/s The fuel economy via designed controller is investigated by driving cycle time for 3 weeks, which is given as T = Tend = 80, 430 s. Figure 4a illustrates the simulation system model of the benchmark problem that is described by GT-SUITE of Gamma Technologies, Inc. and by using MATLAB/Simulink. The HEV system of benchmark problem has sample controller units in advance. The sample controller has four controller units, and each controller controls the ICE, EM1, EM2, and SOC of charge. This HEV drivetrain system can run by the sample controller, and the sample controller units attain the fuel economy, 41.44 mpg. We modify the sample controller units, and challenge to the higher fuel economy by using the online HEV drivetrain system. 3. ON-LINE HEV POWERTRAIN CONTROL WITH SEMI-OPTIMIZATION GAINS AND EXTREMUM SEEKING ALGORITHM The strategy of power division via ICE, EM1, and EM2 are important for a decreasing of fuel economy from the power flows. Thus, we add the output gain of sample controllers, and then the controller gains are designed using the information of convexity of the index function, i.e., fuel economy. Figure 4b indicates the structure of our proposed controller. The proposed HEV powertrain system uses the sample controllers, and the proposed system sets gains on T each sample controller unit. Let K = [k1 k2 k3 k4 k5 k6 ] be a vector entries corresponding to the controller gains that are connected to controller units shown in figure 4b. k1 k2 k3 , and k4 correspond to the reference speed in engine controller unit, the torque required to the EM1, the torque required to the EM2, and the electrical power to charge the battery in battery controller unit, respectively.
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Sun gear EM
Pdrive , Pbrak invertor
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Motor for generator ( EM1 )
Ring gear EM
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Vd
Driving cycle manager driving data for three day (DCM)
invertor Gear
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Fuel tank
Plant outputs y(t)
Battery
Driver model
+(9ZLWK%DWWHU\
Plant
Drive Motor ( EM2)
EneUgy management
wheel
u(t) Control inputs
Split type hybrid drive system
Fig. 1. Structure of split hybrid electric powertrain
(a) simulation system model of the benchmark problem
Mechanical power floow Electrical power floow Pg = Pm
Control Inputs U(t)
Generator EM1
Inverter
Pg
Driver
Battery
Torque of electrical motor
K1
Battery power
K2
Torque of generator
Pm
Electric motor EM2 Zg Tg
Internal combustion engine ICE
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Planetary gear
Pe
K4
Engine start/stop
sun gear
Ze Te
Tm
+
P
Pr Zr
Tr
Differential gear
Po
Throttle angle of Engine
K5
Controller Energy management system
K6
SOC
HEV
tires
ring gear
carrier
Output signals Y(t)
K3
Ignition of engine
* Zeng
0 limiter
Fig. 2. Power flows via ICE, EM1, and EM2 of HEV
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1
s
+ Integrator
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Velocity [km/h]
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Velocity [km/h]
T t
J(t) = Fc(t)
J(t) : cost function Fc(t) Fuel consumption
Extremum seeking (ES)
Controller
Fuel HFRQRP\
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Fc(t)
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)Fmax 0
5
10
15
20
25
30
35
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(b) Configuration of HEV controller system
45
)F(kmin) +
cloud
Fig. 4. GT-SUITE system (upper) and proposed ES system (lower)
50 0
0
5
10
15
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25
T
30
(Step 3) Decide the semi-optimal controller gains Kopt ∈ R6 according to (9) Kopt = arg max Fc (Kj , Ts )
rain kmin
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time [mim]
(a) Driving cycles of HEV system; upper: fine, middle: could, bottom: rain
(b) Semi optimal gain based on piecewise linear approximation of cost function.
Fig. 3. Driving cycles(left) and example of semi optimal gains(right) The other gains, k5 and k6 , are the relationship with the proposed SOC in battery controller unit, and the accelerator pedal position in the engine controller unit. For these gains, we select the semi-optimal gains by the following algorithm. l l (Step 1) Given {kmin , kmax }, (l = 1 to 6), for each l l controller gain, divide the interval kmax − kmin as follows: l l l {kmin , kmin + T , · · · , kmax } (7) l l − kmin k T = max (8) m � � l l ⊂ [0.5 1.5] in view of the controller where kmin kmax signal gain. (Step 2) Decide the convex on the fuel economy Fc (K, Ts ) by an approximate lines shown in figure 3b. After that, combine with the gains, and obtain the set of gain vectors Kj ∈ R6 , SK , where j is a combination number and is given by j ≤ 63 . Then, calculate the fuel economy, Fc (Kj , Ts ), using the each combination gain, Kj , to the test running for Ts s.
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The semi optimal gains mean that the gain vector Kopt given by (9) attains the highest efficiency of fuel economy in Ts , which is shown in figure 3b. The Ts , Kmin , and kmax are given in Section 4. Using the decided gains, the hybrid electric powertrain strategy using an ES algorithm with semi-optimal gains is calculated from the following formula (see Dobrivoje (2006), Ariyur (2003)). Note that the GTSUITE can only do simulation on discrete condition. Then, the following ES formula is expressed by discrete system. h (k) = J (k) (10) J (k) = Fhpf [λFc (k) + (1 − λ) Rsoc (k)] , λ ∈ [0, 1] (11) (12) u (k) = h (k) (Kg sin (ωTsp k) + ωmin ) 1 � w (k) = αw (k − 1) + β u (k − n) (13) n=0
ωe (k) = Kg sin (ωTsp k) + K
k � l=0
w (l) + ωmin
(14)
⎧ ⎨ 1, 150 , ωe (k) ≤ 1, 150 ωe (k) , 1, 150 < ωe (k) < 5, 000 ωe∗ (k) = Fs (ω1 (k)) = ⎩ 5, 000 , 5, 000 ≤ ω (k) e (15) where Fhpf [•] is a high pass filter, Fc (k) Rsoc (k) are a fuel economy of k time, and a SOC at k time. Tsp is a sampling period and ωmin is a idling speed given as 1, 150 rpm. α and β are the coefficients of a low pass filter. 5, 000
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rpm is the maximum speed of ICE. This strategy perturbs the reference engine speed, ω ∗ around ωmin to both the cost function, i.e., J (k) = Fc (k) and the cost functions, i.e., J (k) = J [Fc (k) , RSOC (k)]. Note that this reference engine speed is the input of the EM1 controller unit. The output of the powertrain is a desired power of wheel torque, and the controllers regulate each torque based on the speeds while referring to SOC. As indicating (1), ω1 can control ω2 , thus the power of electrical drivetrain is regulated via ω1 , the torque of EM1 is controlled by EM1 controller unit according to ωe∗ . 4. SIMULATION SETUP AND RESULTS 4.1 Simulation setup This section illustrates the simulation setting of our proposed method. The GT-SUITE simulator is used for this simulation, and test running time, Ts is decided as Ts = 10, 000 s (see Koguchi (2015)). The parameters of determination algorithm in semi optimal gains, K ∈ R6 , are T given by Kopt = [1.2, 0.8, 0.8, 1.2, 1.0, 1.1] . The cost functions J for ES given as J (k) = J [Fc (k) RSOC (k)] are using the two types: (i) J (k) = Fc (k), (ii) J (k) = 0.5Fc (k) + 0.5RSOC (k). The switching threshold for controllers is SOC = 48%. To compare the fuel economy and SOC according to cost function, the combination of ES and gains as follows: 1) ES-1, 2) ES-5, and 3) ES0. The cost function in ES-1 is J (k) = Fc (k) and the using controller gain vector is Kopt . The cost function in ES-5 is J (k) = 0.5Fc (k) + 0.5RSOC (k) and the using gain vector T is K1 = [1, 1, 1, 1, 1, 1] , and J (k) and the using gain vector in ES0 are J (k) = Fc (k) and K1. The efficiency of cost functions investigates from the results of ES-5 and ES. The Low pass filter (LPF) and the high pass filter (HPF) in ES are given by z−1 LPF = (16) (1 + Tsp πfcl ) z + Tsp πfcl − 1 Tsp πfch z + Tsp πfch (17) HPF = (1 + Tsp πfch ) z + (Tsp πfch − 1) where z is a time shift operator. These discrete filters can be obtained from the continuous systems, i.e., 1/ (1 + τL s) and τH S/ (1 + τH s), by s = 2/Tsp · 1 − z −1 / 1 + z −1 , and the coefficients fcl and fch adjusted from the response of engine speed. The cutoff frequencies of the LPF and HPF are given as fcl and fch , and the values are shown in Table. 1. 4.2 Simulation results
