implementation of an equivalent consumption minimization ... · equivalent consumption minimization...

Implementation of anEquivalent ConsumptionMinimization Strategyin a Hybrid truck

D.J. van Mullem

CST.2010.19

Master’s thesis

Supervisory committee:

prof.dr.ir. M. Steinbuch 1

dr.ir. A.G. de Jager 1

dr.ir. J.T.B.A. Kessels2

ir. T.A.C. van Keulen1

1 EINDHOVEN UNIVERSITY OF TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING

CONTROLS SYSTEMS TECHNOLOGY GROUP

2 TNO BUSINESS UNIT AUTOMOTIVE

ADVANCED POWERTRAINS TECHNOLOGY

Eindhoven, March 2010

Abstract

In their attempts to reduce fuel consumption, vehicle manufacturers have developed Hybrid Electric Vehicles

(HEV). These vehicles have two energy converters: usually an Internal Combustion Engine (ICE) and an

Electric Machine (EM). The EM enables energy recovery during braking or driving down hill, this energy can

be used at a latter, more convenient, time to propel the vehicle.

The algorithm that deals with the power split between the ICE and the Electric EM of a hybrid vehicle, is

called the Energy Management Strategy (EMS). The main objective of such an algorithm is to minimize

fuel consumption. EMS methods can be divided into two classes: non-causal methods that require exact

knowledge of the upcoming velocity and load trajecotries, and causal methods, that try to minimize fuel

consumption without this a-priori knowledge.

Optimal control theory can be used to rewrite the non-causal optimization problem to an optimization in-

dependent of time. The optimal solution is characterized by one constant Lagrange parameter of which the

value is determined by the velocity and load conditions. Online estimation of this Lagrange parameter makes

the method suitable for real-time implementation. Estimation can be done by feedback on the battery State-

Of-Charge (SOC). Hence, a real-time implementable strategy is obtained, in literature often referred to as

Equivalent Consumption Minimization Strategy (ECMS).

Nevertheless, after the simplification of the optimization problem, to find an optimal powersplit in real time,

it is still required to solve a nonconvex optimization problem with limited on-board computational power.

To cope with this constraint, the optimization problem is solved off-line for different values of the Lagrange

parameter, rotational speed and torque requests. The resulting optimal look-up tables can be stored in a

onboard vehicle Electronic Computation Unit (ECU).

To develop the ECMS for a hybrid DAF CF, a simulation model is used that contains the hybrid supervisory

controller and the several drivetrain components (ICE, EM and batteries). This simulation model is validated

on the chassis dynamometer at the Eindhoven University of Technology for several distance velocity profiles.

The cumulative fuel consumption error between simulation and experiment is within 2%.

The online estimation of the Lagrange parameters, requires feedback on the SOC. For real-time implementa-

tion of the ECMS, the feedback gain and initial value of the Lagrange parameter require tuning. The validated

simulation model is used to find an optimal setting, and to determine their influence on the vehicle’s fuel

consumption. Simulations result show that the ECMS has a fuel consumption reduction in the range of 1%

to 4%, when compared to the existing heuristic controller.

Samenvatting

Om het brandstofverbruik van een voertuig te reduceren hebben automobiel fabrikanten Hybride Elektrische

Voertuigen (HEV) ontwikkeld. Deze voertuigen zijn naast de standaard verbrandingsmotor (Internal Com-

bustion Engine, ICE) uitgerust met een Elektrische Machine (EM). De EM maakt het mogelijk om energie

terug te winnen tijdens remacties of tijdens bergaf rijden. Deze energie kan later gebruikt worden, om het

voertuig aan te drijven.

Het algoritme dat de vermogensvraag regelt tussen de verbrandingsmotor en de elektrische machine in een

hybride voertuig wordt een Energie Management Strategie (EMS) genoemd. Het voornaamste doel voor dit

algoritme is het minimaliseren van het brandstofverbruik. EMS methodes kunnen in twee groepen gesplitst

worden: niet-causale methodes die exacte kennis vereisen over het komende snelheidstraject en causale meth-

odes die zonder deze kennis proberen brandstofverbruik te reduceren.

Optimale Control theorie kan gebruikt worden om het niet-causale optimalisatieprobleem te herschrijven

naar een optimalisatie, onafhankelijk van tijd. De optimale oplossing wordt dan gegeven door één snelheids-

en last afhankelijk Lagrange parameter. Terugkoppeling op de referentiewaarde van de batterij wordt gebruikt

om deze Lagrange parameter online te schatten. Deze oplossingsmethode wordt Equivalente Consumptie

Minimalisatie Strategie (ECMS) genoemd, en maakt real-time implemenatatie mogelijk.

Hoewel hiermee het optimalisatieprobleem versimpeld wordt, blijft de beperkte rekenkracht van de controller

op het voertuig een beperkende factor bij het oplossen van het resterende non-convexe optimalistatieprob-

leem. Daarom is het probleem off-line opgelost voor verschillende waardes van de Lagrange parameter, het

toerental van de aandrijflijn en het gewenst koppel. De resulterende optimale vermogenssplit, kan vervolgens

worden opgeslagen in een voertuig controller (Electronic Computation Unit, ECU).

Om de ontwikkeling van de ECMS mogelijk te maken, is een simulatiemodel waarin alle aandrijflijn com-

ponenten (ICE, EM en batterijpakket) zijn gemodelleerd gebruikt. Dit simulatiemodel bevat de besturing-

shiërarchie zoals deze ook op de ECU van de DAF CF aanwezig is. Het simulatiemodel is gevalideerd voor

verschillende afstand snelheids trajectories. Brandstofverbruik over een ritcyclus kan daarmee voorspeld wor-

den binnen 2% nauwkeurigheid.

Om de Lagrange parameters online te schatten, is een terugkoppeling van de batterij refentiewaarde nodig. De

waardes die gebruikt worden om deze terugkoppeling te realiseren, moeten vooraf bepaald worden voor het

realtime implementeren van ECMS op een voertuig. Het gevalideerde simulatie model is gebruikt om deze

terugkoppelings kalibratiewaardes te vinden en hun invloed op het brandstofverbruik te onderzoeken. Simu-

laties tonen aan dat ECMS een brandstofbesparing van 1 tot 4% realiseert, in vergelijking met de bestaande

heuristische regelaar.

Contents

Abstract i

Samenvatting ii

1 Introduction 2

2 Hybrid vehicle specification 3

2.1 Drivetrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Internal combustion engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Electric machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5 Control hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.6 Vehicle model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Hybrid electric vehicle control strategies 8

3.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Rule based controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Equivalent consumption minimization strategy (ECMS) . . . . . . . . . . . . . . . . . . . . . 11

3.5 Energy managment strategy using route information . . . . . . . . . . . . . . . . . . . . . . . 12

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Implementation of Equivalent Consumption Minimization Strategy 14

4.1 Off-line optimization for positive torque request . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 Negative torque request . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Simulation model validation 18

5.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

CONTENTS 1

5.2 Road load settings and drive train properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.3 Engine map validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4 Transient fuel consumption validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Simulation results 29

6.1 Drive cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.3 Comparison with heuristic controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7 Conclusions and recommendations 34

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

A Appendix A: Dynanometer Control Scheme 37

Bibliography 38

CHAPTER 1

Introduction

Hybrid Electric Vehicles (HEV’s) have, at least, two energy converters: usually an Internal Combustion Engine

(ICE) as prime mover, and an Electric Machine (EM) as secondary converter. The EM enables energy recovery

during braking or driving down hill. This energy can be used at a latter, more convenient, time to propel

the vehicle. The supervisory control algorithm, dealing with the balanced generation and re-use of the stored

energy, is called Energy Management Strategy (EMS).

Several contributions have been made regarding the EMS design for HEVs, see, e.g., [12, 16] for an overview.

EMS methods can be divided in two classes. Firstly, non-causal methods [4] that require exact knowledge

of the power and velocity trajectories and secondly, causal or real-time implementable methods [5] that try

to minimize fuel consumption without knowledge of the upcoming trajectories. In general, the non-causal

strategies are used to benchmark and to design real-time implementable strategies.

One method to obtain such a causal solution is the method of Lagrange, which simplifies the fuel minimiza-

tion problem to an optimization independent of time. This is exploited by real-time strategies that estimate

the Lagrange parameter based upon real-time available vehicle information, e.g., the battery State-Of-Charge

(SOC) [10]. Nevertheless, assuming that the Lagrange parameter could be predicted or estimated in a suitable

way, the resulting optimization is non-convex. Furthermore, for a real-time EMS, additional demands on the

EMS are imposed by limited on-board computational power and battery SOC estimation accuracy.

