Project 1
Project
The development of a Forward Energy-Based Fuel Consumption Model of a Conventional Vehicle.
The main goal of this project is to get familiar with the modeling process, writing scripts in Matlab, modeling in Simulink, analyzing data and generating plots.
In this project, a typical midsize car with a 1.9L engine and a 4-speed automatic transmission is considered. Data is taken from ADVISOR data base developed by NREL, USA. Transmission shift map and controller is taken from Matlab/Simulink example database.
The model developed has the capability to simulate the vehicle on different drive cycles like UDDS, HWFET, FTP, NEDC, etc.
“Project1_InitFile.m” is a Matlab script used to load all the variables required for running the Simulink model and for post-processing. The drive cycle selection is also done here. Before running the Simulink vehicle model, run this initialization script.
“Project1_VehicleModel.slx” is the Simulink model of the vehicle. 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.
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. It consists of an ‘Engine’ connected to the ‘Automatic Transmission’ through a ‘Torque
Converter’.
The output of the transmission is connected to the ’Differential’, which powers the ‘Wheels’, that provides the tractive force for vehicle acceleration. The longitudinal dynamics of the vehicle along with the road load is represented in the ‘Vehicle Dynamics’ block. The solver selected is ode3 with a fixed step size of 0.01 sec.
After running this Simulink model, data from the model will be loaded in the Matlab workspace.
“Project1_ProcessingFile.m” is the Matlab script used to analyze this data and to generate plots. This script needs to be executed after the Simulink model data has been loaded into the workspace. Here we rename the variables loaded from the model (if desired), do some basic post-process calculations and generate results and plots.
Task: The task of this project is to compute the fuel economy numbers for the given vehicle (kmpl) on the urban cycle (UDDS) and highway cycle (HWFET). Also, to analyze and understand the vehicle operating points in terms of engine speed, torque, transmission speeds, pedal positions, gear, distance traveled, etc.
To do that, the following steps need to be followed:
1) Load the Project1 folder as the Current Folder in Matlab.
2) Run the “Project1_InitFile.m” Matlab script.
3) The provided vehicle Simulink model “Project1_VehicleModel.slx” is incomplete. The engine and vehicle dynamics block contents have been deleted. Build the Simulink blocks by referring to the course lecture and example block images provided. You can run the model and analyze the results using a ‘Scope’ for debugging.
4) Add additional ‘To Workspace’ blocks for transferring the desired Simulink vehicle data into the Matlab workspace.
5) Modify the “Project1_ProcessingFile.m” as per the desired plots and required calculations.
6) Write a project report that contains the following:
a. Tabulate the fuel economy numbers (kmpl) for UDDS and HWFET cycle. This forms the baseline numbers for comparing with the future hybrid version.
b. Plot the time trace for engine, transmission input, transmission output and wheel speed on one plot.
c. Plot engine torque, engine power, fuel rate and fuel consumption using subplots.
d. Plot accelerator and brake pedal, gear command, vehicle desired and actual speed, vehicle distance using subplots.
e. Plot the engine operating points on the engine fuel map.
f. Write down appropriate brief comments on each of these plots, describing the vehicle behavior throughout the drive cycle.
g. Generate the plots for both drive cycles.
Solution:
Energy Based Model
An energy-based model is a probabilistic model governed by an energy function that describes the probability of a certain state.
There are two basic types of structure for the energy-based models:
A) Forward Model
B) Backward Model
A) Forward Models:
Forward models are utilized for detailed simulations, whereas dynamic models are used for forward models (refer Figure 1). The input is force/torque/power, and the outputs are the vehicle state variables velocity and acceleration. Because physical casualty makes models and simulations more realistic, they are better for control development. To achieve the desired vehicle state, there is a feedback loop. Because of the dynamics, the simulation is slower, and the approach is mostly used to model a vehicle drive cycle and study the system's dynamic behavior. Significantly aids in the management of development.
B) Backward Models:
Backward models are calculated in a quasi-static manner. The inputs include vehicle conditions like velocity and acceleration, whereas the output is the force, torque, and power required at the source, i.e. the engine. They are simple and quick to use, making them ideal for quick computations and comparisons. They lack dynamics, and the method is mostly used to calculate simple fuel consumption and optimize energy management
Conventional Vehicle
Conventional vehicle means any self -propelled, motorized vehicle designed for transporting persons or property on a public highway and must be registered.
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit.