Table. 1
parameters of simulation Parameters values m 5 {kmin , kmax } {0.8 , 1.2} {fcl , fch } {1Hz , 10Hz} {Kg , K} {1 , 10} ωmin 1150rpm Tsp 0.02 sec
have a similar trend. Then, it can be decided that the cost function is only necessary to the fuel economy. The driving by ES-1 has the state that the controller switches to the sample controller with optimal gains during the less than the SOC, 48%. The final fuel economy of ES-1 is 59.30mpg, which decreases by only 0.32 mpg to the fuel economy at Ts , and SOC is 64.45%. However, the minimum SOC is 46.75%, the values is lower than 52.98% of the semioptimal gains without ES. The results shown in figure 9, figure 10, and figure 11 seem that the control using ES-1 is driving in the fuel economy area of engine power, which results are BSFC (Brake Specific Fuel Consumption), ωe map, and the root mean square (RMS) of the power of EM1, EM2, ICE and SOC. It is known that the low BSFC is the high performance of fuel economy (see Dobrivoje (2006)). The drivetrain strategy, i.e., driving strategy of wheels, for the high performance, is that ICE uses only range the high load factors to the engine speed. The results of BSFC and engine speed are examined to investigate the fuel economies of ES1, ES2, ES3, and sample controllers. The results in figure 7 are the driving cycle of second Sunday. The results include the more than 70 km/h speed, and the consumptions of SOC are the highest in all weeks. Figure 8 shows that the sample controller tend to use actively ICE power to drive the drivetrain. On the other hand, the controllers using ES-1, ES-5, and ES0 tend to use the EM2 power to assist the driving of wheels. In the same period, the reference speed of ES-1 is fluctuating around 1, 300 rpm. The results can be recognized from the BSFC - engine speed of drive train shown in figure 9 and figure 10 which show the 3D histogram between BSFC and engine speed. The BSFC histogram by the sample controller spreads over 1, 200 rpm to 2, 700 rpm, and 210 g/kW-h to 240 g/kW-h. Whereas the BSFC histogram of ES0 and ES-5 concentrates near 1, 600 rpm - 210 g/kW-h, the histogram of ES-1 shows near 1, 300 rpm - 210 g/kW-h. Figure 8 indicates the situations; SOC and ICM power for sample controller are high. Operation in the driving assist mode uses the engine mainly. The drive of wheels results in causing the low SOC. As the results of simulations, the final fuel economy of controller using ES-1 is the high performance by 43% compared to sample controller. Table 2. Fuel economies and SOCs using each controller
The fuel economy of the semi-optimal gains without ES is 58.98 mpg for Ts = 10, 000 s shown in figure 5. This value is almost 44.6 % higher than the fuel economy of sample controller for the same time. Figure 5 and figure 6 show the fuel economies for each day. The fuel economies and SOCs at Tend show in Table 2. The fuel economies in figure 5 are decreasing day by day, where the final value is 44.22 mpg. Figure 5 shows that the gains achieving higher performance of fuel economy at the test time are not necessarily able to perform the same performance in total time, Tend . Figure 6 indicates the results of each controller. The daily variations in fuel economy using ES-5 and ES0 255
ES-1 ES-5 ES0 Fix-gain sample
Fuel economy [mpg] 59.30 56.62 56.69 44.22 41.44
SOC [%] 64.45 64.45 65.17 64.13 64.97
5. DISCUSSION Here, we point out the key idea and the role of semioptimal gain of the proposed method. The sample controller is decided the speed at t s by using the map data
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Fig. 7. Driving cycle of second Sunday. based on the driver demand power and battery power. The relationship between the fuel economy and engine speed were introduced in subsection 4.2. We verified the sample controller with output gains were able to increasing the fuel economy and the using the convex information is useful for the decision of effective gains (see Koguchi (2015)). Assuming that the semi optimal reference engine speed exists near the output gains decided by convex of fuel economy, this method was proposed. Assuming that the fuel economy can be expressed as Fc (K, ωe∗ , T ), the the following inequalities are satisfied. Fc (K, ωe∗ , T ) ≤ Fc (Kopt , ωe∗ , T ) ≤ max{Fc } ∗ Fc (Kopt , ωe∗ , T ) ≤ Fc Kopt , ωeopt ,T
(18) (19) 256
This paper has proposed the drive strategy of split hybrid electric powertrain, i.e., controller of HEV drive system, using ES algorithm and semi-optimal gains. Regarding the cost function of the ES algorithm, the simulation results made it clear that the fuel economy is more useful than SOC. From the result, Fc (T ) is used as the cost function in ES with semi-optimal gains. The simulation results for three controllers, ES-1, i.e., ES using the cost function of fuel economy and semi-optimal gains, ES-5, i.e., ES using the cost function of fuel economy and SOC, and all 1 gains, and ES0, i.e., ES using the cost function of fuel economy and all 1 gains indicate that the final fuel economy of ES-1 can be obtained the highest value, 59.30 mpg. The controller using the ES algorithm with semi-optimal gains operates the engine near 1, 300 rpm, BSFC can be obtained near 210 g/kW-h, which is high performance range. By
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Fig. 11. RMS of EM1, EM2, ICE, and SOC; upper left: power of EM1, Upper right : power of EM2, Lower left : power of ICE, Lower right: SOC comparing both the controller without semi-optimal gains and the ES with semi-optimal gains, the controller using ES with the semi-optimal controller can maintain the fuel economy. However, the ES with semi-optimal gain was observed to tend to use the battery on the large change of the driving cycle. The improvement for decreasing of SOC is future work. ACKNOWLEDGEMENTS Some simulation results are a collaboration study with Daichi Ishida, who is a graduate student of our laboratory. We are grateful to Mr. Ishida for helpful his work. REFERENCES Egardt B., Murgovski N., and Pourabdollah M. (2014) “ Electromobility Studies Based on Convex Optimization ”, IEEE Control System Magazine, Vol. 34, No.2, pp. 32 – 49. Lin, C. C., Peng, H., Grizzle, J. W., and Kang, J. M. (2003), “ Power management strategy for a parallel hybrid electric truck ”, IEEE Trans. on Control Systems Technology, Vol.11, No.6, pp.839 – 849. Dextreit C., Kolmanovsky I., V. (2014), “ Game Theory Controller for Hybrid Electric Vehicles ”, IEEE Trans. on Control System Technology, Vol. 22, No. 2, pp.652 – 663. Larsson V., Mardh, L. J., Egardt, B., and Karlsson, S. (2014), “ Commuter Route Optimized Energy Management of Hybrid Electric Vehicles ”, IEEE Trans. on Intelligent Transportation Systems, Vol. 15, No. 3, pp.1145 – 1154. Musardo, C., Rizzoni, G., and Staccia, B. (2005), “ A-ECMS: An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management ”, Proc. the 44th IEEE CDC & ECC 2005, Seville, Spain, pp.1816-1823. Kim, Y., Salvi, A. A., Stefanopoulou, G., and Ersal, T. (2015), “ Reducing Soot Emissions in a Diesel Series Hybrid Electric Vehicle Using a Power Rate Constraint Map ”, IEEE Trans. Vehicular Technology, Vol. 64, No. 1, pp. 2 – 12. Mura, R., Utkin, V., and Onori, S. (2015), “ Energy Management Design in Hybrid Electric Vehicles: A 257