In this report the real-time EMS that estimates the feedback parameter online, as presented in [8, 10], is im-

plemented in a DAF CF. Since on-board computational power is limited, real time implementation requires

extra effort. Therefore, a computationally efficient method to implement the remaining non-convex optimiza-

tion problem is presented in which the optimization problem is solved off-line for different values of the

Lagrange parameter, crankshaft rotational speeds, and torque requests. The resulting optimal torque split is

stored in look-up tables that can be implemented in the onboard vehicle Electronic Computation Unit (ECU).

To facilitate the development of an EMS on the DAF CF, a simulation model of the hybrid vehicle is used in

which the different controllers of the gearbox, battery, engine and electric machine are modeled. This model

is validated on several distance velocity trajectories, relevant for trucks on a chassis dynamometer. The goal

of the validation, is to predict fuel consumption within an accuracy of 5 %. Besides, the simulation model is

used to obtain tuning rules for the SOC feedback parameters.

This report is organized as follows: in Chapter 2 the vehicle model and the different components are pre-

sented, Chapter 3 gives an overview of different EMS methods. Chapter 4 describes the implementation of a

real-time EMS for the given vehicle configuration. The method that is used to validate the simulation model is

presented in Chapter 5. The simulation results to derive tuning rules for the feedback gain and a comparison

with the existing rule-based strategy are given in Chapter 6. Finally, conclusions and recommendations are

given in Chapter 7.

CHAPTER 2

Hybrid vehicle specification

The hybrid vehicle, used for testing and which is simulated, is a DAF CF 65. First the drivetrain components

as well as their models used for simulation Since the components of the drivetrain which are described in

this chapter are used both in the simulation model, as well as for the development of the Energy Management

Strategy (EMS) they are introduced first. After that the control hierarchy and the vehicle model is presented.

2.1 Drivetrain

The truck is an two axle configuration DAF CF, with a gross vehicle weight of 8230 kg. It is equipped with

a hybrid driveline, consisting of an Electric Machine (EM) and an Internal Combustion Engine (ICE). The

components have a parallel hybrid configuration, so the two sources may operate in parallel to accelerate the

vehicle. Physically, the EM is placed between the clutch and gearbox. A schematic overview of the driveline is

given in Figure 2.1.

Figure 2.1 / Schematic overview of the hybrid driveline

2.2 Internal combustion engine

The internal combustion engine is the primary power source of the vehicle. The main specifications of this

engine are given in Table 2.1. The engine is modeled by a non-linear static map, relating the engine torque

Tice and rotational speed ω towards mass fuel rate mf . Such a map does not take thermal and transient effects

into account, but has great advantages in terms of calculation speed. To obtain accurate values for this engine

map, a validation of the fuel map is performed and the resulting fuel map is given in Figure 2.2. More details

on the validation procedure are given in Chapter 5


Table 2.1 / Engine specificationsEngine displacement 5883 [cm3]

type 6 cylinder inline, 24 valves

max power 185 kW

max torque 910 Nm @ 1600 RPM

230

230

230

240

240

240

240

250

250

250

250

250

270

270

270

270

290

290

290

290

310310

310

330330

330

370 370

370

Brake Specific Fuel Consumption [g/kWh]

rotational velocity [RPM]

Tor

que

[Nm

]

800 1000 1200 1400 1600 1800 2000 2200 24000

100

200

300

400

500

600

700

800

900

Figure 2.2 / Fuel consumption in [g/kWh].

The fuel consumption is obtained by integrating the mass fuel flow at the instantaneous engine speed and

torque. In equation form it holds that:

Pf = mf (Tice, ω) HLV (2.1)

Here, Pf is the amount of power delivered by the fuel, and HLV the lower heating value of the fuel, for diesel

42.5 MJ/kg.

2.3 Electric machine

The secondary power source is an electric motor/generator coupled to a battery through an inverter. The

electric motor is an internal permanent magnet type synchronous motor. The combined efficiency of the

electric motor and inverter are depicted in Figure 2.3. Both the inverter and electric motor are liquid-cooled.

The required electric power Pb as function of the EM efficiency ηem(ω, Tem) is given by:

Pb(ω, Tem) = f(Tem, ω) (2.2)

In which Tem is the torque output from the EM. The model has the drawback that it does not take spinning

losses into account when Tem = 0. This does not correspond to the physical behavior of the EM. However,


20

20

20

20

4040

40

4050

50

50

5060

60

60

6070

70

70

70

80

80

80

80

85

85

88

88

90

90

Rotational speed ω [rpm]

Tor

que

[Nm

]

EM efficiency [%]

0 500 1000 1500 2000 2500

−400

−300

−200

−100

0

100

200

300

400

Figure 2.3 / Electric motor and inverter efficiency [%].

since characterization of the EM without the other drivetrain components is difficult, this model is used for

EMS development.

2.4 Batteries

The power for the electric motor is supplied by Magnesium type lithium-ion batteries with a total capacity

of 2.0 kWh. The total package consists of two parallel modules with 48 cells placed in series. The nominal

voltage of the package is 340 Volt. The State of Charge (SOC) of the battery depends on the battery current Isaccording to:

SOC(t) =Q(t)

Qmax=

∫ t

0

Is(t)

Qmaxdt+ SOC(0) (2.3)

in which Q(t) is the battery charge as function of time and Qmax is the maximum charge capacity of the

battery. For the losses in the battery, an internal resistance model is used:

Ps = Is V = Pb +

(PbV

)2

R(SOC) (2.4)

Here, V is the battery voltage, and R a SOC dependent resistance, the relation is shown in Figure 2.4.


0 0.2 0.4 0.6 0.8 12

2.5

3

3.5

4

SOC

Res

ista

nce

[mΩ

]

SOC depending resistance for battery cells

Figure 2.4 / SOC depending resistance of battery cells

2.5 Control hierarchy

The inverter, the batteries, the engine, the EM and the transmission all have their own control unit, supervised

by the hybrid controller. This is shown schematically in Figure 2.5. In this thesis, only decisions on supervisory

level are considered. Gear shifts, torque allocation and so on are performed by the underlaying controllers and

are therefore not taken into account.

Hybrid Controller

Transmissioncontroller

EMcontroller

ECUBattery

Controller

Gearbox Inverter ICE BatteryEM

Figure 2.5 / Structure of the control hierarchy on the truck

The main control variable for the controller is the split ratio u, which represents a power-split ratio between

the primary and secondary power source, here defined as:

Tice = u Treq (2.5)

Tem = (1− u) Treq

In which Treq represents requested torque by the driver. An overview of the drivetrain topology is given in

Fig. 2.6.


+

Figure 2.6 / Drive train topology.

2.6 Vehicle model

For simulation purposes of the hybrid truck and to compare fuel consumption for different velocity trajecto-

ries and EMS controllers, the vehicle dynamics are modeled by means of a point mass for the vehicle inertia.

As input for this model the current speed is compared with a desired setpoint for the speed, where a Propor-

tional Integrating (PI) controller actuates the accelerator and brake pedal.

y(t) = kp(v(t)− vdes) + ki

∫ t

0

(v(τ)− vdes)dτ (2.6)

Here y is a normalized pedal position, v the actual velocity and vdes the actual velocity. Note that the controller

will have to translate a positive value of y in a accelerator pedal actuation, and a negative value into brake pedal

actuation.

Road load and drive train losses:

the road load force is modeled with a second order function, depending on the vehicle speed. The drive train

and road load loss model in the simulation is compared with the losses encountered at the dynamometer.

More details about these models are in the validation procedure, presented in Chapter 5.

CHAPTER 3

Hybrid electric vehicle control strategies

HEVS can achieve better fuel economy by using two different energy sources. Their main advantage is that the

kinetic energy can be (partially) recovered during braking or driving down hill. To improve the performance

of such vehicles compared to regular internal combustion engine driven ones, they depend on their EMS, see

e.g. [3]. In this Chapter an overview of different control strategies for parallel hybrid-electric vehicles will be

presented. Addressed first are heuristic control and the current controller implemented on the DAF. Secondly,

various optimization techniques are covered and a derivation of the Equivalent Consumption Minimization

Strategy (ECMS) is presented.