ICEs are typically powered by hydrocarbon-based fuels like natural gas, gasoline, diesel fuel, ethanol.
In an internal combustion engine, the expansion of the high-temperature and high-pressure gases produced by combustion applies direct force to some component of the engine. The force is typically applied to psitons (piston engine), turbine bladers (gas turbine), a rotor, or a nozzle. This force moves the component over a distance, transforming chemical energy into kinetic energy which is used to propel, move or power whatever the engine is attached to. This replaced the external combustion engine for applications where the weight or size of an engine was more important.
Conventional Vehicle Modeling
Energy Demand for Drive Cycle
Energy demand at the wheel, due to a drive cycle can be computed. The force at the wheels are given by,
The power at the wheels is given by,
Energy demand for the drive cycle is computed by integrating power over time for the entire cycle,
Assuming mass, air density, drag coefficient, frontal area, rolling resistance coefficient and acceleration due to gravity are constant for the drive cycle,
where, ki is the coefficient of inertial resistance, ka is the coefficient of aerodynamic drag, and kr is the coefficient of rolling resistance, and they are given by,
To calculate energy, the integrals can be discretized. Generally, time step of 1 sec is sufficient for the drive cycles.
Energy Based Model - Element Model
A) Map Based Model
B) Analytical Model
A) Map Based Model :
Elements are modeled using maps, which characterize the relationship between the input & output and output & losses etc.
B) Analytical Model :
Elements are modeled using the physical equations, that represent the internal dynamics.
Given:
1. In this project, a typical midsize car with a 1.9L engine and a 4-speed automatic transmission is considered.
2. Data is taken from ADVISOR data base developed by NREL, USA.
3. The model developed has the capability to simulate the vehicle on different drive cycles like UDDS, HWFET, FTP, NEDC, etc.
4. A basic PI controller that generates accelerator and brake pedal outputs to match the desired and actual vehicle speeds.
5. 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. It consists of an ‘Engine’ connected to the ‘Automatic Transmission’ through a ‘Torque Converter’.
6. The output of the transmission is connected to the ’Differential’, which powers the ‘Wheels’, that provides the tractive force for vehicle acceleration.
7. The longitudinal dynamics of the vehicle along with the road load is represented in the ‘Vehicle Dynamics’ block. The solver selected is ode3 with a fixed step size of 0.01 sec.
8. The vehicle, power train and driver parameters are prepared as a script in MATLAB.
Following program is writen in MATLAB Script Window:
%% 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);
%% 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);
Simulink Vehicle Model
The Simulink model consist of three main subsystems: Driver, Controller and Powertrain, as shown in below figure. The Driver subsytem generates the accelerator and brake pedal outputs to match the desired and actual vehicle speed. The Controller block represents the electronic control units, which generates the desired engine torque, desired transmission gear and desired brake torque based on the driver inputs. The Powertrain subsytem represents the actual vehicle consisting of all vehicle components which inputs the control signals from Controller and provides actual vehicle motion characteristics.
Following steps to be followed
1. Load the Project1 folder as the Current Folder in Matlab.
2. Run the “Project1_InitFile.m” Matlab script.
3.Build a Simulink blocks by referring to the course lecture and example block images provided.
4. Run the model and analyze the results using a ‘Scope’ for debugging
Driver Model
Driver Model 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 fro the based on these results of fuel consumption and emissions the vehicle gets certified and it also forms a basis of uniform asessment. It is based on time, velocity then its all integrate and creates output accelration pedal and brake pedal.
Following Graph is obtained
Controller Model
The output of the driver block which is the acceleration and brake pedal signal is passed on to the Controller block. The controller block consists of three control units: Engine Control Unit, Transmission Control Unit and Brake Control Unit. All these data from the three Control Unit goes to the bus creator. The bus creator is used to combine all these three signals to a one signal. This combined signal is then sent to the Powertrain block.
Power Train Model
The powertrain encompasses every component that converts the engine's power into movement. This includes the engine, transmission, the driveshaft, differentials, axles; basically anything from the engine through to the rotating wheels.
1. The ‘Controller’ block is the brains of the vehicle, representing the electronic controls units.
2. Based on the driver inputs, it generates desired engine torque, desired transmission gear
and desired brake torque.
3. These inputs are fed to the ‘Powertrain’ block which represents the drivetrain of the vehicle.
4. It consists of an ‘Engine’ connected to the ‘Automatic Transmission’ through a ‘Torque Converter’.
5. The Engine Block is developed by applying torque characteristics and fuel consumption details.
Engine Model
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.
