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OpenLAP.m
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%% OpenLAP Laptime Simulation Project
%
% OpenLAP
%
% Lap time simulation using a simple point mass model for a racing vehicle.
% Instructions:
% 1) Select a vehicle file created by OpenVEHICLE by assigning the full
% path to the variable "vehiclefile".
% 2) Select a track file created by OpenTRACK by assigning the full path to
% the variable "trackfile".
% 3) Select an export frequency in [Hz] by setting the variable "freq" to
% the desired value.
% 4) Run the script.
% 5) The results will appear on the command window and inside the folder
% "OpenLAP Sims". You can choose to include the date and time of each
% simulation in the result file name by changing the
% "use_date_time_in_name" variable to true.
%
% More information can be found in the "OpenLAP Laptime Simulator"
% videos on YouTube.
%
% This software is licensed under the GPL V3 Open Source License.
%
% Open Source MATLAB project created by:
%
% Michael Chalkiopoulos
% Cranfield University MSc Advanced Motorsport Engineer
% National Technical University of Athens MEng Mechanical Engineer
%
% LinkedIn: https://www.linkedin.com/in/michael-chalkiopoulos/
% email: [email protected]
% MATLAB file exchange: https://uk.mathworks.com/matlabcentral/fileexchange/
% GitHub: https://github.com/mc12027
%
% April 2020.
%% Clearing memory
clear
clc
close all force
diary('off')
fclose('all') ;
%% Starting timer
tic
%% Filenames
trackfile = 'OpenTRACK Tracks/OpenTRACK_FSAE Skidpad_Closed_Forward.mat' ;
vehiclefile = 'OpenVEHICLE Vehicles/OpenVEHICLE_BFR 2019_Open Wheel.mat' ;
%% Loading circuit
tr = load(trackfile) ;
%% Loading car
veh = load(vehiclefile) ;
%% Export frequency
freq = 50 ; % [Hz]
%% Simulation name
use_date_time_in_name = false ;
if use_date_time_in_name
date_time = "_"+datestr(now,'yyyy_mm_dd')+"_"+datestr(now,'HH_MM_SS') ; %#ok<UNRCH>
else
date_time = "" ;
end
simname = "OpenLAP Sims/OpenLAP_"+char(veh.name)+"_"+tr.info.name+date_time ;
logfile = simname+".log" ;
%% HUD
[folder_status,folder_msg] = mkdir('OpenLAP Sims') ;
delete(simname+".log") ;
logid = fopen(logfile,'w') ;
disp_logo(logid)
disp('=================================================')
disp("Vehicle: "+veh.name)
disp("Track: "+tr.info.name)
disp("Date: "+datestr(now,'dd/mm/yyyy'))
disp("Time: "+datestr(now,'HH:MM:SS'))
disp('=================================================')
fprintf(logid,'%s\n','=================================================') ;
fprintf(logid,'%s\n',"Vehicle: "+veh.name) ;
fprintf(logid,'%s\n',"Track: "+tr.info.name) ;
fprintf(logid,'%s\n',"Date: "+datestr(now,'dd/mm/yyyy')) ;
fprintf(logid,'%s\n',"Time: "+datestr(now,'HH:MM:SS')) ;
fprintf(logid,'%s\n','=================================================') ;
%% Lap Simulation
[sim] = simulate(veh,tr,simname,logid) ;
%% Displaying laptime
disp(['Laptime: ',num2str(sim.laptime.data,'%3.3f'),' [s]'])
fprintf(logid,'%s','Laptime : ') ;
fprintf(logid,'%7.3f',sim.laptime.data) ;
fprintf(logid,'%s\n',' [s]') ;
for i=1:max(tr.sector)
disp(['Sector ',num2str(i),': ',num2str(sim.sector_time.data(i),'%3.3f'),' [s]'])
fprintf(logid,'%s','Sector ') ;
fprintf(logid,'%3d',i) ;
fprintf(logid,'%s',': ') ;
fprintf(logid,'%7.3f',sim.sector_time.data(i)) ;
fprintf(logid,'%s\n',' [s]') ;
end
%% Ploting results
% figure window
set(0,'units','pixels') ;
SS = get(0,'screensize') ;
H = 900-90 ;
W = 900 ;
Xpos = floor((SS(3)-W)/2) ;
Ypos = floor((SS(4)-H)/2) ;
f = figure('Name','OpenLAP Simulation Results','Position',[Xpos,Ypos,W,H]) ;
figname = ["OpenLAP: "+char(veh.name)+" @ "+tr.info.name,"Date & Time: "+datestr(now,'yyyy/mm/dd')+" "+datestr(now,'HH:MM:SS')] ;
sgtitle(figname)
% setting rows & columns
rows = 7 ;
cols = 2 ;
% x axis limits
xlimit = [tr.x(1),tr.x(end)] ;
