Project 1

Development of a forward energy-based fuel consumption model of a conventional vehicle

AIM

Compute the fuel economy numbers for the given vehicle (kmpl) on the urban cycle (UDDS) and highway cycle (HWFET). Also, analyze and understand the vehicle operating points in terms of engine speed, torque, transmission speeds, pedal positions, gear, distance travelled, etc.

• Build Simulink model using blocks and complete the vehicle Model
• Write scripts in MATLAB to load all the variables needed to run the simulation model.
• Analyze data and create plots using MATLAB scripts.

OBJECTIVES

• Tabulate the fuel economy numbers (kmpl) for UDDS and HWFET cycle.
• Plot the time trace for engine, transmission input, transmission output and wheel speed on one plot.
• Plot engine torque, engine power, fuel rate and fuel consumption using subplots.
• Plot accelerator and brake pedal, gear command, vehicle desired and actual speed, vehicle distance using subplots.
• Plot the engine operating points on the engine fuel map.
• Write down appropriate brief comments on each of these plots, describing the vehicle behavior throughout the drive cycle.
• Generate the plots for both drive cycles.

THEORY

Forward Modeling Approach :

The forward modeling approach is also known as cause-effect, engine-to-wheel or rear-to-front method. The direction of calculation is the same as the direction of positive power flow, from engine-to-wheel.

This approach is based on vehicle dynamics equations and the behavior of each power train components and their dynamic interaction.

Moreover, a driver controller is required to control the vehicle to follow a desired speed and set the start of the calculations. The controller is implemented to model the driver that will either push the accelerator or the brake pedal to match the desired speed which enables to study the driver behavior. The controller is used as part of a feedback loop that will determine the energy required to drive the vehicle.

Vehicle Energy Consumption Estimation Model :

Energy consumption estimation models can be classified in three main categories:

• Analytical models :

Analytical models are representative of the Vehicle behavior and can be developed in MATLAB/Simulink by creating a vehicle model. They are based on fundamental theoretical equations. A model of the vehicle dynamics is built based on vehicle dynamics theory to calculate the power required at the wheels to overcome the resistances forces opposed to the vehicle motion: Aerodynamic Drag, Rolling, Inertia, and Gradient and Transmission resistances. The power required derives from the tractive force expressed as the sum of the resistances forces above

• Statistical models :

Statistical models are built based on real world driving data analysis to derive empirical relationships between the different factors affecting Vehicles energy consumption.

• Computational Model :

There are mainly two kinds of computational models for energy consumption estimation: Artificial Neural Networks (ANN) based model. Clustering based models.

Conventional Vehicle Modeling :

Architecture of the forward conventional vehicle model is presented in Figure:

This model includes a driver model that provides input commands acceleration and brake torque depending on the drive cycle and the actual speed of the vehicle.

A control model that controls the engine torque to the desired range and changes the gear command and control brake torque according to the driver input.

The transmission model that gives the actual speed of the vehicle as feedback to the driver model. The model includes the engine, transmission, differential, wheel and vehicle dynamics models separately.

VEHICLE MODEL

Pre Processing :

A MATLAB script has been created to load all the variables needed to run and post-process the Simulink model. Drive cycle selection is also done from here. Before running the Simulink vehicle model, the script is initialized at MATLAB to load all the variables in the workspace.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Project 1 - Conventional Vehicle Model

%% Vehicle Parameters

M = 1500; % Vehicle weight [kg]

Cr = 0.015; % Rolling resistance coefficient

Rw = 0.35; % Rolling radius [m]

Cd = 0.33; % Drag coefficient

Af = 2; % Frontal area [m2]

rhoa = 1.225; % Air density [kg/m3]

Vwind = 0; % Wind velocity [kmph]

g = 9.81; % Gravitational acceleration [m/s2]

theta = 0; % Slope [deg]

myu_road_tire = 1; % Coefficient of friction between tire - road interface

%% Powertrain Parameters

FDR = 3.73; % Final Drive Ratio / Diff Ratio

DiffEff = 0.99; % Differential efficiency (assumed independent of operating conditions)

NumGear = 4; % Number of gears in transmission

TransGear = [1:NumGear]; % Transmission Gears

TransRatio = [3.06, 1.62, 1, 0.7]; % Corresponding Transmission ratios

TransEff = 0.90; % Transmission efficiency (assumed independent of operating conditions)

TC_SR = [0, .5, .6, .7, .8, .87, .92, .94, .96, .97, 1]; % Torque Converter Speed Ratio (Matlab default) -> TurbSpd/PumpSpd

TC_TR = [2.232, 1.5462, 1.4058, 1.2746, 1.1528, 1.0732, 1.0192, 1, 1, 1, 1]; % Torque Converter Torque Ratio (Matlab default) -> TurbTrq/PumpTrq