Novel Optimality and Stability Framework ”, IEEE Trans. Control System Technology, Vol. 23, No. 4, pp. 1307 – 1322. Overington, S., Rajakaruna, S. (2015), “ High-Efficiency Control of Internal Combustion Engines in Blended Charge Depletion/Charge Sustenance Strategies for Plug-In Hybrid Electric Vehicles ”, IEEE Trans. on Vehicular Technology, Vol. 64, No. 1, pp.48 – 61. Yasui, T. (2012), “ JSAE-SICE Benchmark Problem2: Fuel Consumption Optimization of Commuter Vehicle Using Hybrid Powertrain ”, Proc. of 10th World Conf. on Intelligent Control and Automation, pp. 606 – 611. Yu. K., Mukai, M., and Kawabe, T. (2013), “ Model Predictive Control of a Power-Split Hybrid Electric Vehicle System with Slope Information ”, Proc. SICE Annual Conf, Vol. 14, NO.17, pp. 2311– 2316. Ahmad, M. A., Azuma, S., Baba, I., and Sugie, T. (2014), “ Switching Controller Design for Hybrid Electric Vehicles ”, SICE Journal of Control, Measurement, and Integration, Vol. 7, No.5, pp.273 – 282. Iyama H., Sudo T., and Namerikawa T. (2015) , “ Fuel Consumption Optimization for an HEV considering Ignition Timing of Engine ”, Proc. of Systems, Control and Information Engineers (SCI’15), CD-ROM. Koguchi, K., Hidaka, K. (2015), “ Fuel Efficiency Strategy for the Hybrid Electric Vehicle by the Simultaneous Perturbation Using the Partitioned Data ”, Proc. 1th IEEJ international workshop on Sensing, Actuation, and Motion Control (SAMCON2015), V19 (CD-ROM). Dobrivoje, P., Mrdjan, J., Steve, M., and Andre R. T, (2006), “ Extremum Seeking Methods for Optimization of variable Cam Timing Engine Operation ”, IEEE Trans. on Control System Technology, Vol. 14, No. 3, pp. 398 – 407. Ariyur, K. B., Krstic, M. (2003), “ Real-time optimization by extremum-seeking control ”, Wiley.
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On-Line Controller for On-Line Controller for On-Line Controller for on Spilt-Type Hybrid on Spilt-Type Hybrid on Spilt-Type Hybrid ∗
Fuel Consumption Fuel Consumption Fuel Consumption Electric Vehicle Electric Vehicle Electric Vehicle ∗∗
Hiroki Koguchi ∗ Koichi Hidaka ∗∗ Hiroki Koguchi ∗ Koichi Hidaka ∗∗ Hiroki Koguchi ∗ Koichi Koichi Hidaka Hidaka ∗∗ Hiroki Koguchi ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗∗ ∗ Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: ∗ NIDEC ELESYS Corporation, Kawasaki, Kanagawa, Japan. ∗∗ NIDEC Corporation, Kawasaki, Kanagawa, Japan. TokyoELESYS Denki University, Adachi, Tokyo, Japan, (e-mail: ∗∗ [email protected]) ∗∗ Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: Tokyo Denki University, Adachi, Tokyo, Japan, (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper proposes a controller used by an extremum seeking (ES) algorithm with Abstract: This paper proposes controller used vehicle by an extremum seeking (ES) algorithm with semi-optimal controller gains for a hybrid electric (HEV) system. The semi-optimization Abstract: This paper a used by seeking (ES) algorithm Abstract: This paper proposes proposes aaa controller controller used vehicle by an an extremum extremum seeking (ES) algorithm with with semi-optimal controller gains for hybrid electric (HEV) system. The semi-optimization gains connectcontroller at each gains output ofa sampleelectric controllers that are system. given byThe benchmark problem semi-optimal controller gains for a hybrid electric vehicle (HEV) system. The semi-optimization semi-optimal for hybrid vehicle (HEV) semi-optimization gains connect at each output of sample controllers that are given by benchmark problem in advance. These gainsoutput are decided according to thethat approximate on fuel economy gains connect at of controllers are by problem gains connect at each each of sample sample controllers that are given given convex by benchmark benchmark problem in advance. These gainsoutput are target decided according to the approximate convex on fuel economy ∗ function via each gains. The engine speed of EM1 controller, ω , is perturbed with the in advance. These gains are decided according to the approximate convex on fuel economy ∗ in advance. These gainsThe are target decided according to the approximate convex on fuel economy function via each gains. engine speed of EM1 controller, ω , is perturbed with the ∗ ES algorithm based on fuel economy and State of Charge (SOC). Furthermore, the proposed ∗ , is perturbed function via each gains. The target engine speed of EM1 controller, ω with function via each gains. Theeconomy target engine speedofofCharge EM1 controller, ω , is perturbed with the the ES algorithm based on fuel and State (SOC). Furthermore, the proposed algorithm switches depending SOCof restraining the decline of The ES algorithm based controller on fuel fuel economy economy andon State of for Charge (SOC).of Furthermore, theSOC. proposed ES algorithm based on and State Charge (SOC). Furthermore, the proposed algorithm switches controller depending on SOC for restraining of the decline of SOC. The sample controllers four units, and each unit controller controls driving of algorithm switches controller depending on for of SOC. algorithm switches have controller depending on SOC SOC for restraining restraining of the the decline decline of HEV. SOC. The sample controllers have four the units, andFor each unit controller controls drivingcontroller, HEV. The sample controllers can drive HEV. showing the validity of our proposed fuel have four units, and each unit controller controls the driving of HEV. sample controllers can havedrive four the units, andFor each unit controller controls the drivingcontroller, of HEV. The The HEV. showing the validity of our proposed fuel economies of the proposed controller and sample controller are compared by simulator for this sample controllers can drive the HEV. For showing the validity of our proposed controller, fuel sample controllers can drivecontroller the HEV.and Forsample showing the validity of our proposed controller, fuel economies of the proposed controller are compared by simulator for this benchmark. While the fuel controller economy achieved by controller the sampleare controller is by 41.44 mpg, the final economies of the proposed controller and sample controller are compared by simulator for this economies of the proposed and sample compared simulator for this benchmark. While the fuel economy achieved by the sample controller is 41.44 mpg, the final fuel economyWhile on the method is almost 59.29 mpg,controller and the is final SOC is 64.45 %. benchmark. the fuel achieved by sample 41.44 mpg, the benchmark. While theproposed fuel economy economy achieved by the the sample is 41.44 mpg, the final final fuel economy on the proposed method is improved almost 59.29 mpg,controller and thecompared final SOC is 64.45 %. The performance of fuel economy can be by almost 43 % to the sample fuel economy on the proposed method is almost 59.29 mpg, and the final SOC is 64.45 %. fuel economy on the proposed method is improved almost 59.29 mpg, and thecompared final SOC is 64.45 %. The performance of fuel economy can be by almost 43 % to the sample controller. The performance of fuel economy can be improved by almost 43 % compared to the sample The performance of fuel economy can be improved by almost 43 % compared to the sample controller. controller. controller. © 2016, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Hybrid electricFederation Vehicle control, Control system, Model-free Controller Design, Keywords: Hybrid electric Vehicle control, Control system, Model-free Controller Design, Extremum seeking electric algorithm, Splitcontrol, hybrid Control electric powertrain Keywords: Vehicle system, Keywords: Hybrid Vehicle system, Model-free Model-free Controller Controller Design, Design, Extremum Hybrid seeking electric algorithm, Splitcontrol, hybrid Control electric powertrain Extremum seeking algorithm, Split hybrid electric powertrain Extremum seeking algorithm, Split hybrid electric powertrain 1. INTRODUCTION The control task is referred to as energy management. The 1. INTRODUCTION The control task is referred to has as energy management.