% xlimit = [4000,4500] ;
% setting legend location
loc = 'east' ;
% speed
subplot(rows,cols,[1,2])
hold on
plot(tr.x,sim.speed.data*3.6)
legend({'Speed'},'Location',loc)
xlabel('Distance [m]')
xlim(xlimit)
ylabel('Speed [m/s]')
ylabel('Speed [km/h]')
grid on
% elevation and curvature
subplot(rows,cols,[3,4])
yyaxis left
plot(tr.x,tr.Z)
xlabel('Distance [m]')
xlim(xlimit)
ylabel('Elevation [m]')
grid on
yyaxis right
plot(tr.x,tr.r)
legend({'Elevation','Curvature'},'Location',loc)
ylabel('Curvature [m^-^1]')
% accelerations
subplot(rows,cols,[5,6])
hold on
plot(tr.x,sim.long_acc.data)
plot(tr.x,sim.lat_acc.data)
plot(tr.x,sim.sum_acc.data,'k:')
legend({'LonAcc','LatAcc','GSum'},'Location',loc)
xlabel('Distance [m]')
xlim(xlimit)
ylabel('Acceleration [m/s^2]')
grid on
% drive inputs
subplot(rows,cols,[7,8])
hold on
plot(tr.x,sim.throttle.data*100)
plot(tr.x,sim.brake_pres.data/10^5)
legend({'tps','bps'},'Location',loc)
xlabel('Distance [m]')
xlim(xlimit)
ylabel('input [%]')
grid on
ylim([-10,110])
% steering inputs
subplot(rows,cols,[9,10])
hold on
plot(tr.x,sim.steering.data)
plot(tr.x,sim.delta.data)
plot(tr.x,sim.beta.data)
legend({'Steering wheel','Steering \delta','Vehicle slip angle \beta'},'Location',loc)
xlabel('Distance [m]')
xlim(xlimit)
ylabel('angle [deg]')
grid on
% ggv circle
subplot(rows,cols,[11,13])
hold on
scatter3(sim.lat_acc.data,sim.long_acc.data,sim.speed.data*3.6,50,'ro','filled','MarkerEdgeColor',[0,0,0])
surf(veh.GGV(:,:,2),veh.GGV(:,:,1),veh.GGV(:,:,3)*3.6,'EdgeAlpha',0.3,'FaceAlpha',0.8)
legend('OpenLAP','GGV','Location','northeast')
xlabel('LatAcc [m/s^2]')
ylabel('LonAcc [m/s^2]')
zlabel('Speed [km/h]')
grid on
set(gca,'DataAspectRatio',[1 1 3])
axis tight
% track map
subplot(rows,cols,[12,14])
hold on
scatter(tr.X,tr.Y,5,sim.speed.data*3.6)
plot(tr.arrow(:,1),tr.arrow(:,2),'k','LineWidth',2)
legend('Track Map','Location','northeast')
xlabel('X [m]')
ylabel('Y [m]')
colorbar
grid on
axis equal
% saving figure
savefig(simname+".fig")
% HUD
disp('Plots created and saved.')
fprintf(logid,'%s\n','Plots created and saved.') ;
%% Report generation
% csv report generation
export_report(veh,tr,sim,freq,logid) ;
% saving .mat file
save(simname+".mat",'veh','tr','sim')
% HUD
toc
fprintf(logid,'%s','Elapsed time is: ') ;
fprintf(logid,'%f',toc) ;
fprintf(logid,'%s\n',' [s]') ;
fclose('all') ;
%% Functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [sim] = simulate(veh,tr,simname,logid)
%% initialisation
% solver timer
timer_solver_start = tic ;
% HUD
disp('Simulation started.')
fprintf(logid,'%s\n','Simulation started.') ;
%% maximum speed curve (assuming pure lateral condition)
v_max = single(zeros(tr.n,1)) ;
bps_v_max = single(zeros(tr.n,1)) ;
tps_v_max = single(zeros(tr.n,1)) ;
for i=1:tr.n
[v_max(i),tps_v_max(i),bps_v_max(i)] = vehicle_model_lat(veh,tr,i) ;
end
% HUD
disp('Maximum speed calculated at all points.')
fprintf(logid,'%s\n','Maximum speed calculated at all points.') ;
%% finding apexes
[v_apex,apex] = findpeaks(-v_max) ; % findpeaks works for maxima, so need to flip values
v_apex = -v_apex ; % flipping to get positive values
% setting up standing start for open track configuration
if strcmp(tr.info.config,'Open')
if apex(1)~=1 % if index 1 is not already an apex
apex = [1;apex] ; % inject index 1 as apex
v_apex = [0;v_apex] ; % inject standing start
else % index 1 is already an apex
v_apex(1) = 0 ; % set standing start at index 1
end
end
% checking if no apexes found and adding one if needed
if isempty(apex)
[v_apex,apex] = min(v_max) ;
end
% reordering apexes for solver time optimisation
apex_table = sortrows([v_apex,apex],1) ;
v_apex = apex_table(:,1) ;
apex = apex_table(:,2) ;
% getting driver inputs at apexes
tps_apex = tps_v_max(apex) ;
bps_apex = bps_v_max(apex) ;
% HUD
disp('Found all apexes on track.')
