Inversion-based Control of Series-Parallel HEV for ...

Inversion-based Control of Series-Parallel HEV for Municipal Trucks 1

S. A. Syed1,4, W. Lhomme1,4, A. Bouscayrol1,4, B. Vulturescu2,4, S. Butterbach2,4 O. Pape3,4, B. Petitdidier3,4

L2EP Lille, University of Lille 1, Villeneuve d’Ascq, France, 2 IFSTTAR, Versailles, France,3 NEXTER Systems, France, 4 MEGEVH French National Network on Hybrid Electrical Vehicles

Corresponding Author: Dr. Walter Lhomme Tel: 33-3-20-43-42-53, Fax: 33-3-20-43-69-67, E-mail: [email protected] Abstract — This paper will undertake simulation of seriesparallel Hybrid Electric Vehicles (HEVs) with application to municipal truck. The height, weight and power requirement of these types of vehicles makes them increasingly complex and complicated. The first step to understanding the complexity is to use a model for the vehicle. This will then lead to a simulation of an overall system. To accomplish this, the modeling and the control of municipal truck are realized with the assistance of Energetic Macroscopic Representation (EMR) and implemented into MATLAB-Simulink®. Keywords — Hybrid Electric Vehicle (HEV), Heavy-Duty Vehicle, Waste Collection Trucks, Modeling, Energetic Macroscopic Representation (EMR), Inversion-based Control

I.

INTRODUCTION

In recent years, governments and international agencies have devoted growing attention to fossil fuel depletion and environmental issues. Because land transportation, specifically those with Internal Combustion Engines (ICEs) contributes greatly to these problems, growing attention has been focused on trying to reduce both the fuel consumption and the polluting emissions of these ICE vehicles [1]. However, a pathway towards efficient and clean land transportation can be made with the transition from ICE-based vehicles to ones equipped with electric propulsion or a mix between both thermal and electric vehicles known as Hybrid Electric Vehicle (HEV) [2]. The environmental impact caused by municipal solid waste has received special social and environmental attention, especially in the larger cities of developing countries [3]. It has been reported that waste collection trucks are classified as one of the five least fuel-efficient vehicles because they burn a great deal of fuel while idling and waiting for the collector to empty waste bins [4] – [5]. Therefore, research and development has been widely pursued for such vehicles to equip them with electric propulsions. Applying hybridization to municipal trucks can offer significant advantages in terms of fuel economy and CO2 emission reduction. An additional advantage is that the mechanical decoupling of the engine allows it to operate at optimum points with higher efficiency. Furthermore, due to the large weight of these vehicles, the ability to regenerate kinetic and potential energy is extremely beneficial in certain conditions (e.g. braking) [6] - [7].

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In this study, series-parallel architecture has been chosen for the vehicle. The advantage of this architecture is that it combines both the merits of series and parallel HEVs. This combination is done at the price of implementing a more complicated structure called a Power-Split Device (PSD). Here, the Ravigneaux geartrain is used as the PSD [8] due to the fact that weight is the most significant factor in heavy-duty vehicles. Another prominent feature of this geartrain is to make the ICE available in all conditions. In Figure 1, all power sources such as EM (Electric Machines) and transmission line are directly connected with the drivetrain [9] - [11].

EM1

EM2

Ravigneaux Geartrain

Transmission

ICE

Figure 1- Series-Parallel HEV Configuration with Ravigneaux Geartrain

This paper implements the heavy-duty series-parallel military HEV architecture mentioned in [12] with application to municipal trucks. Although both vehicles have a similar architecture, the size of the EMs, ICE and battery capacity are different. This is due to the fact that the propulsion requirements of each vehicle are different. The aim of this paper is to build a control structure and strategy for the municipal trucks. In order to obtain the control structure, Energetic Macroscopic Representation (EMR) is used [13][14]. EMR has two distinct advantages: primarily, it is an energy-based graphical representation which respects strictly physical laws; and secondly, using inversion rules [15], control schemes can be systematically deduced. In the second and third part, the modeling of the PSD and studied system with inversion-based control is presented, respectively. Finally, the simulation results are analyzed and compared.

II.

