Forward energy-based fuel consumption model using Simulink
Aim:- Development of a forward energy-based fuel consumption model of a conventional vehicle.
Objective:-
- Build Simulink model using blocks and complete the vehicle model.
- Writting scripts in MATLAB to load all the variables required for running the Simulink model.
- 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.
Theory:
Conventional Vehicle:-
Conventional vehicles use an internal combustion engine fueled by gasoline or diesel to power the wheels. In this the heat engine uses the principle of heat release through combustion of a fuel with an oxidizer in a combustion chamber to create expanding gases which pushes against a piston creating forcce and torque output.
In this vehicle engine converts chemical energy stored in the fuel into heat which is used to produce useful work. Typically use fossil fuels like petroleum (petrol and diesel).
The most popular type of engine is used in this system is 4 stroke reciprocating engine. Engine in cyclinder process can be represented by ideal thermodynamic cycles such as Otto cycle, Diesel cycle. Otto cycle is a ideal cycle thet describes the cycle process for spark ignited SI engine. and the Diesel cycle is the ideal cycle thet describes the cycle process for a compression ignited CI engine.
Energy and performance:-
In this system trge power demand on the wheel need to instant supplied by the powertrain. In otyher word the power coming from the powertrain dictates the power demand on the wheels (as per performance viz, acceleration, speed etc is determined by it.
In tis vehicle the powertrain is consists of an engine connected to the wheels through a transmission therefore the power comes from the engine through the transmission.
Conventional powertrain :-
The engine generates power by converting chemical energy stored into the mechanical energy by the process of combustion. This process of energy conversion also has an efficiency and the energy input is in the form of fuel consumption.
- Instantaneous fuel consumption is given as
m.f=Peηe⋅ηt⋅QLHV">.mf=Peηe⋅ηt⋅QLHVm.f=Peηe⋅ηt⋅QLHV
Where,
mf = mass flow rate in [kg]
pe = Power of engine
pt = power of transmission
nt = efficiency of transmission
ne = efficiency of engine
QLHV = it is th ecalorific value/ lower heating value of fuel.
In this model We use Forward Model:-
It also known as dynamic simulation. Dynamic models are used for detailed simulations. In this model force/torque/power is the input and the vehicle state variable velocity and acceleration are outputs. The models and simulatios are more realistic due to phhysical casualty hence appropriate for control development. There is feedback loop to meet the desired vehicle state. It is mainly used to simulate a vehicle on a driving cycle to analyse the dynamic behaviour of the system helps significantly in control development.
MATLAB scripts:-
%% 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 model:
Scope in Driver Model:-
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 ‘Powertrain’ block which represents the drivetrain of the vehicle.
1] Engine control Unit:-
In this control model We use engine control unit in that give input Engine speed through creating look up table. in that table we give input Maximum torque and map speed then also create 2nd look up trable in that give input ct torque and map speed then it substracts and multiplied. the engine speed also give to ideal contro speed to integrate from this we meet output of engine required torque.
Graph created from Scope in Driver Model:-
2] Transmission Control Unit:-
In this unit we create steadfy 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.
3] Brake Control Unit:-
In this calculate brake torque and then all three control signals output is give to powertrain.
3] PowerTrain:-
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] Engine:-
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 give output then saturated torque and speed map give fuel consumption takes the speed and torque then the output goes into saturated then its integrated.
Graph created from Scope in Driver Model:- Engine Torque
2] Transmission:-
In these model we take engine torque, gear selector from controllerb 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.
3] Differential:-
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.
4] Wheels:-
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.
5] Vehicle Dynamics:-
In this takes tractive force and road load. It is dictates vehicle speed based on tractive force and road load.
Graph created from Scope in Driver Model:- 1] Road load 2] Acceleration 3] Tractive force
Graph created from Scope in Driver Model:- 1] Road load
Now,
We compute the Fuel economy numbers using UDDS and HWFET cycle:-
1] UDDS Drive cycle
1] Time VS Speed:- In this the speed is increasing continuously.
2] Aerodyanamic drag:- Drag as increase when the power increase.
3] Rolling Resistance:- Its also increase when power is increase wrt time.
4] Total power = aerodynamic drag+rolling resistance+inertial resistance
Total Power is increase slowly as increasing rolling resistance, aerodynamic drag and inertial resistance.
2] HWFET Drive Cycle:-
1] Time VS Speed:- Speed is continuosly increase wrt time.
2] Aerodynamic Drag:- Drag as increase when the power increase.
3] Rolling Resistance:- In this resistance is decrease wrt time.
4] Total Power:- aerodynamic drag+rolling resistance+inertial resistance
Total Power is increase slowly as increasing aerodynamic drag and inertial resistance. but in this drive cycle bad impact occurs due to decreasing rolling resistance.
Result:-
As comparing both cycles we used to UDDS drive cycle. Its best for asses of fuel consumption and Pollutants emission of vehicle in a normalised way.
MATLAB code:-
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]
Wheel_Speed = out.wh_speed; % 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, Wheel_Speed, 'linewidth',1, 'color', 'blue')
ylabel('Speed [rpm]')
xlabel('Timem [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);
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)]);Plotting vehicle characteristics time trace transmission IN/OUT and Wheel Speed:-
Plotting vehicle characteristics time trace to Engine speed, Engine Torque, Engine Power, And Engine fuel rate, Engine fuel consumption
In this engine torque, Engine power, engine fuel rate and engine fuel consumption is increase increasing wrt time.
Plotting fuel economy Vs Engine Fuel consumption:-
In this the engine fuel consumption is suddensly increase as incresing fuel economy but if fuel economy is constant then the fuel consumption is also constant.
Potting Accelerator pedal, Brake pedal and gear command with respect to time:-
In this the as comparing brake of vehicle the accelaration of vehicle is more so the brake torque is min required. and the gear shifting is also required wrt time.
Plotting gear command vehicle desired with actual speed:-
In this the gear shifting is required as increase vehicle speed. as shifting order is gear1, then gear2, then gear3, and then gear4.
Plotting engine operating points on engine fuel map:-