fprintf(logid,'%s\n','Found all apexes on track.') ;
%% simulation
% memory preallocation
N = uint32((length(apex))) ; % number of apexes
flag = false(tr.n,2) ; % flag for checking that speed has been correctly evaluated
% 1st matrix dimension equal to number of points in track mesh
% 2nd matrix dimension equal to number of apexes
% 3rd matrix dimension equal to 2 if needed (1 copy for acceleration and 1 for deceleration)
v = single(inf*ones(tr.n,N,2)) ;
ax = single(zeros(tr.n,N,2)) ;
ay = single(zeros(tr.n,N,2)) ;
tps = single(zeros(tr.n,N,2)) ;
bps = single(zeros(tr.n,N,2)) ;
% HUD
disp('Starting acceleration and deceleration.')
fprintf(logid,'%s\n','Starting acceleration and deceleration.') ;
prg_size = 30 ;
prg_pos = ftell(logid) ;
fprintf(['Running: [',repmat(' ',1,prg_size),'] '])
fprintf('% 3.0f',0)
fprintf(' [%%]')
fprintf(logid,'%s',['Running: [',repmat(' ',1,prg_size),'] ']) ;
fprintf(logid,'% 3.0f',0) ;
fprintf(logid,'%s\n',' [%]') ;
fprintf(logid,'________________________________________________\n') ;
fprintf(logid,'|_Apex__|_Point_|_Mode__|___x___|___v___|_vmax_|\n') ;
% running simulation
for i=1:N % apex number
for k=uint8(1:2) % mode number
switch k
case 1 % acceleration
mode = 1 ;
k_rest = 2 ;
case 2 % deceleration
mode = -1 ;
k_rest = 1 ;
end
if ~(strcmp(tr.info.config,'Open') && mode==-1 && i==1) % does not run in decel mode at standing start in open track
% getting other apex for later checking
[i_rest] = other_points(i,N) ;
if isempty(i_rest)
i_rest = i ;
end
% getting apex index
j = uint32(apex(i)) ;
% saving speed & latacc & driver inputs from presolved apex
v(j,i,k) = v_apex(i) ;
ay(j,i,k) = v_apex(i)^2*tr.r(j) ;
tps(j,:,1) = tps_apex(i)*ones(1,N) ;
bps(j,:,1) = bps_apex(i)*ones(1,N) ;
tps(j,:,2) = tps_apex(i)*ones(1,N) ;
bps(j,:,2) = bps_apex(i)*ones(1,N) ;
% setting apex flag
flag(j,k) = true ;
% getting next point index
[~,j_next] = next_point(j,tr.n,mode,tr.info.config) ;
if ~(strcmp(tr.info.config,'Open') && mode==1 && i==1) % if not in standing start
% assuming same speed right after apex
v(j_next,i,k) = v(j,i,k) ;
% moving to next point index
[j_next,j] = next_point(j,tr.n,mode,tr.info.config) ;
end
while 1
% writing to log file
fprintf(logid,'%7d\t%7d\t%7d\t%7.1f\t%7.2f\t%7.2f\n',i,j,k,tr.x(j),v(j,i,k),v_max(j)) ;
% calculating speed, accelerations and driver inputs from vehicle model
[v(j_next,i,k),ax(j,i,k),ay(j,i,k),tps(j,i,k),bps(j,i,k),overshoot] = vehicle_model_comb(veh,tr,v(j,i,k),v_max(j_next),j,mode) ;
% checking for limit
if overshoot
break
end
% checking if point is already solved in other apex iteration
if flag(j,k) || flag(j,k_rest)
if not(isempty(i_rest))
if max(v(j_next,i,k)>=v(j_next,i_rest,k)) || max(v(j_next,i,k)>v(j_next,i_rest,k_rest))
break
end
end
end
% updating flag and grogress bar
flag = flag_update(flag,j,k,prg_size,logid,prg_pos) ;
% moving to next point index
[j_next,j] = next_point(j,tr.n,mode,tr.info.config) ;
% checking if lap is completed
switch tr.info.config
case 'Closed'
if j==apex(i) % made it to the same apex
break
end
case 'Open'
if j==tr.n % made it to the end
flag = flag_update(flag,j,k,prg_size,logid,prg_pos) ;
break
end
if j==1 % made it to the start
break
end
end
end
end
end
end
% HUD
progress_bar(max(flag,[],2),prg_size,logid,prg_pos) ;
fprintf('\n')
disp('Velocity profile calculated.')
disp(['Solver time is: ',num2str(toc(timer_solver_start)),' [s]']) ;
disp('Post-processing initialised.')