POWER-SPLIT DEVICE

A. Kinematics of the Ravigneaux Geartrain In this, Ravigneaux geartrain is utilized as the PSD due to its compactness and higher efficiency in comparison to other planetary geartrain. This PSD consists of a ring gear (R), a planet-carrier (PC) with two layers of pinion gears i.e. outer and inner and two sun gears such as large sun (LS) and small sun (SS). The fundamental equations for this type of complex device are derived from Willis equation. The basic principle of Willis equation is that one gear must rotate so as to maintain a fixed ratio of angular speeds relative to one fixed body (planetcarrier). Keeping this in consideration, the ratio of the relative speeds of the ring gear (ΩR) and the sun gear (ΩLS and ΩSS) to the speed of the planet-carrier (ΩPC) can be written as: Ω LS − Ω PC Ω R − Ω PC Ω SS − Ω PC Ω R − Ω PC

=− =

rR rLS

rR rSS

=n 1

=n

(1) (2)

electric machine EM2 (Motor/Generator) through an additional gearbox of gear ratio (k2). The ring gear is attached to the other electric machine EM1 (Motor/Generator) through an additional gearbox of gear ratio (k1), allowing for increased and/or decreased speed. The planet-carrier provides the resultant torque and is connected through the gearbox of gear ratio (k3) with the wheels of the vehicle. The planet-carrier output shaft transmits the summation power to the vehicle driveline. iConv 1

Gearbox 2

TEM1 fEM1

ΩEM1

k1

TICE

TR

ΩEM1 TSS

fICE

After simplification, equation (1) and (2) reduces to the more general form as below:

ΩICE

fEM2 TEM2 JEM2

ΩEM2

TPC

PC

EM 2

ΩEM2 Fbrake

Ω LS

SS ΩPC

JICE

ΩICE

LS R

ΩR

k2 Tx

TLS

Gearbox 1

Ty

JEM1

EM 1

2

where the fixed ratios n1 and n2 are defined as the radius of the ring gear rR to the radius of the large sun gear rLS and small sun gear rSS. The negative sign shows the exterior epicyclic.

iConv 2

uDC

Gearbox 3

k3

TW

ΩW

vveh Fenv.

Fbrake Figure 2- Studied System Layout

(3) Ω LS − n1 Ω R + (n1 − 1)Ω PC = 0 (4) Ω SS − n 2 Ω R + (n2 −1)Ω PC = 0 The above equations show the inherent speed summing the nature of the Ravigneaux geartrain and the reason it is used in the power split. From these relationships, it is possible to deduce the other speed (e.g. ΩLS and ΩSS) if two independent speeds are known (e.g. ΩR and ΩPC).

In this architecture, on the transmission line, a gearbox is installed which allows the ICE to be available in all circumstances. Furthermore, additional gearboxes are provided with electric machines in order to increase the torque in hybrid mode, if only electric traction is needed, and for rapid recharging of the batteries with high torque. For simplification, in this modeling the clutch is not taken into account.

If the losses are not considered between the elements of the Ravigneaux geartrain then the torque relationships will be as follows:

B. EMR of the Studied System EMR (Energetic Macroscopic Representation) is a synthetic graphical tool based on the principle of action and reaction between connected elements. The principle of EMR is strictly based on only integral causality. It also uses normalized shapes and colors to represent energy sources, conversion elements, storage elements and coupling elements (see Appendix).

TR = −( n1 TLS + n 2 TSS )

(5)

TPC = TLS (n − 1) + TSS ( n − 1) 1 2

(6)

In the above equations (5) and (6), TR, TLS, TSS and TPC represent the torque of the Ravigneaux geartrain elements such as ring, large sun, small sun and planet-carrier respectively. III.

MODELING AND CONTROL

A. Studied System The studied structure consists of a PSD mounted with shafts connected to two electric machines (EM1 and EM2) through gearboxes, an ICE and transmission through a gearbox as shown in Figure 2. The PSDs are the mechanisms of several degrees of freedom. In its design, one element of the PSD has two rotational movements. In the above system, the ICE drives the small sun wheel (SS), while the large sun gear (LS) is connected to the

The studied system is organized in EMR (Figure 3) and simplified to highlight the exchange variables of the elements of an energetic conversion. The modeling and EMR shown in Figure 3 is similar to what is described in [12]. Therefore, the final relationships of the whole system are presented in Table1, focusing on the control part only. C. Inversion-based Control An inversion-based control can be systematically deduced from EMR using specific inversion rules [13] - [16]. Firstly, According to the purpose and limitations of the system, tuning chains are defined. Then, the control chains are realized from the inversions of the tuning chains. In Figure 3, all control blocks illustrated by blue parallelog-

Battery

Electric Machines

Invertor

Gearboxes

Mechanical Coupling 3 (17)

(19, 20)

uDC Batt. iConv

uDC iCon1 uDC

iCon2

TEM1

TGB1

Ω EM1

Ω GB1

TEM2

Ω EM2 TEM2_ref

TGB2

Ω GB2 TGB2_ref

Mechanical Coupling 2

Equivalent Shafts

TA

(14, 16)

TB

Gearbox

Wheels

Mechanical Coupling 1

(10)

(8)

(7)

(12)

Ω ICE Ω PC

Ω GB3

TW

Env. Fenv Fbrake Bra.