TC_Cf = 1e-4 * [.72558, .66322, .63463, .59042, .51331, .4144, .29287, .22444, .12186, .04386, 0]; % Torque Converter Capacity Factor (Matlab default) -> PumpTrq/PumpSpd^2 [Nm/rpm^2]

load('Trans_Shift_map.mat')

load('Torque_Converter_data.mat')

load('Engine_data_1_9L_Saturn_95kW.mat')

%% Driver Parameters

Kp = 10; % P gain for driver PI model

Ki = 1; % I gain for driver PI model

Drive_Cycle_Select = 1; % Drive cycle selection

% Drive cycle values in m/s

if Drive_Cycle_Select == 1

% load DriveCycles/UDDS;

load('UDDS.MAT')

elseif Drive_Cycle_Select == 2

%load DriveCycles/HWFET;

load('HWFET.mat')

elseif Drive_Cycle_Select == 3

%load DriveCycles/FTP;

load('FTP.mat')

elseif Drive_Cycle_Select == 4

%load DriveCycles/US06;

load('US06.mat')

elseif Drive_Cycle_Select == 5

%load DriveCycles/NEDC;

load('NEDC.mat')

elseif Drive_Cycle_Select == 6

%load DriveCycles/WLTP;

load('WLTP.mat')

end

time_end = cyc_time(end);

vel_end = cyc_vel(end);

The Drive Cycle can be selected from this MATLAB Script, by changing the variable Drive Cycle Select to,

1	UDDS
2	HWFET
3	FTP
4	US06
5	NEDC
6	WLTP

SIMULINK MODELING

The Simulink model for the convection model is created using 3 main sub blocks for the driver model, control model and power train block.

The actual vehicle speed is given as feedback to the driver block, and the driver block gives the controller block the required acceleration or brake output, while the controller block provides control signals for engine torque, gear shifting and brake torque to the Power train model.

Driver Model

Driver Model is a basic PI controller that generates accelerator and brake pedal outputs to match the desired and actual vehicle speeds. It is modeled using a ‘Driver’ block, which is a basic PI controller that generates accelerator and brake pedal outputs to match the desired and actual vehicle speeds. In this we use drive cycles forward based on these results of fuel consumption and emissions the vehicle gets certified and it also forms a basis of uniform assessment. It is based on time, velocity then it’s all integrate and creates output acceleration pedal and brake pedal.

Graph created from Scope in Driver Model:-

UDDS: Drive Cycle and Actual Velocity

HWFET: Drive Cycle and Actual Velocity

UDDS: Acceleration

HWFET: Acceleration

UDDS: Brake

HWFET: Brake

Control Model:-

The ‘Controller’ block is the brains of the vehicle, representing the electronic controls units. It is based on the driver inputs; it generates desired engine torque, desired transmission gear and desired brake torque. These inputs are fed to the ‘Power train’ block which represents the drive train of the vehicle. The controller consists of an engine control unit, a transmission control unit and a brake control unit.

• ENGINE CONTROL UNIT

Engine Control Unit Compare engine speed with the maximum torque and minimum torque curves of the lookup table and give the required torque command to the engine block. The throttle input is combined with the idle speed throttle and gains with the torque output from the lookup table to estimate the torque input required for the engine.

Throttle input, idle throttle and their sum can be scoped from this block.

Idle speed controller

UDDS: Engine Control Unit

HWFET: Engine Control Unit

Graph created from Scope in Control Model:-

UDDS: scope

HWFET: scope

TRANSMISSION CONTROL UNIT:-

The transmission control block controls the gear shifting using the study flow Variable chart. In this unit we create steady flow variable state for controlling of gears of vehicle as in ascending and descending order with respect to time, speed, distance. And give input to this steady state is vehicle speed in m/s to mph.

The Gear shifting is Controlled according to the vehicle speed and throttle input. The gear command is passed to the Transmission block to select the desired gear ratio.

BRAKE CONTROL UNIT

Brake Control unit Produce required brake torque according to the brake pedal input and passes the brake torque in to the wheel block in the transmission model.

In this calculate brake torque and then all three control signals output is give to power train.

POWERTRAIN MODEL:

The power train model includes all the components that convert the power of the engine into vehicle motion. This includes Engine, Transmission, Differential, Wheels and the vehicle body dynamics subsystems.

Engine Model:

Based on the engine speed the required torque from the controller is saturated between max torque curve and min torque curve and passes the engine torque to the transmission block. the 2d lookup table is used to calculate the fuel flow rate based on engine speed and engine torque. the fuel flow rate is then integrated to find the fuel consumption.

Estimated fuel flow rate, fuel consumption, engine torque and engine speed are passed to the MATLAB workspace using the to-workspace block.