fprintf(logid,'________________________________________________\n') ;
if sum(flag)<size(flag,1)/size(flag,2)
fprintf(logid,'%s\n','Velocity profile calculation error.') ;
fprintf(logid,'%s\n','Points not calculated.') ;
p = (1:tr.n)' ;
fprintf(logid,'%d\n',p(min(flag,[],2))) ;
else
fprintf(logid,'%s\n','Velocity profile calculated successfully.') ;
end
fprintf(logid,'%s','Solver time is: ') ;
fprintf(logid,'%f',toc(timer_solver_start)) ;
fprintf(logid,'%s\n',' [s]') ;
fprintf(logid,'%s\n','Post-processing initialised.') ;
%% post-processing resutls
% result preallocation
V = zeros(tr.n,1) ;
AX = zeros(tr.n,1) ;
AY = zeros(tr.n,1) ;
TPS = zeros(tr.n,1) ;
BPS = zeros(tr.n,1) ;
% solution selection
for i=1:tr.n
IDX = length(v(i,:,1)) ;
[V(i),idx] = min([v(i,:,1),v(i,:,2)]) ; % order of k in v(i,:,k) inside min() must be the same as mode order to not miss correct values
if idx<=IDX % solved in acceleration
AX(i) = ax(i,idx,1) ;
AY(i) = ay(i,idx,1) ;
TPS(i) = tps(i,idx,1) ;
BPS(i) = bps(i,idx,1) ;
else % solved in deceleration
AX(i) = ax(i,idx-IDX,2) ;
AY(i) = ay(i,idx-IDX,2) ;
TPS(i) = tps(i,idx-IDX,2) ;
BPS(i) = bps(i,idx-IDX,2) ;
end
end
% HUD
disp('Correct solution selected from modes.')
fprintf(logid,'%s\n','Correct solution selected from modes.') ;
% laptime calculation
if strcmp(tr.info.config,'Open')
time = cumsum([tr.dx(2)./V(2);tr.dx(2:end)./V(2:end)]) ;
else
time = cumsum(tr.dx./V) ;
end
sector_time = zeros(max(tr.sector),1) ;
for i=1:max(tr.sector)
sector_time(i) = max(time(tr.sector==i))-min(time(tr.sector==i)) ;
end
laptime = time(end) ;
% HUD
disp('Laptime calculated.')
fprintf(logid,'%s\n','Laptime calculated.') ;
% calculating forces
M = veh.M ;
g = 9.81 ;
A = sqrt(AX.^2+AY.^2) ;
Fz_mass = -M*g*cosd(tr.bank).*cosd(tr.incl) ;
Fz_aero = 1/2*veh.rho*veh.factor_Cl*veh.Cl*veh.A*V.^2 ;
Fz_total = Fz_mass+Fz_aero ;
Fx_aero = 1/2*veh.rho*veh.factor_Cd*veh.Cd*veh.A*V.^2 ;
Fx_roll = veh.Cr*abs(Fz_total) ;
% HUD
disp('Forces calculated.')
fprintf(logid,'%s\n','Forces calculated.') ;
% calculating yaw motion, vehicle slip angle and steering input
yaw_rate = V.*tr.r ;
delta = zeros(tr.n,1) ;
beta = zeros(tr.n,1) ;
for i=1:tr.n
B = [M*V(i)^2*tr.r(i)+M*g*sind(tr.bank(i));0] ;
sol = veh.C\B ;
delta(i) = sol(1)+atand(veh.L*tr.r(i)) ;
beta(i) = sol(2) ;
end
steer = delta*veh.rack ;
% HUD
disp('Yaw motion calculated.')
disp('Steering angles calculated.')
disp('Vehicle slip angles calculated.')
fprintf(logid,'%s\n','Yaw motion calculated.') ;
fprintf(logid,'%s\n','Steering angles calculated.') ;
fprintf(logid,'%s\n','Vehicle slip angles calculated.') ;
% calculating engine metrics
wheel_torque = TPS.*interp1(veh.vehicle_speed,veh.wheel_torque,V,'linear','extrap') ;
Fx_eng = wheel_torque/veh.tyre_radius ;
engine_torque = TPS.*interp1(veh.vehicle_speed,veh.engine_torque,V,'linear','extrap') ;
engine_power = TPS.*interp1(veh.vehicle_speed,veh.engine_power,V,'linear','extrap') ;
engine_speed = interp1(veh.vehicle_speed,veh.engine_speed,V,'linear','extrap') ;
gear = interp1(veh.vehicle_speed,veh.gear,V,'nearest','extrap') ;
fuel_cons = cumsum(wheel_torque/veh.tyre_radius.*tr.dx/veh.n_primary/veh.n_gearbox/veh.n_final/veh.n_thermal/veh.fuel_LHV) ;
fuel_cons_total = fuel_cons(end) ;
% HUD
disp('Engine metrics calculated.')