Following Graph is obtained
1.The output of the transmission is connected to the ’Differential’, which powers the ‘Wheels’, that provides the tractive force for vehicle acceleration.
2. The longitudinal dynamics of the vehicle along with the road load is represented in the ‘Vehicle Dynamics’ block. The solver selected is ode3 with a fixed step size of 0.01 sec.
3. The Vehicle dynamics block is developed using the equations. Equations for aerodynamic drag, rolling resistance, and gradient are created and summed up to get the road load.
4. Road load is subtracted from the tractive force to get the force. This force is then divided by the mass to get the acceleration component.
5. Integrator is used to integrate the acceleration and get the velocity component.
6. Road load and velocity are multiplied to get the power required for the vehicle.
7. Power is then multiplied by the total time to get the energy required.
8. All the blocks of velocity, acceleration, road load, the power required, and energy required are attached to the 'scope' block to see the output variations with respect to the time.
Vehicle Dynamics Model
In this takes tractive force and road load. It is dictates vehicle speed based on tractive force and road load.
Following Graph is obtained
Transmission Model
In these 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.
Differential Model
In this taking input is the transmission output then its going to the differential ratio multiplied the output and input torque then meet axle torque. The axle torque is a lower than the transmission torque and differential ratio.
Wheel Model Model
In this model we take the axle torque from differentail and brake torque from controller. it is substracts and multiplied rolling radius and velocity then we meet the tractive force from axle and brake torque. and the wheelspeed is meet using velocity.
1. The following file is to used with the Initialization file and Simulink
2. Results for post-processing of the data.
3. The file is incomplete, has some examples of how the data is imported
4. Into a readable format, data analysis and plotting examples.
5. Based on the project task, use commands in a similar format as given
6.Below, to analyse the data and generate required plots.
7.You can change variable names if desired
The MATLAB script "Project1_ProcessingFile" is used to analyze the data from the Simulink model and to generate plots. After the Simulink vehicle model is run, some of the data are sent to the workspace which is used to plot different parameters for the study of conventional vehicle in MATLAB.
Following command is written in MATLAB Script window
%% 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]
%% 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]
%% 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]
%% 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]
1. Plot the time trace for engine, transmission input, transmission output and wheel speed on one plot.
2.Plot engine torque, engine power, fuel rate and fuel consumption using subplots.
3. Plot accelerator and brake pedal, gear command, vehicle desired and actual speed, vehicle distance using subplots.
4.Plot the engine operating points on the engine fuel map.
figure()
subplot(3,1,1)
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(3,1,2)
hold on
grid on
plot(Time, Trans_In_Spd, 'linewidth', 1, 'Color', 'black');
plot(Time, Trans_Out_Spd, 'linewidth', 1, 'Color', 'red');
ylabel('Speed [rpm]')
xlim([0, Time(end)]);
ylim([0, 6000]);
legend('Trans Input','Trans Output');
subplot(3,1,3)
hold on
grid on
plot(Time, Gear_Cmd, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Gear');
figure()
subplot(3,1,1)
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(3,1,2)
hold on
grid on
plot(Time, Trans_In_Spd, 'linewidth', 1, 'Color', 'black');
plot(Time, Trans_Out_Spd, 'linewidth', 1, 'Color', 'red');
ylabel('Speed [rpm]')
xlim([0, Time(end)]);
ylim([0, 6000]);
legend('Trans Input','Trans Output');
subplot(3,1,3)
hold on
grid on
plot(Time, Gear_Cmd, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Gear');
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]');
p4 = plot(Eng_Spd,Eng_Trq,'.','color','k');
legend([p1 p4],{'Max Curve','Operating Points'});
axis([Eng_map_spd(1)*30/pi Eng_map_spd(end)*30/pi 0 Eng_map_trq(end)]);
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]');
p4 = plot(Eng_Spd,Eng_Trq,'.','color','k');
legend([p1 p4],{'Max Curve','Operating Points'});
axis([Eng_map_spd(1)*30/pi Eng_map_spd(end)*30/pi 0 Eng_map_trq(end)]);
Conclusion:
The MATLAB script for both initializing and post processing has be successfully made, and a forward energy-based fuel consumption Simulink model of a conventional vehicle is also developed successfully, and the functionality is checked.