In this model we used map based model to model the fuel consumption of engine. It is based on maximum Torque and minimum torque from the controller. And then it saturated torque and gives output then saturated torque and speed map give fuel consumption takes the speed and torque then the output goes into saturated then it’s integrated.

Engine Torque

UDDS

HWFET

Engine fuel flow rate and Fuel consumption are scoped.

UDDS

HWFET

Transmission Model:

The engine block is connected to the automatic transmission via a torque converter. The output of the transmission is connected to the differential. In this model we take engine torque, gear selector from controller for transmission of gear ratio. The ratio is multiply by transmission input torque and then the transmission efficiency positive torque and negative torque gives transmission input speed. In this case torque converter connects the engine to transmission it is part of transmission. In it basically engine dynamics and that is decoupled.

Scope : -

UDDS

HWFET

Torque Converter:

The gear selection from the transmission control unit is multiplied by the engine torque in this block, and the efficiency and engine dynamics of the torque converter are applied in this model

Scope Result

UDDS

HWFET

Differential Model:

The transmission output torque is multiplied by the differential ratio and differential efficiency in this block and the torque is transmitted to the wheel as the axle torque. In this taking input is the transmission output then its going to the differential ratio multiplied the output and input torque then meets axle torque. The axle torque is a lower than the transmission torque and differential ratio.

Wheels:-

In this model we take the axle torque from differential and brake torque from controller. It is subtracts and multiplied rolling radius and velocity then we meet the tractive force from axle and brake torque. And the wheel speed is meet using velocity. The brake torque from the control model is subtracted from the Axle torque and divides from the rolling radius to determine the tractive force. The Wheel speed is calculated from the vehicle velocity and saved in the workspace.

Vehicle Dynamics:

Tractive Force and Road loads are used to calculate the vehicle velocity. In this takes tractive force and road load. It is dictates vehicle speed based on tractive force and road load.

The dynamic equation for calculating road load is

`(ηt*λt*Te)/Rw=M(dV(veh))/dt+1/2 ρa*Af*Cd(Vveh+Vwd)^2+Cr*M*g*cosθ+M*g*sinθ`

`(ηt*λt*Te)/Rw=Tractive force`

`1/2 ρa*Af*Cd(Vveh+Vwd)^2+Cr*M*g*cosθ+M*g*sinθ =Road Load`

Where,

ρ a - Air Density

A f - Frontal Ares

C d - Drag Coefficient

C r - Rolling Coefficient

M - Mass of Vehicle

g - Acceleration due to gravity

θ - Slope

Scope result

UDDS

HWFET

The variables are loaded on the workspace using MATLAB Script.

The Acceleration, Velocity and Distance travelled are Calculated and stored in the workspace.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Post-Processing File

%% Renaming variables

Time = out.tout;

Acc_Pdl = out.Acc_Pdl; % Accelerator pedal [%]

Brk_Pdl = out.Brk_Pdl; % Brake pedal [%]

Gear_Cmd = out.Gear_Cmd; % Transmission gear

Trans_In_Spd = out.Trans_In_Spd*30/pi; % Transmission input speed [rpm]

Trans_Out_Spd = out.Trans_Out_Spd*30/pi;% Transmission output speed [rpm]

Eng_Trq = out.Eng_Trq; % Engine brake torque [Nm]

Eng_Spd = out.Eng_Spd*30/pi; % Engine speed [rpm]

Eng_Fuel_Consump = out.Eng_Fuel_Consumption; % Engine fuel consumption [g]

Veh_Dist = out.Veh_Dist/1000; % Distance traveled by vehicle [km]

Veh_Spd = out.Veh_Spd*18/5; % Vehicle speed [kmph]

Whl_Spd = out.Whl_spd; % Wheel speed [kmph]

Eng_Fuel_Rate = out.Eng_Fuel_Rate; % Engine fuel rate [%]

%% Data Analysis

Eng_Pwr = Eng_Spd*pi/30*Eng_Trq/1000; % Engine brake power [kW]

rho_petrol = 0.7197; % Density of petrol [kg/L]

kmpl = Veh_Dist(end)/(Eng_Fuel_Consump(end)/1000/rho_petrol); % Fuel economy [kmpl]

%% Plotting vehicle characteristics time trace transmission IN/OUT and Wheel Speed

figure(1)

hold on

grid on

plot(Time, Trans_In_Spd, 'linewidth', 1, 'Color', 'black');

plot(Time, Trans_Out_Spd, 'linewidth', 1, 'Color', 'red');

plot(Time, Whl_Spd, 'linewidth',1, 'color', 'blue')

ylabel('Speed [rpm]')

xlabel('Time [s]')

xlim([0, Time(end)]);

ylim([0, 6000]);

legend('Trans Input','Trans Output','Wheel Speed');