fprintf(logid,'%s\n','Engine metrics calculated.') ;
% calculating kpis
percent_in_corners = sum(tr.r~=0)/tr.n*100 ;
percent_in_accel = sum(TPS>0)/tr.n*100 ;
percent_in_decel = sum(BPS>0)/tr.n*100 ;
percent_in_coast = sum(and(BPS==0,TPS==0))/tr.n*100 ;
percent_in_full_tps = sum(tps==1)/tr.n*100 ;
percent_in_gear = zeros(veh.nog,1) ;
for i=1:veh.nog
percent_in_gear(i) = sum(gear==i)/tr.n*100 ;
end
energy_spent_fuel = fuel_cons*veh.fuel_LHV ;
energy_spent_mech = energy_spent_fuel*veh.n_thermal ;
gear_shifts = sum(abs(diff(gear))) ;
[~,i] = max(abs(AY)) ;
ay_max = AY(i) ;
ax_max = max(AX) ;
ax_min = min(AX) ;
sector_v_max = zeros(max(tr.sector),1) ;
sector_v_min = zeros(max(tr.sector),1) ;
for i=1:max(tr.sector)
sector_v_max(i) = max(V(tr.sector==i)) ;
sector_v_min(i) = min(V(tr.sector==i)) ;
end
% HUD
disp('KPIs calculated.')
disp('Post-processing finished.')
fprintf(logid,'%s\n','KPIs calculated.') ;
fprintf(logid,'%s\n','Post-processing finished.') ;
%% saving results in sim structure
sim.sim_name.data = simname ;
sim.distance.data = tr.x ;
sim.distance.unit = 'm' ;
sim.time.data = time ;
sim.time.unit = 's' ;
sim.N.data = N ;
sim.N.unit = [] ;
sim.apex.data = apex ;
sim.apex.unit = [] ;
sim.speed_max.data = v_max ;
sim.speed_max.unit = 'm/s' ;
sim.flag.data = flag ;
sim.flag.unit = [] ;
sim.v.data = v ;
sim.v.unit = 'm/s' ;
sim.Ax.data = ax ;
sim.Ax.unit = 'm/s/s' ;
sim.Ay.data = ay ;
sim.Ay.unit = 'm/s/s' ;
sim.tps.data = tps ;
sim.tps.unit = [] ;
sim.bps.data = bps ;
sim.bps.unit = [] ;
sim.elevation.data = tr.Z ;
sim.elevation.unit = 'm' ;
sim.speed.data = V ;
sim.speed.unit = 'm/s' ;
sim.yaw_rate.data = yaw_rate ;
sim.yaw_rate.unit = 'rad/s' ;
sim.long_acc.data = AX ;
sim.long_acc.unit = 'm/s/s' ;
sim.lat_acc.data = AY ;
sim.lat_acc.unit = 'm/s/s' ;
sim.sum_acc.data = A ;
sim.sum_acc.unit = 'm/s/s' ;
sim.throttle.data = TPS ;
sim.throttle.unit = 'ratio' ;
sim.brake_pres.data = BPS ;
sim.brake_pres.unit = 'Pa' ;
sim.brake_force.data = BPS*veh.phi ;
sim.brake_force.unit = 'N' ;
sim.steering.data = steer ;
sim.steering.unit = 'deg' ;
sim.delta.data = delta ;
sim.delta.unit = 'deg' ;
sim.beta.data = beta ;
sim.beta.unit = 'deg' ;
sim.Fz_aero.data = Fz_aero ;
sim.Fz_aero.unit = 'N' ;
sim.Fx_aero.data = Fx_aero ;
sim.Fx_aero.unit = 'N' ;
sim.Fx_eng.data = Fx_eng ;
sim.Fx_eng.unit = 'N' ;
sim.Fx_roll.data = Fx_roll ;
sim.Fx_roll.unit = 'N' ;
sim.Fz_mass.data = Fz_mass ;
sim.Fz_mass.unit = 'N' ;
sim.Fz_total.data = Fz_total ;
sim.Fz_total.unit = 'N' ;
sim.wheel_torque.data = wheel_torque ;
sim.wheel_torque.unit = 'N.m' ;
sim.engine_torque.data = engine_torque ;
sim.engine_torque.unit = 'N.m' ;
sim.engine_power.data = engine_power ;
sim.engine_power.unit = 'W' ;
sim.engine_speed.data = engine_speed ;
sim.engine_speed.unit = 'rpm' ;
sim.gear.data = gear ;
sim.gear.unit = [] ;
sim.fuel_cons.data = fuel_cons ;
sim.fuel_cons.unit = 'kg' ;
sim.fuel_cons_total.data = fuel_cons_total ;
sim.fuel_cons_total.unit = 'kg' ;
sim.laptime.data = laptime ;
sim.laptime.unit = 's' ;
sim.sector_time.data = sector_time ;
sim.sector_time.unit = 's' ;
sim.percent_in_corners.data = percent_in_corners ;
sim.percent_in_corners.unit = '%' ;
sim.percent_in_accel.data = percent_in_accel ;
sim.percent_in_accel.unit = '%' ;
sim.percent_in_decel.data = percent_in_decel ;
sim.percent_in_decel.unit = '%' ;
sim.percent_in_coast.data = percent_in_coast ;
sim.percent_in_coast.unit = '%' ;
sim.percent_in_full_tps.data = percent_in_full_tps ;
sim.percent_in_full_tps.unit = '%' ;
sim.percent_in_gear.data = percent_in_gear ;
sim.percent_in_gear.unit = '%' ;
sim.v_min.data = min(V) ;
sim.v_min.unit = 'm/s' ;
sim.v_max.data = max(V) ;
sim.v_max.unit = 'm/s' ;
sim.v_ave.data = mean(V) ;
sim.v_ave.unit = 'm/s' ;
sim.energy_spent_fuel.data = energy_spent_fuel ;
sim.energy_spent_fuel.unit = 'J' ;
sim.energy_spent_mech.data = energy_spent_mech ;
sim.energy_spent_mech.unit = 'J' ;
sim.gear_shifts.data = gear_shifts ;
sim.gear_shifts.unit = [] ;
sim.lat_acc_max.data = ay_max ;
sim.lat_acc_max.unit = 'm/s/s' ;
sim.long_acc_max.data = ax_max ;
sim.long_acc_max.unit = 'm/s/s' ;
sim.long_acc_min.data = ax_min ;
sim.long_acc_min.unit = 'm/s/s' ;
sim.sector_v_max.data = sector_v_max ;
sim.sector_v_max.unit = 'm/s' ;
sim.sector_v_min.data = sector_v_min ;
sim.sector_v_min.unit = 'm/s' ;
% HUD
disp('Simulation results saved.')