(e.g., The energy management problem been investigated. 1. INTRODUCTION The control task to as management. The 1. INTRODUCTION The control task is is referred referred to has as energy energy management.(e.g., The energy management problem been investigated. (2003), Dextreit (2014), Larsson (2014)). On the other The Hybrid electric vehicles (HEVs) are gaining mar- Lin energy management problem has been investigated. (e.g., energy management problemLarsson has been investigated. (e.g., Lin (2003), Dextreit (2014), (2014)). On the other The Hybrid electric vehicles (HEVs) are gaining marthe split configuration in the(2014)). commuter vehicles, ket and accelerating propelled by a mix of hand, Lin (2003), Dextreit (2014), Larsson Larsson (2014)). On the the other The popularity Hybrid electric electric vehicles (HEVs) (HEVs) are gaining gaining mar(2003), Dextreit (2014), On other The Hybrid vehicles are marhand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by abusiness mix of Lin e.g., Toyota’s Prius, is used. The split configuration has environmental concerns, rising fuel prices, and hand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by a mix of hand, the split configuration in the commuter vehicles, ket popularity and accelerating propelled by a mix of e.g., Toyota’s Prius, is used. The split configuration configuration and has environmental The concerns, rising fuel prices, anddegrees business the both features between the parallel opportunities. typical HEV has multiple of e.g., Toyota’s Prius, is used. The split configuration has environmental The concerns, rising fuel prices, anddegrees business e.g., Toyota’s Prius, is used. The split configuration configuration and has environmental concerns, rising fuel prices, and business the both features between the parallel opportunities. typical HEV has multiple of serial configuration, and the structures are complex. Thus, freedom for delivering wheel torque, unlike conventional the both features between the parallel configuration and opportunities. The typical HEV has multiple degrees of both features between the parallelare configuration and opportunities. The typical HEV has unlike multiple degrees of the serial configuration, and the structures complex. Thus, freedom for delivering wheel torque, conventional control system ofand the the energy management is important. vehicles. Thedelivering conventional have threeconventional powertrain the serial configuration, structures are complex. complex. Thus, freedom for for wheelHEVs torque, unlike conventional serial configuration, structures are Thus, freedom wheel torque, unlike the control system(2015)). ofand the the energy management is important. vehicles. Thedelivering conventional HEVs have three powertrain (See Overington The control systems for HEV configurations, known as series, parallel, and split (series the control system of the energy management is important. vehicles. The conventional HEVs have three powertrain the control system of the energy management is important. vehicles. The conventional HEVs have three powertrain Overington The control HEV known asInseries, parallel,type, and the splitinternal (series (See system have(2015)). been proposed. (e.g.,systems Musardofor -configurations, parallel), respectively. the parallel (See Overington The systems for HEV configurations, known as asInseries, series, parallel,type, and the splitinternal (series drive (See Overington (2015)). The control control systems for(2005), HEV configurations, known parallel, and split (series drive systemMura have(2015)). been proposed. (e.g., Musardo (2005), -combustion parallel), respectively. the parallel Kim (2015), (2015)), However, these systems are for engine (ICE) and the electric machine (EM) drive system have been proposed. (e.g., Musardo (2005), --combustion parallel), respectively. In the parallel type, the internal drive systemMura have (2015)), been proposed. (e.g., Musardo (2005), parallel), respectively. Inand the the parallel type, the internal Kim (2015), However, these systems are for engine (ICE) electric machine (EM) series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled to the drive shaft of the vehicle, Kim (2015), Mura (2015)), (2015)), However, these systems are are for combustion engine (ICE) to and the electric machine (EM) Kim (2015), Mura However, these systems for combustion engine (ICE) and the electric machine (EM) series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled the drive shaft of the vehicle, neers of Japan) and SICE (The Society of InstrumentEngiand and the wheel power is the sum of the individual power. series HEV. Therefore, JSAE (Society of Automotive are mechanically coupled to the drive shaft of the vehicle, series HEV. Therefore, JSAE (Society of Automotive Engiare mechanically coupled to the drive shaft of the vehicle, neers of Japan) and SICE (Thethree Society of Instrument and and the wheeltopology power iscan the reduce sum of drivetrain the individual power. Control Engineers) provided benchmark problems The parallel losses, and neers of and (The Society of and and the the wheeltopology power is iscan the reduce sum of of drivetrain the individual individual power. neers of Japan) Japan) and SICE SICE (Thethree Society of Instrument Instrument and and wheel power the sum the power. Control Engineers) provided benchmark problems The parallel losses, and in 2011, and the one of the benchmark problems is given lead to a lower average ICE operating efficiency. The parControl Engineers) provided three benchmark problems The parallel topology can reduce drivetrain losses, and Engineers) provided three benchmark problems The parallel topology can reduce drivetrain losses, and Control in 2011, and the one of the benchmark problems is given lead to a lower average ICE operating efficiency. The par“Fuel and economy optimization of the commuter allel structure ICE in 2011, and the one one of the the benchmark benchmark problems is isvehicle given lead to to lower limits average ICEoperating, operatinghowever. efficiency.The Theseries par- as in 2011, the of problems given lead aa lower average ICE operating efficiency. The paras “Fuel economy optimization of the(2012)). commuter vehicle allel structure limits ICE operating, however. The series using hybrid powertrain”. (See Yasui The hybrid powertrain is characterized by directly uncoupled between as “Fuel economy optimization of the commuter vehicle allel structure limits ICE operating, however. The series as “Fuel economy optimization of the commuter vehicle allel structure limits ICE operating, however. The series using hybrid powertrain”. (See Yasui (2012)). The hybrid powertrain is characterized by directly uncoupled between using the split the ICE and EM. This powertrain can operate the ICE powertrain using hybrid (See Yasui The hybrid powertrain is characterized characterized by directly directly uncoupled between hybridis powertrain”. (Seeconfiguration. Yasui (2012)). (2012)).The The control hybrid powertrain is by uncoupled between powertrain ispowertrain”. using the split configuration. The control the ICE and EM. This powertrain can operate the ICE using designs for the benchmark problem have been proposed, speed and torque regardless of the vehicle speed. Thus, powertrain is using the split configuration. The control the ICE and EM. This powertrain can operate the ICE is using the split configuration. The control the ICE and EM. regardless This powertrain can operate theThus, ICE powertrain designs for the benchmark problem have been proposed, speed and torque of the vehicle speed. are as modelproblem free types and model based the topology can operate theof optimal conditions designs for known the benchmark benchmark problem have been proposed, speed and torque torque regardless ofICE theat vehicle speed. Thus, which designs for the have been proposed, speed and regardless the speed. Thus, which are known as model free(2014)). types and model based the topology can operate thethe ICE atvehicle optimal conditions types. (e.g., Yu (2013), Ahmad Model-based conthat minimize emissions and combined loss of the ICE which are known as model free types and model the topology topology can operateand thethe ICE at optimal conditions which are known as model free(2014)). types and model based based the can operate the ICE at optimal conditions types. (e.g., Yu (2013), Ahmad Model-based conthat minimize emissions combined loss of the ICE trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large types. (e.g., Yu (2013), Ahmad (2014)). Model-based conthat minimize emissions and the combined loss of the ICE (e.g., Yufor(2013), Ahmad (2014)). Model-based conthat minimize emissions and the combined loss ofthe thelarge ICE types. trol is useful the energy management for HEV. The and generator. (See Egardt (2014)). However, present proposed model-based controllers have not be able size battery is needed. The split topology is a mixture trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large trol is useful for the energy management for HEV. The and generator. (See Egardt (2014)). However, the large present proposed model-based controllers have not be able size battery is needed. The split topology is a mixture to obtain more than 25 km/Lcontrollers of the fuel economy yet. topology and the features of both topologies have. The present proposed model-based have not be able size battery is needed. The split topology is a mixture present proposed model-based controllers have not be able size battery isthe needed. Theofsplit is have. a mixture to obtain more than On 25 km/L of the fuelthe economy yet. topology and features bothtopology topologies The (e.g., Iyama (2015)). the other hand, model-free ICE, EM, and generator (GEN) are coupled with the to obtain more than 25 km/L of the fuel economy yet. topology and thegenerator features (GEN) of both both are topologies have. The to obtain more than On 25 km/L of the fuelthe economy yet. topology and the features of topologies have. The (e.g., Iyama (2015)). the other hand, model-free ICE, EM, and coupled with the control approaches are effective and useful for the energy planetary gear. The both EM and generator drive the (e.g., Iyama (2015)). On the other hand, the model-free ICE, EM, and generator (GEN) are coupled with Iyama (2015)). On the other hand, the model-free ICE, EM, gear. and generator (GEN) aregenerator coupled drive with the (e.g., control approaches are effective and useful for the energy planetary The both EM and controlare of effective the commuter vehicle. model vehicle. a strategy for agenerator control system to management control approaches are effective and useful useful for The the energy energy planetaryThere gear.needs The both both EM and and drive the the control approaches and for the planetary gear. The EM drive management control of weakness the commuter vehicle. The model vehicle. There needs a power strategy for agenerator control system to free controls have the on the changes of drivadjust between the two sources, the ICE and EM in management control of the commuter vehicle. The vehicle.between There needs needs strategy for aathe control system to management control of weakness the commuter vehicle. Theofmodel model vehicle. There aa power strategy for control system to free controls have the on the changes drivadjust the two sources, ICE and EM in ing conditions. The EV controller based ES algorithm, the parallel configuration, and the engine-generator unit free controls have the weakness on the changes of adjust between the two power sources, the ICE and EM in controls have weakness on based the changes of drivdrivadjust between the two power sources, the ICE and EM in free ing conditions. ThetheEV controller ES algorithm, the parallel configuration, and the engine-generator unit which is a model-free and on-line controller, has been and the electric storage system in theengine-generator series configuration. conditions. The controller based ES the parallel parallel configuration, and in thethe engine-generator unit ing ing conditions. The EV EVand controller based ES algorithm, algorithm, the configuration, and the unit which is a model-free on-line controller, has been and the electric storage system series configuration. described by Yasui (2012). However, Yasui (2012) does which is a abymodel-free model-free and However, on-line controller, controller, has been been and the electric storagebysystem system in the the series configuration. which is and on-line has and the electric storage in series configuration. This work is supported JSAE and IDAJ Co., Ltd., Japan. described Yasui (2012). Yasui (2012) does This work is supported by JSAE and IDAJ Co., Ltd., Japan. described by Yasui (2012). However, Yasui (2012) described by Yasui (2012). However, Yasui (2012) does does
This This work work is is supported supported by by JSAE JSAE and and IDAJ IDAJ Co., Co., Ltd., Ltd., Japan. Japan. Copyright © 2016 IFAC 252 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 252 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 252 Copyright © 2016 IFAC 252Control. 10.1016/j.ifacol.2016.08.037
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not investigate the fuel economy of the driving for a total time, but only was tested to the fuel economy for 1500 sec. Furthermore Yasui (2012) does not investigate the performance via the cost function of Fc and SOC. In this paper, the controller using ES with semi-optimization gains is proposed. Our proposed method joins the six gains in sample controllers that are given by benchmark problem in advance. The target engine speed of EM1 controller, ω ∗ , is perturbed with the ES algorithm based on fuel economy. Furthermore, the proposed algorithm switches controller depending on SOC since restraining of the decline of SOC. We simulate the two ES algorithms and two kinds of controller gain vector, test each on the fuel economy and SOC. By comparing these results and the sample controller, the proposed algorithm can improve the fuel economy of HEV by almost 43% to the sample controller. This paper is organized as follows. Section 2 addresses the outline of the benchmark problem and the subject HEV structure. The same optimal controller gains decision process and the proposed hybrid electric powertrain controller using ES with the semi-optimal gains are described in Section 3. The simulation setup and results are presented and discussed in Section 4. In Section 5, we introduce the key idea of our proposed controller and discuss the effectiveness on this algorithm. Conclusions are drawn in Section 6.