%% Plotting vehicle characteristics time trace to Engine speed, Engine Torque, Engine Power,

% And Engine fuel rate, Engine fuel consumption

% Data conversion from Double Timeseries

Eng_spd = Eng_Spd.Data(:,1); % engine speed

Eng_trq = Eng_Trq.Data(:,1); % engine torque

Eng_pwr = Eng_Pwr.Data(:,1); % engine power

Eng_fuel_rate = Eng_Fuel_Rate.Data(:,1); % engine fuel rate

Eng_fuel_consumption = Eng_Fuel_Consump.Data(:,1); % engine fuel consumption

Veh_dist = Veh_Dist.Data(:,1); % vehicle distance

Veh_spd = Veh_Spd.Data(:,1); % vehicle speed

% Plotting Engine speed, Engine Torque, Engine Power,Engine fuel rate,Engine fuel consumption wrt Time

figure(2)

subplot(2,2,1)

plot(Time,Eng_trq,'linewidth',1,'color','black')

xlabel('Time [s]')

ylabel('Torque [Nm]')

legend('Engine Torque')

grid on

subplot(2,2,2)

plot(Time,Eng_pwr,'linewidth',1,'color','blue')

xlabel('Time [s]')

ylabel('Power [KW]')

legend('Engine Power')

grid on

subplot(2,2,3)

plot(Time,Eng_fuel_rate,'linewidth',1,'color','red')

xlabel('Time [s]')

ylabel('Fuel Rate [%]')

legend('Engine Fuel Rate')

grid on

subplot(2,2,4)

plot(Time,Eng_fuel_consumption,'linewidth',1,'color','green')

xlabel('Time [s]')

ylabel('Fuel Consumption')

legend('Engine Fuel Consumption')

grid on

% Plotting fuel economy Vs Engine Fuel consumption

figure(3)

plot(Eng_fuel_consumption,Eng_fuel_rate,'color','r')

xlabel('Fuel consumption')

ylabel('Fuel Rate [%]')

title('Fuel economy Vs Fuel Consumption')

grid on

%% Potting Accelerator pedal, Brake pedal and gear command with respect to time

figure(4)

subplot(2,1,1)

hold on

plot(Time, Acc_Pdl, 'linewidth', 1, 'Color', 'black');

plot(Time, Brk_Pdl, 'linewidth', 1, 'Color', 'red');

ylabel('Pedal [%]')

xlabel('Time [s]');

xlim([0, Time(end)]);

grid on

legend('Accel','Brake');

title('Acceleration & Brake Pedal wrt Time')

subplot(2,1,2)

plot(Time, Gear_Cmd, 'linewidth', 1, 'Color', 'black');

xlim([0, Time(end)]);

xlabel('Time [s]');

ylabel('Gear');

grid on

title('Gear command wrt Time')

% Plotting gear command vehicle desired with actual speed

figure(5)

subplot(2,1,1)

plot(Veh_spd, Gear_Cmd, 'linewidth', 1, 'Color', 'black');

xlabel('Speed [rpm]');

ylabel('Gear');

grid on

title('Gear command wrt vehicle speed')

subplot(2,1,2)

plot(Veh_dist, Gear_Cmd, 'linewidth', 1, 'Color', 'red');

xlabel('Distance [kmpl]');

ylabel('Gear');

grid on

title('Gear command wrt Distance')

%% Plotting engine operating points on engine fuel map

figure('Name','Engine Operating Points');

hold on

grid on

title('Engine Operating Points','fontsize',12);

p1=plot(Eng_map_spd*30/pi,Eng_max_trq,'linewidth',2,'color','r');

p2=line([Eng_map_spd(end)*30/pi Eng_map_spd(end)*30/pi],[0 Eng_max_trq(end)]);

set(p2,'linewidth',1,'linestyle','--','color','k');

p3=line([Eng_map_spd(1)*30/pi Eng_map_spd(1)*30/pi],[0 Eng_max_trq(1)]);

set(p3,'linewidth',1,'linestyle','--','color','k');

[c,h] = contour(Eng_map_spd'*30/pi,Eng_map_trq,Eng_fuel_map');

clabel(c,h);

% [e,h] = contour(Eng_map_spd'*30/pi,Eng_map_trq,Eng_fuel_map');

% elabel(e,h);

xlabel('Engine Speed [rpm]');

ylabel('Engine Torque [Nm]');

title('Engine Fuel Consumption Map [g/s]');

legend([p1 p3],{'Max Curve','Operating Points'});

axis([Eng_map_spd(1)*30/pi Eng_map_spd(end)*30/pi 0 Eng_map_trq(end)]);

Simulink output is uploaded by clicking on out mat file to be uploaded in variable form

UDDS PLOT

HWFET PLOT