disp('Simulation completed.')
fprintf(logid,'%s\n','Simulation results saved.') ;
fprintf(logid,'%s\n','Simulation completed.') ;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [v,tps,bps] = vehicle_model_lat(veh,tr,p)
%% initialisation
% getting track data
g = 9.81 ;
r = tr.r(p) ;
incl = tr.incl(p) ;
bank = tr.bank(p) ;
factor_grip = tr.factor_grip(p)*veh.factor_grip ;
% getting vehicle data
factor_drive = veh.factor_drive ;
factor_aero = veh.factor_aero ;
driven_wheels = veh.driven_wheels ;
% Mass
M = veh.M ;
% normal load on all wheels
Wz = M*g*cosd(bank)*cosd(incl) ;
% induced weight from banking and inclination
Wy = -M*g*sind(bank) ;
Wx = M*g*sind(incl) ;
%% speed solution
if r==0 % straight (limited by engine speed limit or drag)
% checking for engine speed limit
v = veh.v_max ;
tps = 1 ; % full throttle
bps = 0 ; % 0 brake
else % corner (may be limited by engine, drag or cornering ability)
%% initial speed solution
% downforce coefficient
D = -1/2*veh.rho*veh.factor_Cl*veh.Cl*veh.A ;
% longitudinal tyre coefficients
dmy = factor_grip*veh.sens_y ;
muy = factor_grip*veh.mu_y ;
Ny = veh.mu_y_M*g ;
% longitudinal tyre coefficients
dmx = factor_grip*veh.sens_x ;
mux = factor_grip*veh.mu_x ;
Nx = veh.mu_x_M*g ;
% 2nd degree polynomial coefficients ( a*x^2+b*x+c = 0 )
a = -sign(r)*dmy/4*D^2 ;
b = sign(r)*(muy*D+(dmy/4)*(Ny*4)*D-2*(dmy/4)*Wz*D)-M*r ;
c = sign(r)*(muy*Wz+(dmy/4)*(Ny*4)*Wz-(dmy/4)*Wz^2)+Wy ;
% calculating 2nd degree polynomial roots
if a==0
v = sqrt(-c/b) ;
elseif b^2-4*a*c>=0
if (-b+sqrt(b^2-4*a*c))/2/a>=0
v = sqrt((-b+sqrt(b^2-4*a*c))/2/a) ;
elseif (-b-sqrt(b^2-4*a*c))/2/a>=0
v = sqrt((-b-sqrt(b^2-4*a*c))/2/a) ;
else
error(['No real roots at point index: ',num2str(p)])
end
else
error(['Discriminant <0 at point index: ',num2str(p)])
end
% checking for engine speed limit
v = min([v,veh.v_max]) ;
%% adjusting speed for drag force compensation
adjust_speed = true ;
while adjust_speed
% aero forces
Aero_Df = 1/2*veh.rho*veh.factor_Cl*veh.Cl*veh.A*v^2 ;
Aero_Dr = 1/2*veh.rho*veh.factor_Cd*veh.Cd*veh.A*v^2 ;
% rolling resistance
Roll_Dr = veh.Cr*(-Aero_Df+Wz) ;
% normal load on driven wheels
Wd = (factor_drive*Wz+(-factor_aero*Aero_Df))/driven_wheels ;
% drag acceleration
ax_drag = (Aero_Dr+Roll_Dr+Wx)/M ;
% maximum lat acc available from tyres
ay_max = sign(r)/M*(muy+dmy*(Ny-(Wz-Aero_Df)/4))*(Wz-Aero_Df) ;
% needed lat acc make turn
ay_needed = v^2*r+g*sind(bank) ; % circular motion and track banking
% calculating driver inputs
if ax_drag<=0 % need throttle to compensate for drag
% max long acc available from tyres
ax_tyre_max_acc = 1/M*(mux+dmx*(Nx-Wd))*Wd*driven_wheels ;
% getting power limit from engine
ax_power_limit = 1/M*(interp1(veh.vehicle_speed,veh.factor_power*veh.fx_engine,v)) ;
% available combined lat acc at ax_net==0 => ax_tyre==-ax_drag
ay = ay_max*sqrt(1-(ax_drag/ax_tyre_max_acc)^2) ; % friction ellipse
% available combined long acc at ay_needed
ax_acc = ax_tyre_max_acc*sqrt(1-(ay_needed/ay_max)^2) ; % friction ellipse
% getting tps value
scale = min([-ax_drag,ax_acc])/ax_power_limit ;
tps = max([min([1,scale]),0]) ; % making sure its positive
bps = 0 ; % setting brake pressure to 0
else % need brake to compensate for drag
% max long acc available from tyres
ax_tyre_max_dec = -1/M*(mux+dmx*(Nx-(Wz-Aero_Df)/4))*(Wz-Aero_Df) ;