FTot

TGB3 TICE k3 ICE

Ω ICE TC Ω PC TD

vveh

vveh

ΩW

vveh

Ω ICE TICE_ref

FBrake_ref

TA_ref

Ω GB3_ref

TB_ref

TEM1_ref

Ω ICE_ref TGB1_ref

Enviornment

Ω W_ref

vveh_ref

Ω ICE_ref

Ω PC_ref

Strategy

Figure 3- Modeling of the studied system by EMR approach

rams handle only information. Since accumulation elements (rectangle with an oblique bar) indicate a time-dependence relationship; they cannot be inverted physically. Therefore a controller is necessary for their inversion. This relationship is determined in (15). The gearboxes and wheels are the conversion elements (square) and are directly inverted through relationships (9, 11, 20 and 22). Coupling elements (overlapped pictogram) require supplementary inputs for inversion. In this way, maximum control operations and measurements are obtained under the assumption that all variables have a measurable value. From this Maximum Control Structure, a mirror of EMR is achieved. The control scheme deals with the local energy management as well as simultaneously taking into account the global energy management of the system. A strategy is thus defined in this global level in order to manage the whole system. In the following, it is explained that how this inversionbased control is determined for the studied vehicle. 1) Tuning and Control Path The tuning paths link the tuning inputs to act on the system and its outputs for control. In the EMR shown in Figure 3, there are four tuning inputs or variables i.e. TEM1_ref, TEM2_ref, TICE_ref and TBrake_ref to indicate the reference torques of sources EM1, EM2, ICE and brakes, respectively. Here, the objective is to control the vehicle speed i.e. vveh. Therefore, this objective is realized through the tuning inputs and in turns the tuning path is determined, which is shown in Figure 4. The gear ratio k3 is not a tuning input because this speed ratio is chosen by the driver with a manual gear. Therefore, this ratio will be a uncontrolled input for the control scheme. The tuning variable TBrake_ref is used to achieve the mechanical braking which is directly given input from the strategy. The points for ICE: TICE_ref and ΩICE_ref are also directly chosen from strategy level through the performance chart of ICE in such a way that it should work under its optimal region.

Ω GB3 TEM1 TEM1_ref

TEM2

TGB3

k3

TGB1 TA

ΩPC

TC

TB

ΩICE

TD

TGB2

ΩW

vveh TW FTot FBrake FBrake_ref

TICE

TICE_ref

TEM2_ref

Ω ICE

Figure 4- Tuning Path

After finding the tuning paths for the system, it is easy to determine the control paths. This can be achieved by inverting the tuning path step-by-step as shown in Figure 5. Ω ICE_ref

TEM2_ref TICE_ref TGB2_ref TEM1_ref

TB-ref

ΩICE_ref

TD_ref

TA_ref

Ω PC_ref

TC_ref

FBrake_ref

TGB1_ref

Ω GB3_ref

Ω W_ref

vveh_ref

k3

Figure 5- Control Path

2) Maximum Control Structure Along with the control chains, an inversion-based control structure is obtained from the inversion of the EMR (lower part of Figure 3). The equations for each block in Figure 3 are detailed under Table 1.

Table 1- Equations of EMR elements and of control blocks Element Mechanical Coupling 3 Wheels

Gearbox 3

Mechanical Coupling 2

Elements Equation

Elements Equation After Inversion

common ⎧vveh ⎨ F F = Brake + Fenv ⎩ Tot

(7)

⎧TW = RW FTot ⎨ ⎩vveh = RW ΩW

(8)

1 ⎧ ⎪TGB 3 = k TW ⎪ 3 ⎨ 1 ⎪Ω = Ω W GB 3 k3 ⎩⎪

⎧TC ⎨ ⎩TD

= TICE

(10)

(12)

= TGB3

ΩW _ ref =

v veh _ ref

Ω GB 3 _ ref = k 3 Ω W _ ref

(11)

⎧⎪Ω GB3 _ ref ⎨ ⎪⎩Ω ICE _ ref

(13)

Later from variable form to vectorial form

Equivalent Shafts

Mechanical Coupling 1

⎡Ω ICE ⎤ ⎡T1 ⎤ d ⎡Ω ICE ⎤ ⎢T ⎥ = [J ] dt ⎢Ω ⎥ + [ f ]⎢Ω ⎥ ⎣ 2⎦ ⎣ PC ⎦ ⎣ PC ⎦

(14)