ing conditions are changed according to “driving time“, “day of the week“, and “whether“. The driving cycles on Monday to Friday are measured data on commuting driving, and the data on the weekend are measured on driving for leisure. Therefore, the driving cycles on the weekend include the high-speed data. The object of the benchmark problem is the design of the controller for HEV in order to minimum the fuel economy, Fc , under keeping a driver’s satisfaction function, Sd (Tend ), more than 90%, where Tend is the total driving cycle time, and Sd (Tend ) is given as � Tend Sd (Tend ) = 100 − ΔSd (t)dt (2) 0 ⎧ ⎨ 0 , (e (t) ≤ 7.5) 0.1 , (7.5 < e (t) ≤ 15) (3) ΔSd (t) = ⎩ 1 , (15 < e (t)) e(t) = |vd (t) − vc (t)| (4) where vd (t) km/h and vc (t) km/h are the driver’s demanded vehicle speed and the vehicle speed, respectively. Fc at T is defined as Dd (T ) Fc (T ) = (5) Sf (T ) � T � T |vd (t)|dt , Sf (T ) = |sf (t)|dt (6) Dd (T ) = 0
2. OUTLINE OF BENCHMARK PROBLEM AND HEV SYSTEM The controller-plant, HEV, is equipped with split type hybrid powertrain. A driving motor, a generator, and an internal combustion engine are linked by planetary gear set. After this, the driving motor, the generator, and the internal combustion engine are expressed as EM1, EM2, and ICE, respectively. Both EM2 and ICE can drive the vehicle and EM1, and EM2 can generate the electric power and charge the battery. The DCM is the driving cycle manager and HEV and driver model is the target plant. Figure 2 outlines the power flows via ICE, EM1, and EM2 for the HEV drivetrain system, and the figure 1 illustrates the structure of split hybrid electric powertrain. This powertrain has the following 6 modes, which are as (i) an electric vehicle mode driving by EM2, (ii) ICE and EM2 driving mode, (iii) ICE assists mode by EM2, (iV) regenerative braking mode, (v) charge mode by ICE, and (vi) stop mode. The speed of EM1, ω1 , the speed of EM2, ω2 , and the speed of ICE, ωe , in the modes, (ii) and (iii), are given by ε 1 ωe = (1) ω1 + ω2 1+ε 1+ε where ε is a planetary gear ratio, and given as 0.3846. The target HEV is a medium class car with the engine displacement as 1, 339 cc, and the vehicle weight is 1, 460 kg. The maximum powers of ICE, EM1, and EM2 can generate 51 kW, 15 kW, and 25 kW, respectively. The detail conditions and setting of benchmark problem are described in Yasui (2012). The evaluation of energy management in HEV is usually investigated over the New European Driving Cycle (NEDC) in EU, the FTP-75 in the US, and the JC08 in Japan. (See Overington (2015)). However, the driving cycles in this benchmark problem are the actual driving patterns for 3 weeks shown in figure 3a, and the fuel economy is evaluated over the driving cycle. The driv253
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Dd (T ) : Driving distance at T sf (t) : Fuel economy rate per second L/s The fuel economy via designed controller is investigated by driving cycle time for 3 weeks, which is given as T = Tend = 80, 430 s. Figure 4a illustrates the simulation system model of the benchmark problem that is described by GT-SUITE of Gamma Technologies, Inc. and by using MATLAB/Simulink. The HEV system of benchmark problem has sample controller units in advance. The sample controller has four controller units, and each controller controls the ICE, EM1, EM2, and SOC of charge. This HEV drivetrain system can run by the sample controller, and the sample controller units attain the fuel economy, 41.44 mpg. We modify the sample controller units, and challenge to the higher fuel economy by using the online HEV drivetrain system. 3. ON-LINE HEV POWERTRAIN CONTROL WITH SEMI-OPTIMIZATION GAINS AND EXTREMUM SEEKING ALGORITHM The strategy of power division via ICE, EM1, and EM2 are important for a decreasing of fuel economy from the power flows. Thus, we add the output gain of sample controllers, and then the controller gains are designed using the information of convexity of the index function, i.e., fuel economy. Figure 4b indicates the structure of our proposed controller. The proposed HEV powertrain system uses the sample controllers, and the proposed system sets gains on T each sample controller unit. Let K = [k1 k2 k3 k4 k5 k6 ] be a vector entries corresponding to the controller gains that are connected to controller units shown in figure 4b. k1 k2 k3 , and k4 correspond to the reference speed in engine controller unit, the torque required to the EM1, the torque required to the EM2, and the electrical power to charge the battery in battery controller unit, respectively.