% available combined lat acc at ax_net==0 => ax_tyre==-ax_drag
ay = ay_max*sqrt(1-(ax_drag/ax_tyre_max_dec)^2) ; % friction ellipse
% available combined long acc at ay_needed
ax_dec = ax_tyre_max_dec*sqrt(1-(ay_needed/ay_max)^2) ; % friction ellipse
% getting brake input
fx_tyre = max([ax_drag,-ax_dec])*M ;
bps = max([fx_tyre,0])*veh.beta ; % making sure its positive
tps = 0 ; % setting throttle to 0
end
% checking if tyres can produce the available combined lat acc
if ay/ay_needed<1 % not enough grip
v = sqrt((ay-g*sind(bank))/r)-1E-3 ; % the (-1E-3 factor is there for convergence speed)
else % enough grip
adjust_speed = false ;
end
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [v_next,ax,ay,tps,bps,overshoot] = vehicle_model_comb(veh,tr,v,v_max_next,j,mode)
%% initialisation
% assuming no overshoot
overshoot = false ;
% getting track data
dx = tr.dx(j) ;
r = tr.r(j) ;
incl = tr.incl(j) ;
bank = tr.bank(j) ;
factor_grip = tr.factor_grip(j)*veh.factor_grip ;
g = 9.81 ;
% getting vehicle data
if mode==1
factor_drive = veh.factor_drive ;
factor_aero = veh.factor_aero ;
driven_wheels = veh.driven_wheels ;
else
factor_drive = 1 ;
factor_aero = 1 ;
driven_wheels = 4 ;
end
%% external forces
% Mass
M = veh.M ;
% normal load on all wheels
Wz = M*g*cosd(bank)*cosd(incl) ;
% induced weight from banking and inclination
Wy = -M*g*sind(bank) ;
Wx = M*g*sind(incl) ;
% aero forces
Aero_Df = 1/2*veh.rho*veh.factor_Cl*veh.Cl*veh.A*v^2 ;
Aero_Dr = 1/2*veh.rho*veh.factor_Cd*veh.Cd*veh.A*v^2 ;
% rolling resistance
Roll_Dr = veh.Cr*(-Aero_Df+Wz) ;
% normal load on driven wheels
Wd = (factor_drive*Wz+(-factor_aero*Aero_Df))/driven_wheels ;
%% overshoot acceleration
% maximum allowed long acc to not overshoot at next point
ax_max = mode*(v_max_next^2-v^2)/2/dx ;
% drag acceleration
ax_drag = (Aero_Dr+Roll_Dr+Wx)/M ;
% ovesrhoot acceleration limit
ax_needed = ax_max-ax_drag ;
%% current lat acc
ay = v^2*r+g*sind(bank) ;
%% tyre forces
% longitudinal tyre coefficients
dmy = factor_grip*veh.sens_y ;
muy = factor_grip*veh.mu_y ;
Ny = veh.mu_y_M*g ;
% longitudinal tyre coefficients
dmx = factor_grip*veh.sens_x ;
mux = factor_grip*veh.mu_x ;
Nx = veh.mu_x_M*g ;
% friction ellipse multiplier
if sign(ay)~=0 % in corner or compensating for banking
% max lat acc available from tyres
ay_max = 1/M*(sign(ay)*(muy+dmy*(Ny-(Wz-Aero_Df)/4))*(Wz-Aero_Df)+Wy) ;
% max combined long acc available from tyres
if abs(ay/ay_max)>1 % checking if vehicle overshot (should not happen, but check exists to exclude complex numbers in solution from friction ellipse)
ellipse_multi = 0 ;
else
ellipse_multi = sqrt(1-(ay/ay_max)^2) ; % friction ellipse
end
else % in straight or no compensation for banking needed
ellipse_multi = 1 ;
end
%% calculating driver inputs
if ax_needed>=0 % need tps
% max pure long acc available from driven tyres
ax_tyre_max = 1/M*(mux+dmx*(Nx-Wd))*Wd*driven_wheels ;
% max combined long acc available from driven tyres
ax_tyre = ax_tyre_max*ellipse_multi ;
% getting power limit from engine
ax_power_limit = 1/M*(interp1(veh.vehicle_speed,veh.factor_power*veh.fx_engine,v,'linear',0)) ;
% getting tps value
scale = min([ax_tyre,ax_needed]/ax_power_limit) ;
tps = max([min([1,scale]),0]) ; % making sure its positive
bps = 0 ; % setting brake pressure to 0