3.1 Problem statement

The goal of the EMS is to minimize fuel consumption. It is not necessary to minimize the fuel mass-flow rate

at each time instant, but rather total fuel consumption. The aim is to find the value of the control input u(t)

which minimizes the cost function Jf (t, u) defined as:

Jf =

∫ tf

0

mf (t, u, ωeng) HLV dt (3.1)

For a hybrid vehicle, the drive mode that minimizes the problem stated in (3.1), corresponds with a purely

electric strategy where all the traction power is provided by the battery. However, the energy recovered by

regenerative braking is not sufficient to sustain battery SOC. In order to have a charge sustaining EMS, it is

required that the initial SOC is equal to the end SOC level. This is often referred to as the end-point constraint:

SOC(tf ) = SOC(t0)→∫ tf

0

Ps(u, t)dt = 0 (3.2)

Besides this constraint on the battery, the different components should deliver the requested amount of power

from the driver at all times:

Treq =(u Tice + (1− u) Tem

)(3.3)

There are several techniques to solve this problem for a given hybrid vehicle configuration. Fuzzy logic or

rule-based strategies can easy be implemented, but they don’t guarantee an optimal result for all situations.

Other solution techniques such as dynamic programming are able to calculate an optimal solution. However,

to find the optimal solution, knowledge of the complete driving cycle is required and computational efforts

are high.


3.2 Rule based controllers

A straight forward EMS is the heuristic control strategy as stated in [12]. This strategy makes use of event-

triggered rules and uses the EM to assist the engine in torque production. Typically, heuristic rules are based

upon vehicle velocity, battery SOC and torque request. An example, given in [12] is as follows:

Heuristic controller

• if v < vmin the electric motor is used alone (u = 0)

• if v ≥ vmin and Treq < Tmax(ωeng), the engine is used alone (u = 1)

• If SOC is below threshold, the engine is forced to deliver excess torque to recharge the battery.

• If SOC is too high, the motor is used alone.

• Above Tmax(ωeng) the engine maximum torque is required and the EM is used to assist the engine.

In which v is the vehicle speed, vmin is a setpoint for minimum vehicle speed, Tmax(ω) is the maximum

engine torque at the current engine speed (ω) and SOC is the current SOC of the battery. The battery can

only be used between a certain minimum and maximum SOC level SOCmin and SOCmax. When the SOC

is outside this region, the lifespan of the battery will detoriate.

Existing controller

Heuristic controllers can be extended with more rules states and thresholds on e.g. brake and accelerator

pedal as stated in [12]. The hybrid DAF truck which is considered in this thesis also has a heuristic controller

implemented. This controller distinguishes two different modes:

Electrical vehicle mode:

in this mode the truck drives with the ICE disengaged, running solely on the Electrical motor. Split ratio u

is therefore set to zero, and the clutch is opened. This mode is enabled when operator demand torque is

between the limits of the electric motor and vehicle speed is lower than 50 km/h. This mode doesn’t improve

fuel consumption but is rather an extra functionality offered by a hybrid vehicle.

Drive mode:

In this mode the split value, u, is depending on operator torque, Treq and SOC of the battery. To keep the

SOC level between limits, first of all the amount of EM-torque is limited by the following rules:

• for SOC < SOCmin the ICE is run with slightly more torque in order to charge the battery. This

regeneration factor is depending on SOC and engine speed.

• for SOC > SOCmax no charging can occur, to maintain battery lifetime.


The resulting torque command is divided by the torque request to get the split ratio. The maximum regen-

eration torque, when the vehicle is slowing down, is determined by the EM limits. In order to use the stored

electrical energy, a rate limiter is used on the actual engine torque demand. This limit is reset on every clutch

opening and increases over time. By slowing down the response of the engine, the ‘gap’ in drive torque needs

to be filled with the electric machine. In this way, the EM runs most of the time with low vehicle speeds, so

inefficient use of the ICE is avoided.

Since thresholds for heuristic controllers have to be chosen in advance, these kind of strategies can not guar-

anteed to be optimal, especially when considering different driving cycles. Due to the nonlinear behavior of

the propulsion components, every cycle has another optimal solution and therefore rule-based strategies can

not be proven to be optimal in terms of fuel consumption. The main advantage is that heuristic controllers are

intuitive to conceive and easy to implement. If properly tuned, they can provide good results in terms of fuel

consumption reduction and charge sustainability. However, the behavior strongly depends on the choice of

thresholds that are involved. This may result in limited robustness of the heuristic controller, under changing

vehicle operation condition.

3.3 Optimal Control

Dynamic programming

The mathematical tool that is used for the optimization of (3.1) subject to (3.2) is the method of Dynamic

Programming (DP), as e.g. used by [4]. It is commonly used for optimization over a given time period. It gives

an optimal solution when there is a-priori knowledge about the driving cycle. It can be used to minimize the

total amount of fuel as defined in (3.1). Since dynamic programming requires gridding of the state and time

variables, discretization of these variables is required.

The problem requires the introduction of a cost-to-go matrix, defined as the cost along the optimal trajectory

passing through the ’point’ in the time-space to the target point with the desired SOC(tf ). Due to the dis-

cretization of the state space, the values of Ps are either interpolated or approximated by the nearest available

values on the grid. The energy that is introduced or deleted by this method determines whether the adopted

state-space discretization is acceptable or the number of points must be increased.

Analytical optimization method

Direct numerical optimization is inherently non-causal and requires substantial amounts of computational

time. A more practical approach is based on the minimum principle of Pontryagin. This method introduces

a Hamiltonian function to be minimized at each time. First, in order to minimize the cost function (3.1), with

the constraint over the final state of charge of the battery with (3.2). The dynamics from the system are defined

by:˙SOC = −Ps (3.4)

The Hamiltonian for this system can than be defined as:

H(u, t) = mf (u, t) HLV + λ(t)(−Ps) (3.5)

The parameter λ, which corresponds to the adjoint state in classical optimal control theory, is described by


the Euler-Lagrange equation:d

dtλ(t) = −∂H(u, t)

∂SOC= 0 (3.6)

When the influence of the SOC on the internal battery parameters is neglected, λ = 0 and therefore λ will be

constant and> 0. The necessary condition of optimality using the minimum principle are therefore met. With

this result the optimization can be reduced to searching for one constant parameter λ0 that gives minimal

fuel consumption for a given cycle, so with (2.1), (3.5) can be written as:

minu,λ

J(u, t) = minu,λ

(Pf (u, t) + λ Ps(u, t)) (3.7)

λ can here be physically interpretated as the relative incremental cost of the primary and secondary power

converter. For a known velocity and power trajectory, numerical methods can be used to find an optimal

value of the Lagrange parameter, λ∗, and therefore an optimal powersplit trajectory u∗(t), 0 ≤ t ≤ tf which

minimizes fuel can be defined as:

u∗, λ∗ = arg minu∈U,λ∈Λ

Jf (3.8)

Depending on the modeling of the components (3.7) can be solved with Dynamic Programming for nonlinear

and non convex functions or Quadratic Programming for quadratic functions. The non-convex optimization

problem is now reduced to finding the value of λ∗.

3.4 Equivalent consumption minimization strategy (ECMS)

The value of λ∗, which can be obtained with for instance DP or bisection, resembles to one drive cycle.

The calculated optimal value of λ∗ for a given trajectory can be used to find the optimal split ratio u for

any point in time in order to minimize the fuel consumption. However, over- or underestimation yields

towards under- or overcharging of the battery. Since exact knowledge of the upcoming driving conditions is

in real-time applications not available, a fixed value for λ∗ is not adequate to prevent the battery from over- or

undercharging and therefore a charge sustaining EMS.

However, once λ∗ has been estimated, it can also be used in a strategy without a-priori knowledge about the

cycle. There are various techniques to adapt the value of λ to the driving conditions at the current time. In

this way fuel consumption can be lowered substantially without the need of knowing the full driving cycle in

advance.

In literature [5], λ is referred to as the fuel equivalence factor, where the name Equivalant Consumption

Minimization Strategy is derived from. To keep the SOC between the desired limits, in Koot et al. [10] feedback

on the SOC is used. In this case it is a PI-controller with a limited integrating action towards a desired value

for the SOC.

λ(t) = λ0 +Kp(SOCdes − SOC(t)) +KI

∫ τ

0

(SOCdes − SOC(t))dτ (3.9)

As stated before, this algorithm can be used for online calculation of the equivalence factor and than compared

with the optimal solution obtained by the result of 3.1.