⎧ J = F (n1 , n2 , k1 , k 2 , k3 , J EM1 , J EM 2 , J ICE ) ⎨ ⎩ f = F (n1 , n2 , k1 , k 2 , k3 , f EM1 , f EM 2 , f ICE )

(16)

⎧ ⎪ TA ⎪ ⎨ ⎪T ⎪ B ⎩

=

1 n 2

TGB1

n + 1 TGB 2 n 2

(9)

RW

= Ω PC _ ref = Ω ICE _ ref

Later from vectorial form to variable form

⎡Ω ICE _ mea ⎤ ⎡T1 _ ref ⎤ d ⎡Cs1 (t )(Ω ICE _ ref − Ω ICE _ mea ) ⎤ [ ] J = ⎢ ⎥ + [ f ]⎢ ⎢ ⎥ ⎥ (15) dt ⎣ ⎢Cs 2 (t )(Ω PC _ ref − Ω PC _ mea ) ⎦⎥ ⎣T2 _ ref ⎦ ⎣Ω PC _ mea ⎦

First from vectorial form to variable form then (17)

n −1 n −n 1T TGB1 + 2 = 2 GB 2 n n 2 2

Later from variable form to vectorial form

⎧ ⎪ TGB1 _ ref ⎪ ⎨ ⎪T ⎪ GB2 _ ref ⎩

n −n n 1T 1 T = 2 A _ ref − 1− n 1 − n B _ ref 1 1

(18)

1− n 1 2T T = + 1 − n A _ ref 1 − n B _ ref 1 1

Gearbox 1

⎧TGB1 = k1TEM 1 ⎨ ⎩Ω EM 1 = k1Ω GB1

(19)

TEM 1 _ ref =

1 TGB1 _ ref k1

(20)

Gearbox 2

⎧TGB 2 = k 2TEM 2 ⎨ ⎩Ω EM 2 = k 2 Ω GB 2

(21)

TEM 2 _ ref =

1 TGB 2 _ ref k2

(22)

Inversion of mechanical convertors – In the upper part of Figure 3, all gearboxes and wheels (orange square pictogram) are ensuring energy conversion without storing the energy. The inversions of these mechanical converters are shown in the lower part of Figure 3 by the blue parallelograms. Vectorial Speed Controller – In the upper part of Figure 3 the equivalent shafts of the studied system is shown with a vectorial accumulation element (rectangle with an oblique bar). This accumulation element cannot be directly inverted because of time dependent relationships derived (equation (14) in Table 1). Therefore, a vectorial controller is shown in the lower part of Figure 3 (blue parallelogram with an oblique bar). This is required to define the torque vector references [TA_ref, TB_ref] from the speed vector reference [ΩICE_ref, ΩPC_ref]. The compensation of vectorial torque [TC_ref, TD_ref] is represented by dotted line. The equation (15) in Table 1, ΩICE_mea and ΩPC_mea represents the speed measurements of ICE and the transmission shaft connected to the planet-carrier of the PSD. The Cs1 (t) and Cs2 (t) represent the controllers which can be type of PI, IP and vice versa. For the PSD, the output of the vectorial controller

[TA_ref, TB_ref] strictly depends on the two reference speeds i.e. [ΩICE_ref, ΩPC_ref]. Inversion of mechanical couplings – In the top part of Figure 3, there are three mechanical couplings (overlapped parallelograms). The first coupling element (from right to left) is not inverted because it couples the resistive environmental forces and braking force. The environmental force Fenv cannot be measured and is difficult to be estimated but its affect is counted in the velocity controller. The inversion of the second coupling element is just a change of the variable to a vectorial form. In this, the reference speed of ICE (ΩICE_ref) is given directly from the strategy. The inversion of the last coupling element is done through equation (17) and shown in equation (18). 3) Strategy The energy management system should fulfill the driver’s demand for the traction power while sustaining the batteries state of charge (SOC), optimizing the drivetrain efficiency and reducing in fuel consumption and emissions [17]. In the studied HEV, the traction shaft is directly connected with planet-carrier

of the PSD. Therefore, the traction power for propulsion will be the sum or sole power(s) of EM(s) and/or ICE. Due to many multi energy sources for propulsion, the strategy for these types of vehicle gets more complex. Initially, a simple rule based strategy is considered on the basis of the ICE turning ON and OFF. The implemented strategy is based on the following assumptions: 1. The SOC level is constantly maintained between the preset upper and lower limit level (50%-70%). 2. The ICE will be turned OFF if the SOC level is high and the requested traction power from driver is low. In this case, the batteries will provide the requested power through one EM or both of it. 3. The ICE will be turned ON if the SOC level is lower than its minimum allowable value. In this case, the ICE will charge the batteries through the EM1 or EM2 or both. However, one condition for the ICE in this situation is that it should run in its optimal efficiency zone. 4. The ICE will be ON and provide full traction power if the requested power is beyond the maximum output capacity of batteries i.e. 100 kW. 5. The ICE will always be ON, if the driver demand is to cruise the vehicle at high speed. IV.

