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, analyse 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.
- Analyse 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 behaviour throughout the drive cycle.
- Generate the plots for both drive cycles.
THEORY
Forward-Modelling Approach
- The forward modelling 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 behaviour of each powertrain 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 behaviour. The controller is used as part of a feedback loop that will determine the energy required to drive the vehicle.
Vehicle Energy Consumption Estimation Models
Energy consumption estimation models can be classified in three main categories:
- Analytical models:
Analytical models are representative of the Vehicle behaviour and can be developed in MATLAB/Simulink by creating an 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, 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 models:
There are mainly two kinds of computational models for energy consumption estimation: Artificial Neural Networks (ANN) based model. Clustering based models.
Conventional Vehicle Modelling
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.
%% Initialization File
% Initialization file for loading the variables for the Conventional vehicle simulation 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 Vehicle_Data/Engine_data_1_9L_Saturn_95kW
load Vehicle_Data/Trans_Shift_map
%% 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;
elseif Drive_Cycle_Select == 2
load DriveCycles/HWFET;
elseif Drive_Cycle_Select == 3
load DriveCycles/FTP;
elseif Drive_Cycle_Select == 4
load DriveCycles/US06;
elseif Drive_Cycle_Select == 5
load DriveCycles/NEDC;
elseif Drive_Cycle_Select == 6
load DriveCycles/WLTP;
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 MODELLING
- The Simulink model for the convection model is created using 3 main subblocks for the driver model, control model and powertrain 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 Powertrain 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.
- The PI controller controls the error between the required drive cycle and actual vehicle speed by providing acceleration and brake pedal output to the controller.
Controller Model
- The ‘Controller’ block is the brains of the vehicle, representing the electronic controls units. Based on the driver inputs, it generates desired engine torque, desired transmission gear and desired brake torque. These inputs are fed to the ‘Powertrain’ block which represents the drivetrain of the vehicle
- The controller consists of an engine control unit, a transmission control unit and a brake control unit.
- All control signals can be scoped.
Engine Control Unit
Idle Speed Controller:
- 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.
Transmission Control Block
- The transmission control block controls the gear shifting using the study flow Variable chart.
- 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.
Powertrain Model
- The powertrain 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.
- Engine fuel flow rate and Fuel consumption are scoped.
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.
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.
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.
Wheel Model
- 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
- The longitudinal dynamics of the vehicle along with the road load is represented in the ‘Vehicle Dynamics’ block
- Tractive Force and Road loads are used to calculate the vehicle velocity,
SIMULATION RESULTS
1. UDDS Drive Cycle
Drive Cycle and Actual Velocity
Control Signals (Engine Torque, Transmission Gear and Brake torque)
Engine Fuel Rate and Fuel Consumption
Engine Torque
Gear Ratio, Transmission Input and Output Speed
Different Road Loads
Tractive Force, Road Load and Acceleration
2. HWFET Drive Cycle
Drive Cycle and Actual Velocity
Control Signals (Engine Torque, Transmission Gear and Brake torque)
Engine Torque
Engine Fuel Rate and Fuel Consumption
Gear Ratio, Transmission Input and Output Speed
Different Road Loads
Tractive Force, Road Load and Acceleration
Post-Processing
- A MATLAB script is Created to analyse data and to generate plots. Here we rename the variables loaded from the model, do some basic post-process calculations and generate results and plots.