The estimation of λ(t) can be done in several more different ways, one way is pattern recognition on the

drivers profile. Another extension to the strategy of (3.9) is the adaptive strategy proposed by van Keulen et

al.[8]. This uses an estimate of the future recoverable electric energy using online available parameters velocity


and elevation. The estimated amount of brake power to stop a vehicle with a predefined velocity profile is equal

to:

Pbr = (m a+m g sin (α)) v(t) (3.10)

Where a and α represent the assumed deceleration rate and the expected road angle respectively,m the vehicle

mass and v is the expected velocity path. Since it involves a heavy duty, parallel hybrid truck, the approach

uses the assumption that there is a constant average deceleration rate. The recoverable brake power in this

model in time is dependent on the road load Prl (which is described by a third order polynomial of the

expected velocity path), the brake power Pbr and engine drag power Pdrag. Brake power is delivered until the

maximum generator power Pgenmax is reached:

Pr = max(

0, min(Pgenmax, Pbr − Prl − Pdrag))

(3.11)

The expected future recoverable electric energy, given the current vehicle velocity and elevation, can estimated

by integrating the recoverable brake energy over the estimated stop time tstop, while not exceeding maximum

battery capacity ∆SOCcap:

∆SOCrec(v, α, t) = min(∫ tstop

0

Pr V

Qmaxdτ , ∆SOCcap

)(3.12)

This finally leads to a set point for the equivalence factor which now becomes:

λ(SOC, v, h, t) = λ0 +K(SOC(0)−∆SOCrec − SOC(t)) (3.13)

Instead of the vehicle recoverable brake power, one could think of other vehicle parameters that can be used

to estimate the equivalent fuel cost.

3.5 Energy managment strategy using route information

The equivalent consumption minimization strategy can be extended even further if there is route informa-

tion available from on-board Geographical Information Systems (GIS). With the knowledge of the upcoming

route information, a future velocity profile can be estimated. This is done by van Keulen et al. [9] Especially

optimizing the vehicle braking trajectories can be used to maximize the energy recuperation.

Another advantage of the ECMS is that the desired SOC level, SOCdes, is time dependent, and therefore

making the reference SOC dependent for e.g. the elevation of the future driving profile. This could also help

to efficiently charge the battery before entering an enviromental zone, e.g. a city center.


3.6 Conclusion

In this chapter different methods to control HEVs are compared. In general, heuristic controllers provide sub-

optimal results. Besides that tuning these controllers takes a lot of effort, they cannot be proven to be optimal.

An ECMS controller with online estimation of the vehicle parameters can obtain results close to optimal,

while tuning efforts are minimal. However, information about the efficiency of the components is required.

Nevertheless, the focus in the remainder of this thesis lays on implementing and evaluation of an ECMS

controller for a hybrid vehicle. For ease of implementation there is chosen to not considering any integrating

action into the Lagrange parameter estimation, which simplifies (3.9) to:

λ(t) = λ0 +K(SOCdes − SOC(t)) (3.14)

CHAPTER 4

Implementation of Equivalent Consumption Minimization

Strategy

In the previous chapter it was shown that the method of Lagrange multipliers can be applied to arrive at an

optimization independent of time. Besides, it was noticed that the optimal Lagrange multiplier (λ) is constant

and depends on the actual vehicle and drive cycle characteristics. These important observations are used to

design a real-time EMS. Since processor load plays an important role in real-time implementation, efforts have

to be made in order to reduce computational burden: the EMS is implemented on a standard ECU. Therefore,

an accurate calculation of all possible split ratios, u, taking into account the drive trains components, takes

too much effort to perform online. To obtain acceptable computation times, the introduction of look-up tables

is proposed. For a complete set of Treq, λ0 and ω, an accurate calculation of the optimal split ratio based on

(3.7) is used (section 4.1). Since fuel consumption data for Treq < 0, is not available and hard to determine for

the given vehicle setup, implementation for negative torque requests is done on a heuristic base. To find an

instantaneous optimal split ratio, (3.8), the vehicle model of chapter 2 is used. The aim is to find a solution for

u∗, while still fulfilling the driver torque demand Treq which follows from the desired trajectory. The upper

and lower limits on Treq are given by:

(Tem,min(ω)− Tice,min(ω)) ≤ Treq ≤ Tice,max(ω) (4.1)

the subscripts ‘min’ and ‘max’, indicate the lower and upper limits of the EM and ICE, which are defined

as function of rotational speed, ω. Notice that the maximum drive train torque is limited by Tice,max and

therefore only depends on the ICE torque. Therefore, the hybrid system is not used to improve the acceleration

and gradability performance.

4.1 Off-line optimization for positive torque request

To obtain a real-time optimal split ratio, which is able to run on the ECU, an off-line numerical optimization is

performed. The resulting optimal solution for all ‘operating points’ is stored in lookup tables. The schematic

overview is presented in Figure 4.1. The discrete grid of operating points where the split ratio needs to be

defined is indexed by uni,nj . The limits on the EM are given by Tem,max and Trgn. For every point with

Treq > 0 the following calculation is performed:

• Step 1: define a vector of operating points for Treq, ω and λ. Vectors are indicated in boldface:

Treq = 0 +mi ∆T, mi ∈ [0 . . . ni] with ∆T =Tice,maxni

(4.2)


Figure 4.1 / Schematic overview of implementation.

ω = ωmin +mj ∆ω, mj ∈ [0 . . . nj ] with ∆ω =ωmax − ωmin

nj(4.3)

λ = λmin +mk ∆λ, mk ∈ [0 . . . nk] with ∆λ =λmax − λmin

nk(4.4)

Here ni, nj and nk are a discrete number points for which the optimal split ratio will be calculated. Due

to memory limitations of the ECU, the number of points is limited. For ni, nj and nk the values are

48, 21 and 8 respectively. For both the speed ω and torque T , these numbers are taken from the already

available torque and speed vectors.

• Step 2: a feasible EM torque region for every (ni × nj) point given by (4.2) and (4.3) is defined by:

Tem = Tem,min +ml ∆Tem, ml ∈ [0 . . . nl] with ∆Tem =Tem,max(ω)− Trgn

nl(4.5)

here the maximum amount of regeneration torque Trgn is defined by:

Trgn = max(

(Treq − Ticemax(ω)), Temmin

(ω))

(4.6)

Immediately from (2.6), Tice follows:

Tice = Treq −Tem (4.7)

Since this calculation is performed off-line, and is therefore not limited by the ECU memory, ∆Tem can

be kept small, to ensure an accurate calculation of the optimal split ratio.

• Step 3: the equivalent costs can be calculated for the whole set of (ni × nj × nk) operating points by

substituting (4.7) into (2.1), (2.2) and taking into account battery losses by (2.4). The optimal split ratio

for positive torque requests can be calculated by:

u+i,j,k =

arg min(Pf + λ(k) Ps)

Treq(i) ω(j)(4.8)


Rotational velocity ω [rpm]

Tor

que

requ

est [

Nm

]

λ = 2.1

1000 1500 2000 25000

100

200

300

400

500

600

700

800

900


Tor

que

requ

est [

Nm

]

λ = 2.4

1000 1500 2000 25000

100

200

300

400

500

600

700

800

900


Tor

que

requ

est [

Nm

]

λ = 2.7

1000 1500 2000 25000

100

200

300

400

500

600

700

800

900


Tor

que

requ

est [

Nm

]

λ = 3

1000 1500 2000 25000

100

200

300

400

500

600

700

800

900

Full electric

Assist

no EM use

Charge

Figure 4.2 / Iso-split contours for various values of λ. The split-ratio is given as function of Treq and ω. For

λ = 2.2 the battery is nearly charged, and SOC decreases for increasing values of λ. A low speed

and torque region is present, where full electric drive is preferred. The recharging area ‘grows’

for a depleting battery, and vice versa for the assist area.

The result of this calculation for different values of λ is given in Figure 4.2. The split-ratio u+ is given as

function of Treq and ω. For a constantK, and SOCdes, λ is proportional to the SOC. For λ = 2.2 the battery is

charged, and SOC decreases for increasing values of λ. A low speed and torque region is present, where full

electric drive is preferred. The recharging area ‘grows’ for a depleting battery, and vice versa for the assist area.

In the figure, the area where the ICE has its maximum efficiency can be recognized: when engine speeds is

around 1200 RPM and there is a low value Treq, the strategy tries to charge the battery in order to get the

ICE at its maximum efficiency. Besides the operating area from the EM can be seen: when the battery is

completely charged (λ = 2.2), the split-ratio is set to zero only when the EM is able to deliver the required

amount of torque. Between operating points, u is determined by linear interpolation.