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Fig. 3. Driving cycles(left) and example of semi optimal gains(right) The other gains, k5 and k6 , are the relationship with the proposed SOC in battery controller unit, and the accelerator pedal position in the engine controller unit. For these gains, we select the semi-optimal gains by the following algorithm. l l (Step 1) Given {kmin , kmax }, (l = 1 to 6), for each l l controller gain, divide the interval kmax − kmin as follows: l l l {kmin , kmin + T , · · · , kmax } (7) l l − kmin k T = max (8) m � � l l ⊂ [0.5 1.5] in view of the controller where kmin kmax signal gain. (Step 2) Decide the convex on the fuel economy Fc (K, Ts ) by an approximate lines shown in figure 3b. After that, combine with the gains, and obtain the set of gain vectors Kj ∈ R6 , SK , where j is a combination number and is given by j ≤ 63 . Then, calculate the fuel economy, Fc (Kj , Ts ), using the each combination gain, Kj , to the test running for Ts s.
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The semi optimal gains mean that the gain vector Kopt given by (9) attains the highest efficiency of fuel economy in Ts , which is shown in figure 3b. The Ts , Kmin , and kmax are given in Section 4. Using the decided gains, the hybrid electric powertrain strategy using an ES algorithm with semi-optimal gains is calculated from the following formula (see Dobrivoje (2006), Ariyur (2003)). Note that the GTSUITE can only do simulation on discrete condition. Then, the following ES formula is expressed by discrete system. h (k) = J (k) (10) J (k) = Fhpf [λFc (k) + (1 − λ) Rsoc (k)] , λ ∈ [0, 1] (11) (12) u (k) = h (k) (Kg sin (ωTsp k) + ωmin ) 1 � w (k) = αw (k − 1) + β u (k − n) (13) n=0
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rpm is the maximum speed of ICE. This strategy perturbs the reference engine speed, ω ∗ around ωmin to both the cost function, i.e., J (k) = Fc (k) and the cost functions, i.e., J (k) = J [Fc (k) , RSOC (k)]. Note that this reference engine speed is the input of the EM1 controller unit. The output of the powertrain is a desired power of wheel torque, and the controllers regulate each torque based on the speeds while referring to SOC. As indicating (1), ω1 can control ω2 , thus the power of electrical drivetrain is regulated via ω1 , the torque of EM1 is controlled by EM1 controller unit according to ωe∗ . 4. SIMULATION SETUP AND RESULTS 4.1 Simulation setup This section illustrates the simulation setting of our proposed method. The GT-SUITE simulator is used for this simulation, and test running time, Ts is decided as Ts = 10, 000 s (see Koguchi (2015)). The parameters of determination algorithm in semi optimal gains, K ∈ R6 , are T given by Kopt = [1.2, 0.8, 0.8, 1.2, 1.0, 1.1] . The cost functions J for ES given as J (k) = J [Fc (k) RSOC (k)] are using the two types: (i) J (k) = Fc (k), (ii) J (k) = 0.5Fc (k) + 0.5RSOC (k). The switching threshold for controllers is SOC = 48%. To compare the fuel economy and SOC according to cost function, the combination of ES and gains as follows: 1) ES-1, 2) ES-5, and 3) ES0. The cost function in ES-1 is J (k) = Fc (k) and the using controller gain vector is Kopt . The cost function in ES-5 is J (k) = 0.5Fc (k) + 0.5RSOC (k) and the using gain vector T is K1 = [1, 1, 1, 1, 1, 1] , and J (k) and the using gain vector in ES0 are J (k) = Fc (k) and K1. The efficiency of cost functions investigates from the results of ES-5 and ES. The Low pass filter (LPF) and the high pass filter (HPF) in ES are given by z−1 LPF = (16) (1 + Tsp πfcl ) z + Tsp πfcl − 1 Tsp πfch z + Tsp πfch (17) HPF = (1 + Tsp πfch ) z + (Tsp πfch − 1) where z is a time shift operator. These discrete filters can be obtained from the continuous systems, i.e., 1/ (1 + τL s) and τH S/ (1 + τH s), by s = 2/Tsp · 1 − z −1 / 1 + z −1 , and the coefficients fcl and fch adjusted from the response of engine speed. The cutoff frequencies of the LPF and HPF are given as fcl and fch , and the values are shown in Table. 1. 4.2 Simulation results
Table. 1
parameters of simulation Parameters values m 5 {kmin , kmax } {0.8 , 1.2} {fcl , fch } {1Hz , 10Hz} {Kg , K} {1 , 10} ωmin 1150rpm Tsp 0.02 sec
have a similar trend. Then, it can be decided that the cost function is only necessary to the fuel economy. The driving by ES-1 has the state that the controller switches to the sample controller with optimal gains during the less than the SOC, 48%. The final fuel economy of ES-1 is 59.30mpg, which decreases by only 0.32 mpg to the fuel economy at Ts , and SOC is 64.45%. However, the minimum SOC is 46.75%, the values is lower than 52.98% of the semioptimal gains without ES. The results shown in figure 9, figure 10, and figure 11 seem that the control using ES-1 is driving in the fuel economy area of engine power, which results are BSFC (Brake Specific Fuel Consumption), ωe map, and the root mean square (RMS) of the power of EM1, EM2, ICE and SOC. It is known that the low BSFC is the high performance of fuel economy (see Dobrivoje (2006)). The drivetrain strategy, i.e., driving strategy of wheels, for the high performance, is that ICE uses only range the high load factors to the engine speed. The results of BSFC and engine speed are examined to investigate the fuel economies of ES1, ES2, ES3, and sample controllers. The results in figure 7 are the driving cycle of second Sunday. The results include the more than 70 km/h speed, and the consumptions of SOC are the highest in all weeks. Figure 8 shows that the sample controller tend to use actively ICE power to drive the drivetrain. On the other hand, the controllers using ES-1, ES-5, and ES0 tend to use the EM2 power to assist the driving of wheels. In the same period, the reference speed of ES-1 is fluctuating around 1, 300 rpm. The results can be recognized from the BSFC - engine speed of drive train shown in figure 9 and figure 10 which show the 3D histogram between BSFC and engine speed. The BSFC histogram by the sample controller spreads over 1, 200 rpm to 2, 700 rpm, and 210 g/kW-h to 240 g/kW-h. Whereas the BSFC histogram of ES0 and ES-5 concentrates near 1, 600 rpm - 210 g/kW-h, the histogram of ES-1 shows near 1, 300 rpm - 210 g/kW-h. Figure 8 indicates the situations; SOC and ICM power for sample controller are high. Operation in the driving assist mode uses the engine mainly. The drive of wheels results in causing the low SOC. As the results of simulations, the final fuel economy of controller using ES-1 is the high performance by 43% compared to sample controller. Table 2. Fuel economies and SOCs using each controller