%% Post-Processing File
% File for post-processing the Conventional vehicle simulation model data
%% 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_rate = out.Eng_Fuel_Rate; % Engine Fuel Rate [gkW]
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*30/pi; % Wheel speed [rpm]
Desired_spd = out.Desired_Velo*18/5; % Desired Speed [Kmph]
%% 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]
% Display Fuel Economy of the Cycle
fprintf('nFuel Economy = %2.2fKmplnn',kmpl);
%% Plotting vehicle characteristics time trace
% Plotting transmission input, transmission output 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');
xlabel('Time [s]')
ylabel('Speed [rpm]')
xlim([0, Time(end)]);
legend('Trans Input','Trans Output','Wheel Speed');
% Plotting engine torque, engine power, fuel rate and fuel consumption
figure(2)
subplot(4,1,1)
hold on
grid on
plot(Time, Eng_Trq, 'linewidth', 1, 'Color', 'black');
ylabel('Torque [Nm]')
xlim([0, Time(end)]);
subplot(4,1,2)
hold on
grid on
plot(Time, Eng_Pwr, 'linewidth', 1, 'Color', 'black');
ylabel('Power [KW]')
xlim([0, Time(end)]);
subplot(4,1,3)
hold on
grid on
plot(Time, Eng_Fuel_rate, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Engine Fuel rate');
subplot(4,1,4)
hold on
grid on
plot(Time, Eng_Fuel_Consump, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Fuel Consumption [g]');
%Plotting accelerator and brake pedal gear command, vehicle desired and actual speed, vehicle distance
figure(3)
subplot(4,1,1)
hold on
grid on
plot(Time, Acc_Pdl, 'linewidth', 1, 'Color', 'black');
plot(Time, Brk_Pdl, 'linewidth', 1, 'Color', 'red');
ylabel('Pedal [%]')
xlim([0, Time(end)]);
legend('Accel','Brake');
subplot(4,1,2)
hold on
grid on
plot(Time, Gear_Cmd, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Gear');
subplot(4,1,3)
hold on
grid on
plot(Time, Veh_Spd, 'linewidth', 1, 'Color', 'red');
plot(Time, Desired_spd, 'linewidth', 1, 'Color', 'black');
ylabel('Speed [Kmph]')
xlim([0, Time(end)]);
legend('Actual speed','Desired speed');
subplot(4,1,4)
hold on
grid on
plot(Time, Veh_Dist, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Distance [Km]');
%% Plotting Drive Cycle
figure(4)
hold on
grid on
plot(cyc_time, cyc_vel, 'linewidth', 1, 'Color', 'black');
xlabel('Time [s]')
ylabel('Velocity [Mph]')
title('Drive Cycle')
% Test Results
Avg_speed = sum(Veh_Spd)/length(Veh_Spd);
Max_Speed = maxk(Veh_Spd,1);
table(Avg_speed,Max_Speed,kmpl,'VariableNames',{'Average Speed [kmph]','Maximum Speed [kmph]','Fuel Economy [kmpl]'})
%% 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);
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)]);
RESULTS
1.Drive cycles
UDDS:
HWFET:
2. Fuel economy numbers (kmpl) for UDDS and HWFET cycle.
UDDS:
HWFET:
- The City Fuel Economy is much lower than the highway drive as the brake pedal engagement and idle time on the drive cycle is less.
3. The time trace for engine, transmission input, transmission output and wheel speed
UDDS:
HWFET:
- Much of the fluctuating input speed is facilitated by the torque converter, and the transmission input speed fluctuates according to the engine torque required to achieve the drive cycle.
- Wheel speed and transmission output speed vary according to gear and differential ratio.
4. Engine torque, engine power, fuel rate and fuel consumption
UDDS:
HWFET:
- The torque requirements of the drive cycle are different, so the fuel flow rate varies and fuel consumption is calculated.
- The HWFET drive cycle has higher power and torque requirements and less negative torque and power.
5. Accelerator and brake pedal, gear command, vehicle desired and actual speed, vehicle distance
UDDS:
- Acceleration and brake pedals are used more because the drive cycle is not very smooth and the gear has to be shifted frequently.
HWFET:
- Brake requirements are lower, more accelerator pedals are applied on the highway drive cycle, and gear shifts often occur because the drive cycle is smoother.
- Acceleration and brake pedal, the gear command of the transmission control unit, the required speed of the vehicle, the actual vehicle speed and the actual vehicle distance are plotted
6. The engine operating points on the engine fuel map
UDDS:
HWFET:
- The engine operating points are plotted on the fuel map and the operating point is under the maximum torque curve.
CONCLUSION
- Hence, the forward energy-based fuel consumption model of a conventional vehicle has been successfully Simulated using MATLAB and Simulink.
- Analyses and understands vehicle operating points based on engine speed, torque, transmission speed, pedal positions, gear, and distance travelled.
- Post process calculations were performed and the required graphs were successfully plotted.
- Successfully calculated vehicle fuel efficiency numbers (kmpl) for the given city cycle (UDDS) and highway cycle (HWFET).