4.2 Negative torque request

For Treq < 0, two different situations can occur. Firstly, the area which is indicated gray in Figure 4.1, the drive

train is commanded ‘engine only’ mode. Secondly, when (Treq < Tdrag) the EM recuperates the remaining


kinetic energy. Since fuel consumption data for negative torque output is not available, these cases are handled

in a heuristic way. It is assumed that engine braking is more efficient than idling the engine. This situation

changes when stop-start is enabled, than the engine stops when Treq < 0 and engine braking is not used.

u∗ (ω, Treq) =

u+ (Eq. 4.8) for Treq > 0

1 for Tdrag ≤ Treq ≤ 0

Tdrag/Treq for Treq < Tdrag

(4.9)

4.3 Conclusion

The instantaneous split ratio u, is controlled on supervisory level. Therefore, under some conditions the

desired values of this split ratio will be overruled by lower level controllers. This occurs for instance when

performing a gearshift. Another limiting factor is the driveability from the drivetrain: when a clutch closure

is performed, engine torque can not be changed instantaneously. This may lead to sub-optimal results. The

ECMS is implemented on the DAF CF, but for first experiments, a simulation model is preferred. In the next

chapter the validation of the simulation model is described. In Chapter 6, this simulation model is used to

find the values for the SOC-feedback algorithm.

CHAPTER 5

Simulation model validation

The simulation model as presented in chapter 2 consists of the hybrid controller, the drive train component

models, the vehicle model, and the road load characteristics. It is used to validate the existing heuristic con-

troller. To verify the simulation results, several speed-distance trajectories are run, both in the simulation

model and with the test vehicle on the chassis dynamometer, which is available at the TU/e.

Development of the EMS is more practical in a simulation environment than it is on a chassis dynamometer.

Furthermore, to reliably estimate the influence of EMS parameters on fuel consumption, a validation of the

simulation model is essential. Unfortunately, the EMS version implemented in the vehicle is unknown and

as a result, several threshold for the EMS controller need to be found. The validation is performed to match

threshold from the existing controller, have rotational speeds (and therefore drive train characteristics) within

acceptable limits, and check the cycle tracking behavior. The final goal is to obtain a fuel accuracy between

simulation model and chassis dynamometer within 5%.

Firstly, road load and drive train properties, of the vehicle and in the simulation model, are compared with

each other. Secondly, the engine fuel consumption is measured at different engine operating points. Both the

ECMS, and the simulation fuel consumption results, use a the static engine map. Finally, using the results

obtained for drive train efficiency and vehicle characteristics, two velocity profiles are repeatedly driven to

validate the simulation model and the reproducibility of the dyno measurements.

5.1 Test setup

The Heavy Duty Chassis Dynamometer‘, at the Eindhoven University of Technology, is build in order to

fulfil a broad spectrum of automotive test applications. Depending on the application, testing can be done at

circumferential speeds up to 225 km/h. Figure 5.1 shows the test vehicle on the dynamometer. For the purpose

of this research, several safety precautions are added to the system and the velocity tracking controller is tuned.

The test vehicle is equipped with a fuel flow meter to accurate measure fuel consumption. A schematic

overview of the complete setup of the chassis dynamometer and the safety systems is given in Appendix A.

To enhance reproducibility of the test results, the test vehicle is equipped with a drive robot, which is able to

actuate the accelerator and brake pedal. The velocity controllers, that are used in the simulation model and

on the dyno, have a PI-velocity controller and track a reference velocity as function of the driven distance.

Due to the stop-times (idling), it is more difficult to implement a distance based controller, than a time based

controller. However, this way of drive cycle testing has an advantage over the usually used time-speed mode:

different vehicle configurations always drive the same distance, but when vehicle weight is higher, it takes

a longer time to reach the target destination. This is more comparable to real life situations, where drivers

accept longer driving times when a truck is loaded.


Figure 5.1 / DAF CF on the chassis dynamometer at the Eindhoven University of Technology.

5.2 Road load settings and drive train properties

testing procedure

First of all, the losses in the drive train need to be characterized. By means of a coast down measurement,

the drive train steady state losses (independent of the vehicle velocity) are determined. The hybrid system is

unplugged and the gearbox is set to neutral. The chassis dynamometer speeds up the wheels to 95 km/h. The

deceleration time can be used to find the steady state drive train losses. These proved to be:

Tloss,wheels = cr mdyno g = 378 [Nm] (5.1)

here, cr is the rolling resistance coefficient, mdyno is the vehicle mass on the dyno, and g is the gravitational

constant. Since the weight distribution of the vehicle is known, cr can easily be deduced from these tests. In

the second part of the validation, the engine map is validated on the chassis dynamometer and, therefore, the

torque and speed dependent losses require modeling as well. The drivetrain losses are model by a torque loss

model for the differential:

Tloss,diff = Tss + ωinput kω + Tinput kT(5.2)

in which, ωinput and Tinput represent the final drive input speed and torque, respectively. Tss is the steady

state loss torque, kω and kT

are an input speed dependent and input torque dependent loss factor. To find

the appropriate values for these loss factors, the cycle in Figure 5.2 is driven. The torque at the wheels, on the

dyno, is compared with the torque in the simulation model. The simulation model is be tuned to match the

drivetrain losses. The results are given in the next section. For the torque at the wheels it holds that:

Twheels = Tice1

Rwrgb fd + Tloss,diff + Tloss,wheels (5.3)


Where Tdyno is the torque measured at the dynamometer, Rw is the wheel radius, rgb is the gearbox ratio,

and fd is the final drive ratio of the truck.

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100Distance − Velocity profile

distance [m]

Vel

ocity

[km

/h]

SimulationDyno

Figure 5.2 / Validation profile

Besides the loss models (5.2) and (5.3), the road load settings for the simulation model and on the dyno have

to be in accordance with each other. The total driving resistance has to be specified for the simulation model

as well as for the dyno. Although they should deliver the same resistance force there are differences in the

calibration values for both systems. The resistance experienced by the vehicle is given by:

Fres = Froll + Faero (5.4)

= m g cr1 + cr2 v + 1/2 ρair Cw A v2

The vehicle velocity v, for all the other variables, see Table 5.1. Between the simulation and dyno tests there

are some differences, the most important ones are:

• in the simulation drivetrain losses have to be modeled, while during dyno tests, these are experienced.

• on the dyno the rolling resistance for the front tires must be added to the steady state losses to get

comparable results.

• the vehicle mass on the dyno, mdyno should be slightly less than msim, since it has to compensate for

the inertia of the rear wheels.

The various parameters and settings are given in Table 5.1.


0 1000 2000 3000 4000 5000 6000

−4000

−2000

0

2000

4000

6000

Torque at wheels

distance [m]

Tor

que

[Nm

]

dynosimulation

Figure 5.3 / Torque at the wheels for simulation and on the dyno

Table 5.1 / Road Load settingsSymbol description value

msim simulation vehicle mass 8445 [kg]

mdyno dyno mass setting 8320 [kg]

g gravitational constant 9.81 m/s2

A frontal vehicle area 7.68 m2

Cw Drag coefficient 0.673 [-]

ρair Air density 1.29 [kg/m3]

Cr1 1st order rolling resistance factor 0.0075 [N/N]

Cr2 2nd order rolling resistance factor 3.24 [Ns/m]

results

Now that the road load settings coincide with each other, the differential loss model from (5.2) can be tuned,

by looking at the torque at the wheels. The comparison for the amount of wheel torque is given in Figure 5.3.

Notice that for the simulation model, the estimated front wheel resistance (300 Nm) is subtracted to compare

the results.

The final calibration values for the loss model are presented in Table 5.2,


Table 5.2 / Vehicle drive train.Symbol description value

Rw wheel radius 0.519 [m]

rgb gearbox ratios 7.1, 4.1, 2.5, 1.4, 1, 0.8 [-]

fd final drive ratio 5.13 [-]

Tss steady state differential losses 10 [N]

kω speed dependent loss factor 0.12 [Ns/rad]

kT

torque dependent loss factor 250 [N/N]

5.3 Engine map validation

testing procedure

The losses in the drivetrain are properly modeled, so the chassis dynamometer can be used to test the engine

fuel economy at different operation points. The dyno is set to a desired velocity to keep engine speed at a

constant level. The throttle position from the ICE is held stationary for about 10 seconds and than increased

with 5%. This is repeated for several engine speeds with intermittent values of 150 RPM, the evaluated points

are indicated in Figure 5.4(a). As an example, the result for one engine speed is given in Figure 5.4(b). The data

is filtered with a lowpass filter in order to remove signal noise. The fuel flow is measured with a fuelflowmeter

and compared with the CAN data as an extra check to avoid errors.

0

100

200

300

400

500

600

700

800

900

1000

800 1000 1200 1400 1600 1800 2000 2200 2400

Tor

que

[Nm

]

Rotational velocity [rpm]

Maximum TorqueMeasurement points

(a) Measurement points

0 50 100 150 200 250 3000

5

10

15

20

25

30

35

40

time [s]

fuel

use

[L/h

]

Fuelflow for 1600 RPM

FuelFlowmeterCAN data

(b) Fuel consumption at 1600 RPM

Figure 5.4 / Engine map validation procedure.