% final long acc command
ax_com = tps*ax_power_limit ;
else % need braking
% max pure long acc available from all tyres
ax_tyre_max = -1/M*(mux+dmx*(Nx-(Wz-Aero_Df)/4))*(Wz-Aero_Df) ;
% max comb long acc available from all tyres
ax_tyre = ax_tyre_max*ellipse_multi ;
% tyre braking force
fx_tyre = min(-[ax_tyre,ax_needed])*M ;
% getting brake input
bps = max([fx_tyre,0])*veh.beta ; % making sure its positive
tps = 0 ; % seting throttle to 0
% final long acc command
ax_com = -min(-[ax_tyre,ax_needed]) ;
end
%% final results
% total vehicle long acc
ax = ax_com+ax_drag ;
% next speed value
v_next = sqrt(v^2+2*mode*ax*tr.dx(j)) ;
% correcting tps for full throttle when at v_max on straights
if tps>0 && v/veh.v_max>=0.999
tps = 1 ;
end
%% checking for overshoot
if v_next/v_max_next>1
% setting overshoot flag
overshoot = true ;
% resetting values for overshoot
v_next = inf ;
ax = 0 ;
ay = 0 ;
tps = -1 ;
bps = -1 ;
return
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [j_next,j] = next_point(j,j_max,mode,tr_config)
switch mode
case 1 % acceleration
switch tr_config
case 'Closed'
if j==j_max-1
j = j_max ;
j_next = 1 ;
elseif j==j_max
j = 1 ;
j_next = j+1 ;
else
j = j+1 ;
j_next = j+1 ;
end
case 'Open'
j = j+1 ;
j_next = j+1 ;
end
case -1 % deceleration
switch tr_config
case 'Closed'
if j==2
j = 1 ;
j_next = j_max ;
elseif j==1
j = j_max ;
j_next = j-1 ;
else
j = j-1 ;
j_next = j-1 ;
end
case 'Open'
j = j-1 ;
j_next = j-1 ;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [i_rest] = other_points(i,i_max)
i_rest = (1:i_max)' ;
i_rest(i) = [] ;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [flag] = flag_update(flag,j,k,prg_size,logid,prg_pos)
% current flag state
p = sum(flag,'all')/size(flag,1)/size(flag,2) ;
n_old = floor(p*prg_size) ; % old number of lines
% new flag state
flag(j,k) = true ;
p = sum(flag,'all')/size(flag,1)/size(flag,2) ;
n = floor(p*prg_size) ; % new number of lines
% checking if state has changed enough to update progress bar
if n>n_old
progress_bar(flag,prg_size,logid,prg_pos) ;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [] = progress_bar(flag,prg_size,logid,prg_pos)
% current flag state
p = sum(flag,'all')/size(flag,1)/size(flag,2) ; % progress percentage
n = floor(p*prg_size) ; % new number of lines
e = prg_size-n ; % number of spaces
% updating progress bar in command window
fprintf(repmat('\b',1,prg_size+1+8)) % backspace to start of bar
fprintf(repmat('|',1,n)) % writing lines
fprintf(repmat(' ',1,e)) % writing spaces
fprintf(']') % closing bar
fprintf('%4.0f',p*100) % writing percentage
fprintf(' [%%]') % writing % symbol
% updating progress bar in log file
fseek(logid,prg_pos,'bof') ; % start of progress bar position in log file
fprintf(logid,'%s','Running: [') ;
fprintf(logid,'%s',repmat('|',1,n)) ;
fprintf(logid,'%s',repmat(' ',1,e)) ;
fprintf(logid,'%s','] ') ;
fprintf(logid,'%3.0f',p*100) ;
fprintf(logid,'%s\n',' [%]') ;
fseek(logid,0,'eof') ; % continue at end of file
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [] = disp_logo(logid)
lg = [...
'_______ _____________________ ';...
'__ __ \______________________ /___ |__ __ \';...
'_ / / /__ __ \ _ \_ __ \_ / __ /| |_ /_/ /';...
'/ /_/ /__ /_/ / __/ / / / /___ ___ | ____/ ';...
'\____/ _ .___/\___//_/ /_//_____/_/ |_/_/ ';...