SIMULATION RESULTS

Simulation is carried out on Matlab-Simulink® and the results are taken by imposing the reference torque and speed of the ICE. In this simulation, real time driving cycle taken as a reference for this type of vehicle is named ARTEMIS (shown in Figure 6). For this driving cycle, the data was recorded in 1990 over the course of one week in Grenoble (France), when a Renault IV GR191 was instrumented and monitored in normal operation. This cycle includes a liaison trip and a collector phase [18]. For this simulation, it is considered that for the liaison trip the vehicle should propel by ICE mostly and collector phase electric only.

A. Simulation results The simulation results are shown in Figure 7 for the liaison trip of first 250 seconds of ARTEMIS driving cycle. In this, Figure 7.a verifies that the simulated speed is the same as the reference speed. The power of the electric machines EM1 and EM2 are shown in Figure 7.b and 7.c. At this point, to avoid discontinuities in the simulated curve, the clutches between the gears are not considered, just the fourth gear has been used. 1- Only Electric - 0 to 10 seconds - The vehicle is starting up and the ICE is not running. The EM1 and EM2 power is positive (see Figure 7.b and 7.c). The powers of both EMs are declining after certain time (see Figure 7.d) due to decline in power of DC bus. In this mode, only the battery is working to accelerate the vehicle. 2- Regenerative braking - 40 to 50 seconds - The vehicle decelerates and the ICE is not operating. The battery is being recharged due to regenerative braking where the EM2 and EM1 acts as a generator which gives power back to the battery (see Figure 7.f). 3- Only Engine - 52 to 73 seconds – In this mode, the ICE will run alone and directly supply the power through transmission to the wheels. For the liaison trip of ARTEMIS driving cycle it is considered that the vehicle should be propelled by the ICE due to high speed. Therefore, the simulation result verifies that in this trip the ICE is ON most of the time (see Figure 7.b, 7.c and 7.d). The distribution ratio for braking force between mechanical brake and EMs are 0.5. 4- Hybrid traction - 140 to 146 seconds – In this mode, the ICE and both EM (1& 2) provides the traction power to propel the vehicle. In this case, the traction power is drawn from both the fuel tank and the batteries. Therefore the ICE and the EM power are positive (see Figure 7.e, 7.b and 7.c). vveh (km/h)

1

2

3

4

t (s) (a) Vehicle Speed (Liaison Trip)

(b) EM1 Power (kW)

t (s) (d) DC Bus Power (kW)

t (s)

t (s)

(e) ICE Power (kW)

t (s) (c) EM2 Power (kW)

t (s) (f) Braking Force (kN)

Figure 7- Simulation Results

V.

Figure 6- ARTEMIS Driving Cycle

CONCLUSION

This paper presents the modeling and control of waste collection series-parallel HEVs. In this, it is proven that Energetic Macroscopic Representation (EMR) is very beneficial tool for the representation of this complex system and in finding its control structure. The goal of this paper was to obtain a com-

plete and optimum inversion-based control structure for the studied HEV. For this, the Maximum Control Structure (MCS) of the system was deduced from the EMR description using an inversion methodology. In order to check the model and control of the studied system, a simple strategy is taken into account and discussed as such. In the future, a more optimized and detailed strategy will be studied with the same control structure. The simulation results are made under the ARTEMIS driving cycle. In the simulation results, the reference speed of the vehicle is same as the simulated speed.

[7]

[8]

[9] [10]

[11]

ACKNOWLEDGMENT This work has been made in the framework of ARCHYBALD national project supported by ANR on collaboration with NEXTER Systems, IFSTTAR-LTN within MEGEVH French network on HEVs.

[12]

[13]

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Appendix: Synoptic of Energetic Macroscopic Representation (EMR) Element with energy accumulation Mono Physics (without energy accumulation)

Source of energy Multi Physics coupling (distribution without energy accumulation) Control block : inversion of conversion elements Control block : inversion of coupling elements

Control block: controller

Strategy

Strategy Block