The measured torque at the dyno can be calculated back towards Tice with (5.3). A Matlab function is now used

to split the measurements, to use only the steady state parts, where fuel consumption is stabilized, at different

speed and torque points. The measured fuel flow mf is related to the Brake Specific Fuel Consumption (BSFC)

with the following formula:

BSFC(Tice, ωice) =mf (Tice, ωice)

ρdiesel Tice ωice36 · 106 (5.5)


for diesel a density, ρdiesel of 835 kg/m3 is assumed.

results

The resulting BSFC map is already presented in Figure 2.2 and this map is used in the simulation model.

The static engine modeling however, has some limitations which can be seen when driving the velocity profile

from 5.2. When the truck is driving in ‘engine only’ mode, so when power is solely provided by the ICE, driving

torque is not a direct function of pedal position. The engine torque is limited in rise and fall rate, especially at

low speeds ( < 1300 RPM). Due to emission legislation (soot) and turbo lag, a fair amount of time is required

to get towards maximum torque. Details can be seen in Figure 5.5(a). Here, the torque demand (accelerator

pedal position) and the actual engine percentage torque are given. The delay in engine torque is not modeled

in simulation, which causes a small error in trajectory tracking and fuel consumption. Furthermore, the pedal

position is limited at 89 % in order to prevent the gearbox from doing a kickdown: when driving a distance-

velocity profile, shifting down before accelerating, makes the response of the vehicle more non-linear, and is

therefore not desired.

2200 2400 2600 2800 3000 32000

10

20

30

40

50

60

70

80

90

100

perc

enta

ge %

distance

Pedal response from engine

Pedal positionTorque percentage

(a) Turbo lag

0 1000 2000 3000 4000 5000 6000

800

1000

1200

1400

1600

1800

2000

Engine Speed during constant speed cycle

distance [m]

Eng

ine

spee

d [R

PM

]

SimulationDyno

(b) Engine speeds

Figure 5.5 / Engine response during validation cycle.

An extra check can be made to ensure that gearbox ratios and wheel radius are correct, by comparing the

measured velocity from the dynamometer to the calculated velocity from the engine speed using the drivetrain

ratios from Table 5.2. From Figure 5.5(b) we can conclude that gearbox ratios and the wheel radius agree with

each other. One remark is made concerning the shift actions, which can be seen in Figure 5.5(b). Since the

truck on the dyno uses another software version than the simulation model, gear shifts are carried out in a

different way. The simulation model shifts without loss in velocity. The truck on the dyno, however, falls back

in vehicle velocity after each shift action. As a result, transient response during acceleration will differ between

dyno measurements and simulation. Using the measured drivetrain loss and engine map, the transient fuel

consumption and control decisions of the hybrid system can now be validated.


5.4 Transient fuel consumption validation

Road load, drivetrain losses and the engine map are matched between the simulation model and dyno. Hence,

it is possible to drive distance velocity trajectories to validate decisions of the existing rule based controller

and fuel consumption over a cycle. To see whether the velocity controller coincide with each other, the velocity

error for the profile driven in Figure 5.2 is depicted in Figure 5.6.

0 1000 2000 3000 4000 5000 6000 7000−1.5

−1

−0.5

0

0.5

1

1.5

Vel

ocity

err

or [m

/s]

Error signal

distance [m]

SimulationDyno measurements

Figure 5.6 / Velocity error for validation cycle.

From this figure we can conclude that the steady state error remains within 0.2 m/s on the dyno. Transient

responses are in good agreement with each other. However, the experimental results have a more transient

behavior. Overall, the difference in dynamic response can be explained by:

• the dyno velocity signal needs to be filtered to be useful as control input,

• in general, drivetrain and dynamometer dynamics are not modeled.

testing procedure

Since a hybrid vehicle is considered, a compensation for fuel consumption depending on the SOC difference

has to be made. When this compensation would not be performed, battery depletion is the most fuel effi-

cient. The compensation is done by taking into account the difference in SOC as a correction for the fuel

consumption:

mf = mf,original + ∆SOCE%SOC

EDieselλ (5.6)

here, ∆SOC is defined as SOC(t) − SOC(t0), E%SOC is the energy content for 1 % SOC, and EDiesel

the energy content of diesel in kWh/L. λ is the Lagrange parameter corresponding to the cycle dependent


incremental cost, see section 3.3. Hence, the fuel consumption and SOC trajectory for the cycle presented in

Figure 5.2 can be validated. The SOC and fuel consumption results are given in Figure 5.7.

0 1000 2000 3000 4000 5000 60000.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Battery SOC

distance [m]

SO

C [−

]

SimulationDyno

(a) SOC trajectory

0 1000 2000 3000 4000 5000 60000

0.5

1

1.5Corrected cumulative fueluse

distance [m]

Fue

luse

[L]

SimulationDyno

(b) Cumulative fuel consumption

Figure 5.7 / SOC and fuel consumption for validation cycle.

Overall, good agreement exists between EMS control actions for the two systems. The cumulative fuel con-

sumption is within 2% difference between simulation and dyno tests. Since this profile is driven only once

and merely driven to, synchronize controller settings, adapt drivetrain properties, and to check fuel consump-

tion. With the settings adapted for this cycle, two more cycles are driven repeatedly. Their velocity profiles are

depicted in Figure 5.8. The limited dynamics cycle on the dynamometer is driven seven consecutive times,

while UDDS is repeated five times.

−500 0 500 1000 1500 2000 2500 3000 3500 40000

10

20

30

40

50

60

70

80


distance [m]

Vel

ocity

[km

/h]


(a) Limited dynamics cycle

0 1000 2000 3000 4000 5000 6000 7000 8000 9000−20

0

20

40

60

80


distance [m]

Vel

ocity

[km

/h]

SimulationDyno

(b) UDDS cycle

Figure 5.8 / Fuel consumption validation cycles.


Results

For both the limited dynamics cycle and UDDS cycle, the corresponding SOC trajectories, for all the consec-

utive tests, are given in Figure 5.9.

0 500 1000 1500 2000 2500 3000 35000.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Battery SOC

distance [m]

SO

C [−

]

SimulationDyno

(a) SOC trajectory for limited dynamics cycle

0 1000 2000 3000 4000 5000 6000 7000 80000.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7Battery SOC

distance [m]

SO

C [−

]

SimulationDyno

(b) SOC trajectory for UDDS cycle

Figure 5.9 / SOC trajectories for fuel consumption validation cycles.

The SOC trajectories show that the decisions from the heuristic controller on the dyno and in the simulation

agree well with each other. For the limited dynamics cycle the battery gets charged during the cycle. To make

a fair comparison, the truck is driven in electric mode before starting a new test. This ensures that the battery

boundaries are not hit during the cycle. When the measurements are started with a low SOC, we can see that

the EMS tries to charge the battery towards 0.4. Looking at the regeneration actions, we can conclude that

the EM and battery model that is present in the simulation model, agrees very well with the real components:

nearly the same amount of energy is recovered when the vehicle decelerates in the simulation model and

on the dyno. However, the measurements on the dyno have the drawback that their SOC-level is discretized,

and therefore, it is hard to exactly compare the amount of regeneration energy. From the SOC trajectories on

the UDDS cycle, the same result can be concluded: regeneration and the decision to charge the batteries are

based on the same thresholds of the heuristic controller. Notice that it is hard to compare the strategies with

each other, since only SOC trajectories can be evaluated and no intermediate control decisions are available.

Finally, fuel consumption can be validated over the series of tests. With the aid of (5.6) the corrected cumu-

lative fuel consumption over a cycle can be presented. For the two validation profiles, the result is given in

Figure 5.10.


0 500 1000 1500 2000 2500 3000 3500 4000−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Corrected cumulative fueluse

distance [m]

Fue

luse

[L]


(a) Cumulative fuel for limited dynamics cycle

0 1000 2000 3000 4000 5000 6000 7000 80000

0.5

1

1.5

2

2.5

Corrected cumulative fueluse

distance [m]

Fue

luse

[L]

SimulationDyno

(b) Cumulative fuel for UDDS cycle

Figure 5.10 / Cumulative fuel consumption for validation cycles.

For the tests that are driven multiple times on the chassis dynamometer, the average fuel consumption from

the consecutive measurements is taken and compared to the simulation. Results are given in Table 5.3.