The fuel economy of the semi-optimal gains without ES is 58.98 mpg for Ts = 10, 000 s shown in figure 5. This value is almost 44.6 % higher than the fuel economy of sample controller for the same time. Figure 5 and figure 6 show the fuel economies for each day. The fuel economies and SOCs at Tend show in Table 2. The fuel economies in figure 5 are decreasing day by day, where the final value is 44.22 mpg. Figure 5 shows that the gains achieving higher performance of fuel economy at the test time are not necessarily able to perform the same performance in total time, Tend . Figure 6 indicates the results of each controller. The daily variations in fuel economy using ES-5 and ES0 255
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Fuel economy [mpg] 59.30 56.62 56.69 44.22 41.44
SOC [%] 64.45 64.45 65.17 64.13 64.97
5. DISCUSSION Here, we point out the key idea and the role of semioptimal gain of the proposed method. The sample controller is decided the speed at t s by using the map data
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Fig. 7. Driving cycle of second Sunday. based on the driver demand power and battery power. The relationship between the fuel economy and engine speed were introduced in subsection 4.2. We verified the sample controller with output gains were able to increasing the fuel economy and the using the convex information is useful for the decision of effective gains (see Koguchi (2015)). Assuming that the semi optimal reference engine speed exists near the output gains decided by convex of fuel economy, this method was proposed. Assuming that the fuel economy can be expressed as Fc (K, ωe∗ , T ), the the following inequalities are satisfied. Fc (K, ωe∗ , T ) ≤ Fc (Kopt , ωe∗ , T ) ≤ max{Fc } ∗ Fc (Kopt , ωe∗ , T ) ≤ Fc Kopt , ωeopt ,T
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This paper has proposed the drive strategy of split hybrid electric powertrain, i.e., controller of HEV drive system, using ES algorithm and semi-optimal gains. Regarding the cost function of the ES algorithm, the simulation results made it clear that the fuel economy is more useful than SOC. From the result, Fc (T ) is used as the cost function in ES with semi-optimal gains. The simulation results for three controllers, ES-1, i.e., ES using the cost function of fuel economy and semi-optimal gains, ES-5, i.e., ES using the cost function of fuel economy and SOC, and all 1 gains, and ES0, i.e., ES using the cost function of fuel economy and all 1 gains indicate that the final fuel economy of ES-1 can be obtained the highest value, 59.30 mpg. The controller using the ES algorithm with semi-optimal gains operates the engine near 1, 300 rpm, BSFC can be obtained near 210 g/kW-h, which is high performance range. By
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Fig. 11. RMS of EM1, EM2, ICE, and SOC; upper left: power of EM1, Upper right : power of EM2, Lower left : power of ICE, Lower right: SOC comparing both the controller without semi-optimal gains and the ES with semi-optimal gains, the controller using ES with the semi-optimal controller can maintain the fuel economy. However, the ES with semi-optimal gain was observed to tend to use the battery on the large change of the driving cycle. The improvement for decreasing of SOC is future work. ACKNOWLEDGEMENTS Some simulation results are a collaboration study with Daichi Ishida, who is a graduate student of our laboratory. We are grateful to Mr. Ishida for helpful his work. REFERENCES Egardt B., Murgovski N., and Pourabdollah M. (2014) “ Electromobility Studies Based on Convex Optimization ”, IEEE Control System Magazine, Vol. 34, No.2, pp. 32 – 49. Lin, C. C., Peng, H., Grizzle, J. W., and Kang, J. M. (2003), “ Power management strategy for a parallel hybrid electric truck ”, IEEE Trans. on Control Systems Technology, Vol.11, No.6, pp.839 – 849. Dextreit C., Kolmanovsky I., V. (2014), “ Game Theory Controller for Hybrid Electric Vehicles ”, IEEE Trans. on Control System Technology, Vol. 22, No. 2, pp.652 – 663. Larsson V., Mardh, L. J., Egardt, B., and Karlsson, S. (2014), “ Commuter Route Optimized Energy Management of Hybrid Electric Vehicles ”, IEEE Trans. on Intelligent Transportation Systems, Vol. 15, No. 3, pp.1145 – 1154. Musardo, C., Rizzoni, G., and Staccia, B. (2005), “ A-ECMS: An Adaptive Algorithm for Hybrid Electric Vehicle Energy Management ”, Proc. the 44th IEEE CDC & ECC 2005, Seville, Spain, pp.1816-1823. Kim, Y., Salvi, A. A., Stefanopoulou, G., and Ersal, T. (2015), “ Reducing Soot Emissions in a Diesel Series Hybrid Electric Vehicle Using a Power Rate Constraint Map ”, IEEE Trans. Vehicular Technology, Vol. 64, No. 1, pp. 2 – 12. Mura, R., Utkin, V., and Onori, S. (2015), “ Energy Management Design in Hybrid Electric Vehicles: A 257
Novel Optimality and Stability Framework ”, IEEE Trans. Control System Technology, Vol. 23, No. 4, pp. 1307 – 1322. Overington, S., Rajakaruna, S. (2015), “ High-Efficiency Control of Internal Combustion Engines in Blended Charge Depletion/Charge Sustenance Strategies for Plug-In Hybrid Electric Vehicles ”, IEEE Trans. on Vehicular Technology, Vol. 64, No. 1, pp.48 – 61. Yasui, T. (2012), “ JSAE-SICE Benchmark Problem2: Fuel Consumption Optimization of Commuter Vehicle Using Hybrid Powertrain ”, Proc. of 10th World Conf. on Intelligent Control and Automation, pp. 606 – 611. Yu. K., Mukai, M., and Kawabe, T. (2013), “ Model Predictive Control of a Power-Split Hybrid Electric Vehicle System with Slope Information ”, Proc. SICE Annual Conf, Vol. 14, NO.17, pp. 2311– 2316. Ahmad, M. A., Azuma, S., Baba, I., and Sugie, T. (2014), “ Switching Controller Design for Hybrid Electric Vehicles ”, SICE Journal of Control, Measurement, and Integration, Vol. 7, No.5, pp.273 – 282. Iyama H., Sudo T., and Namerikawa T. (2015) , “ Fuel Consumption Optimization for an HEV considering Ignition Timing of Engine ”, Proc. of Systems, Control and Information Engineers (SCI’15), CD-ROM. Koguchi, K., Hidaka, K. (2015), “ Fuel Efficiency Strategy for the Hybrid Electric Vehicle by the Simultaneous Perturbation Using the Partitioned Data ”, Proc. 1th IEEJ international workshop on Sensing, Actuation, and Motion Control (SAMCON2015), V19 (CD-ROM). Dobrivoje, P., Mrdjan, J., Steve, M., and Andre R. T, (2006), “ Extremum Seeking Methods for Optimization of variable Cam Timing Engine Operation ”, IEEE Trans. on Control System Technology, Vol. 14, No. 3, pp. 398 – 407. Ariyur, K. B., Krstic, M. (2003), “ Real-time optimization by extremum-seeking control ”, Wiley.