Table 5.3 / Cumulative fuel consumption for dyno and simulation.Cycle Dyno mean [L] Simulation fuel[L] Difference [%]

Validation 1.246 1.264 + 1.5

Limited dynamics 0.817 0.799 - 1.6

UDDS 2.503 2.529 + 1.1

Note that the validation profile is driven only once, while the limited dynamics and UDDS are driven 7 and

5 times respectively. Fuel usage for the validation cycle is not averaged. Overall simulated fuel consumption

prediction is within 2 % of the experimental results, well within the desired 5 %. Besides, the reproducibility

of the experiments on the chassis dynamometer is between 3%.


5.5 Conclusion

Validation of the simulation model is done in a several steps, to reach the final goal, a fuel accuracy within

5%. First, coast down-measurements and a validation cycle are used to match the road load and drivetrain

properties between the simulation model and the actual vehicle. The torque at the wheels and engine speed

are measured to get these properties into good accordance with each other. Secondly, measurements are

performed to obtain a static engine map. This map suffices when predicting fuel consumption, however the

dynamical aspects of the engine, are not taken into account. Moreover, drivetrain and dynamometer dynamics

are not modeled and in combination with the different shifting procedure, this causes a discrepancy in

velocity tracking between simulation model and dyno.

Overall, from the SOC trajectories it can be concluded from the various validation profiles that the decisions

from the strategy are in good agreement between the simulation model and on the dyno. The drivetrain char-

acteristics and road load settings are comparable with each other and the fuel accuracy from the simulation

model agrees with the measurements well between the desired 5 %.

CHAPTER 6

Simulation results

The adaptive EMS, as presented in Chapter 4, is implemented in the simulation model that is validated in

the previous chapter. The model is used to (i) obtain tuning rules for the feedback parameters (3.14), and (ii)

evaluate the ECMS with the existing rule-based controller.

6.1 Drive cycles

The simulation model is validated, however, for real-time implementation of the ECMS, the parameters λ0

and K of (3.14) have to be chosen in advance. The aim is to find appropriate values for λ0 and K for the

real-time controller. To complete the overview of the ECMS performance, on a wide range of conditions, four

different distance velocities trajectories are evaluated. This results in tuning rules for the feedback parameters

and a comparison of the ECMS and the existing controller. A short description of the cycles and their distance

velocity profile is given in the next Section. The four cycles are firstly, the UDDS cycle, secondly is the Man-

hattan Bus Cycle, thirdly is the Federal Test Procedure (FTP - 75), and finally is the European Transient Cycle

(ETC).

Distance velocity trajectories

A short description of the cycles is given. Besides, for all the cycles their distance velocity trajectories are

depicted in Figure 6.1, the main parameters are given in Table 6.1.

• The Urban Dynamometer Driving Schedule (UDDS) for heavy duty vehicles UDDS, already used for

the validation of the simulation model, is a test with relative high speeds and a total length of 8.9 km.

• The Manhattan bus cycle, is a cycle which has a more transient behavior and is representing typical bus

start stop actions. From the four cycles that are considered, Manhattan has the highest acceleration and

deceleration.

• The Federal Test Procedure (FTP) 75 is a cycle used for emission certification of light duty vehicles in

the United States.

• The ETC cycle has been developed by TUV Automotive and is based on road cycle measurements

of heavy duty vehicles. Different driving conditions are represented by three parts of the ETC cycle,

including urban, rural and motorway driving.


0 1 2 3 4 5 6 7 8 90

20

40

60

80

100

Distance [km]

Vel

ocity

[km

/h]

(a) UDDS

0 0.5 1 1.5 2 2.5 3 3.50

10

20

30

40

50

Distance [km]

Vel

ocity

[km

/h]

(b) Manhattan

0 2 4 6 8 10 12 14 16 180

20

40

60

80

100

Distance [km]

Vel

ocity

[km

/h]

(c) FTP-75

0 5 10 15 20 25 300

20

40

60

80

100

Distance [km]

Vel

ocity

[km

/h]

(d) ETC

Figure 6.1 / Different distance velocity trajectories used for simulation.

Table 6.1 / Parameters for different cycles.Parameter UDDS Manhattan FTP - 75 ETC

total length [km] 8.93 3.32 17.8 29.4

average speed [km/h] 30.3 6.8 34.1 59.0

maximum speed [km/h] 93.0 40.9 91.2 91.1

average acceleration [m/s2] 0.41 0.63 0.56 0.25

average deceleration [m/s2] -0.51 -0.80 -0.65 -0.27

Simulation procedure

From(3.6) it follows that there is a constant λ for which the result is optimal for the given vehicle and driving

cycle combination. For all the cycles, bisection is used to find the value of λ0, with feedback set to zero, for

which the following condition holds:

SOC(t0) = SOC(tf ) (6.1)

The bisection method starts with SOC(t0) = 0.5 and a guess of the Lagrange parameter. The distance velocity

trajectory is than driven, with these settings. SOC(tf ) is used to correct the initial guess of λ0 until (6.1) holds.

According to the theory of Lagrange, this value of λ is considered to be optimal. However, a few remarks can

be made about this assumption:

• implementation of negative Treq is done in a heuristic way,

• the split ratio u is only controlled on supervisory level and is overruled, when for example a gearshift

is performed. Furthermore, the optimal control solution assumes that there are no state constraints on

the battery.

• the calculation is performed with discrete look-up tables. This can cause the solution to differ from the

optimal solution,


• the SOC dependent characteristics of the battery are neglected in the derivation of (3.7), while the sim-

ulation model takes a SOC depending resistance charge into account.

• To maintain driveability, the ICE is limited in its power during clutch closings.

the theory of Lagrange

Despite these differences, the value of λ is used to correct cumulative fuel usage with the aid of (5.6).

6.2 Simulation results

Cumulative fuel consumption for the optimal solution of the four cycles is given in Table 6.2. The cumulative

fuel consumption for the ECT cycle is depicted in Figure 6.2. The value of the feedback parameters for which

the cumulative fuel consumption is the lowest is used to clarify and compare the results for the other cycles.

The relative increase of fuel consumption compared to this ’lowest’ solution is depicted in Figure 6.3.

From Figure 6.3, it can be concluded that the general pattern for the four cycles is the same: with K = 0, the

choice of λ0 has large influence on the fuel consumption, while for larger numbers of K, the choice of λ0

has smaller influence on total fuel consumption. For even higher numbers of K, the fuel consumption rises

slightly and deviates from the optimal solution. Since for real-time implementation an open-loop controller,

(K = 0), is not preferable, some feedback should be implemented.

Although for higher values of K it was expected to see a higher fuel consumption and to follow the desired

SOC more strictly, still energy recuperation is done in a heuristic way. Besides, the look-up tables containing

the optimal split value in the controller are defined preceding the simulation. The creation of this split-maps

is done with predefined settings of the feedback values, which puts a limit on the feedback parameters. For

high values, K > 3 the ‘lookup solution’ will provide the same answer than a smaller value of K gives.

Therefore the influence of very high values of K is limited. However, choosing K very high will result in

very strict tracking the desired SOC and will therefore be less advantageous for battery wear. Besides, these

feedback settings do not provide possibilities for the controller to transfer energy over a period of time: all

the energy that is recuperated will be used immediately. From the fuel consumption figures we can conclude

that tuning parameters for this controller and these cycles should be with λ0 ' 2.55 and K ≥ 1.5

Table 6.2 / Parameters for different cycles.Parameter UDDS Manhattan FTP - 75 ETC

λopt 2.59 2.43 2.47 2.48

Total fuel consumption [L] 2.38 1.09 4.40 2.81

Fuel consumption [L/km] 0.258 0.332 0.247 0.259


01

23

4

2

2.5

32.8

2.9

3

3.1

3.2

K [−]

Fuel consumption for ETC cycle

λ0 [−]

Cum

ulat

ive

fuel

usa

ge [L

]

Figure 6.2 / Fuel consumption for various ECMS feedback parameters on the ETC cycle.

0.5

0.50.5

0.5

0.5

0.5

1

1

1

1

1

1

1.5

1.5

1.5

1.5

1.5

2

2

2 2

2

3

3

34

K

λ0

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

0.5

1

1.5

2

2.5

3

(a) UDDS

0.5

0.5

0.5

11

1

1

1

1.5

1.5

1.5

1.5

1.5

2

2

2

2

2

3

3

3

3

4

4

4

4

55

5

7 7

7

10

K

λ0

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

1

2

3

4

5

6

7

8

9

(b) Manhattan

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1.5

1.5

1.5

1.5

1.5

2

2

2

2

2

3

3

3

3

4

4

4

5

5

7

7

K

λ0

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

0.5

1

1.5

2

2.5

3

3.5

4

(c) FTP-75

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1.5

1.5

1.5

1.5

1.5

1.5

2

2

2

2

2

3

3

3

3

3

4

4

4

4

5

5

5

7

710

K

λ0

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

0.5

1

1.5

2

2.5

3

3.5

4

(d) ETC

Figure 6.3 / Percentage deviation in fuel consumption for different distance velocity trajectories compared

with lowest fuel consumption solution.


6.3 Comparison with heuristic controller

In the previous section, the settings for the ECMS feedback parameters for real-time implementation are

presented. Hence, it is possible to compare the original heuristic controller with the ECMS to see if the

ECMS controller provides any advantage in terms of fuel consumption. All four cycles are simulated with the

heuristic controller and with the ECMS strategy. For the ECMS, feedback settings of λ0 = 2.55 and K = 1.5

are chosen. The heuristic controller is driven with an initial SOC of 0.35. The results are presented in Table

6.3.

Table 6.3 / Fuel consumption on different drive cyclesCycle Heuristic [L] ECMS [L] difference [%]

UDDS 2.94 2.82 -3.9%

Manhattan 4.45 4.39 -1.4%

FTP - 75 2.35 2.32 -1.0%

ETC 1.14 1.09 -3.9%

From this data we can conclude that the ECMS strategy provides a benefit in fuel consumption of at least 1%.

The reduction in fuel consumptions is highly dependent from the cycle that is driven. ECMS seems better on

highway trajectories. A possible explanation for this can be given by the fact that the ECMS controller is not

always free to change the split ratio instantaneous because of driveability limitations . Due to the configuration

of the components, the clutch has to close when going from split ratio u = 0 to higher values. For distance

velocity profiles with a high dynamic behavior, this situation occurs more often than for low dynamic profiles.

However, the ECMS provides better fuel consumption for all cycles. Another advantage over the heuristic

strategy, is that ECMS can cope with a varying SOCdes over time. This makes implementation especially

beneficial when upcoming route profiles (with, e.g., slopes) can be taken into account.

CHAPTER 7

Conclusions and recommendations

7.1 Conclusions

This thesis presents a practical implementation of an Energy Management Strategy (EMS) for a hybrid DAF

CF. The goal of the EMS is to reduce cumulative fuel consumption, while the on board computational power,

limits the complexity of the controller. The method of Lagrange is used to simplify the fuel minimization

problem towards the Equivalent Consumption Minimization Strategy (ECMS).

The simulation model that is used for the EMS development is validated with a test vehicle on the chassis dy-

namometer. As a first step, the chassis dynamometer at Eindhoven University of Technology is made suitable

for validation. Therefore, several adaptations to the control system of the chassis dynamometer have been

made. Extra safety precautions are included and the velocity tracking controller is tuned. Furthermore, for

future development, the dyno is adjusted to simulate elevation in the distance velocity profiles.

The validation is done in three steps: first, the model of the drivetrain losses is validated. Secondly, the fuel

consumption, as function of engine speed and torque is measured and used to predict fuel consumption.

Finally, transient velocity distance profiles are used to match thresholds for the existing heuristic controller

and in this way cumulative fuel consumption for several distance velocity trajectories is predicted within 2%.

Extensive simulations have been performed to find good initial settings for the feedback parameters for the

online estimation of the Lagrange parameter. When providing some feedback towards the desired battery

state-of-charge, the influence of the initial value of the Lagrange parameter, on fuel consumption becomes

limited. It is shown that the ECMS is able to perform well, for a given set of feedback parameters on different

distance velocity trajectories. Fuel savings are at least 1% compared to a properly tuned heuristic controller.

Besides EMS development, the simulation model enables modification of the vehicle Electronic Computa-

tional Unit. Therefore, the ECMS can be tested on the chassis dynanometer as well. Material breakdown

caused some delay in the testing and therefore testing of the ECMS on the dyno has not been finished yet.

However, the first test results with the ECMS on the chassis dynamometer are promising.

7.2 Recommendations

The static map that is used to model the EM efficiency, does not take not include torque losses at zero power

output into account, so when Tem = 0. This model does not correspond very well to the physical behavior of

the component, so for future research a more detailed model of the EM is preferred.

Since not all the appliances are electrified, in the current drivetrain, switching off the engine when it is not

7 Conclusions and recommendations 35

used, is not possible. Together with the limitation on engine torque when a clutch closure occurs, makes that

the hybrid system can be even more efficient with the given vehicle configuration. Switching off the engine,

however, should be penalized by the EMS to maintain driveability and prohibit excessive component wear.

Further research is required to find out what the estimated fuel savings of this measure are.

The test vehicle and dynanometer at Eindhoven University of Technology are fully operational, which enables

validation of the ECMS strategy on a chassis dynamometer in the near future. Since the controller is able to

receive a time dependent battery state of charge trajectory, development of algorithms to calculate optimal

SOC trajectories (e-horizon) along a velocity profile, could make an ECMS even more beneficial. This is

especially the case when route profiles with elevation are considered.

An extension of the ECMS strategy with a gear shifting algorithm could provide an even more fuel economic

EMS, however driveability issues arise when real time implementation is considered: shifting to a higher gear

number will be beneficial under most conditions. On the other hand: the amount of torque available from

the engine will decrease after this shift action. Therefore the driver will encounter a slower dynamic response

from the vehicle. More research is necessary to find an optimum for the trade off between fuel economy and

driveability.

Dankwoord

Het afgelopen jaar is heel erg vlug voorbijgegaan, en na zo’n lange tijd aan één project werken, kan het niet

kwaad om even terug te kijken. Mijn afstudeeropdracht heeft mij bijzonder geboeid en had alles in zich om

een bijzonder veelzijdige, interessante en uitdagende opdracht te zijn. Zo’n opdracht kun je niet alleen doen

en daarom wil ik vanaf deze plaats een paar mensen bedanken. Allereerst, de mensen bij TNO Automotive,

voor de vele mogelijkheden en de leuke tijd die ik in Helmond gehad heb. Hoewel de economische situatie

zo nu en dan zijn weerslag hadden op de afdeling, was het bijzonder leerzaam en interessant om daar een

opdracht te mogen verrichten. De hele afdeling heeft mij daar enorm geholpen, maar een speciaal woord van

dank gaat uit naar Finnis en John. Bij beide kon ik altijd aankloppen voor vragen of extra informatie, hoe vaak

dat ook mocht zijn en immer werden die vragen beantwoord met een niet aflatend enthousiasme.

De laatste maanden van het project vonden voornamelijk plaats op de TU/e. Het in de vingers krijgen van

zo’n gecompliceerde testopstelling heeft aardig wat geduld en hoofdbrekens gekost, maar eindigen met een

werkende testopstelling geeft veel voldoening. Ook de mensen van de Technische Universiteit die het project

ondersteunden, ben ik erg dankbaar. Mijn begeleider Thijs wil ik bijzonder bedanken voor de fijne samen-

werking. De deur die steeds open stond voor verdere uitleg en de vele uren aan de rollenbank heb ik bijzonder

gewaardeerd.

Natuurlijk doe je studeren niet alleen en daarom ook bedankt aan alle studiegenoten voor de broodnodige

bakjes koffie en gezelligheid tussendoor. Bedankt aan alle familie en vrienden die me gesteund hebben

tijdens mijn studie. En als laatste, maar zeker niet als minste: papa en mama voor alle mogelijkheden die ik

gekregen heb tijdens mijn studie, Sophie, die altijd voldoende kan relativeren en Jolanda voor het geduld wat

je met mij wel eens moet hebben.

Dominique

Appendix A

Schematic overview of the different control systems

on the dynanometer

C1 C2

Horiba

SP

iABB roll

inertiaTset

Tm

eT ω

Tm

Trol

chassis dyno

testvehicle

MACS

pedalpositions

iFF

vr(x)

referencetrajectory

-

-

ev

FeedForward

velocitycontrol

αr(x) Tvehvrol

-+

ar, vr, αrγdyno

γpedal

1s

ω+

SOCr(x)

x

Dyno Safety systemSafety control onmax. velocity

ω

ωhybrid

usafe

Figure A.1 / Schematic overview of the different control systems on the dynanometer

In Figure A.1 the different control schemes for the chassis dynanometer are depicted. The MACS-controller

takes care of the velocity trajectory tracking, and handles the dyno safety. For the dyno safety one of the analog

outputs (AO) is coupled towards the Dyno safety input. Giving a high voltage (>5 Volts) on this output results

in switching off the Horiba controller. This output is generated when ωmot or vdyno is above threshold level.

Dynamic heigth profiles

The Horiba controller is able to simulate a dynamica heigth profile (road slope α as function of driven dis-

tance). The MACS-controller AO generates a voltage corresponding to the desired road slope. This voltage is

depending on the driven distance.

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