IDM Car following microspoic model

Hi everyone,

Can someone help why the following code couldn't run? It's an IDM car following microscopic model introduced by the equations and parameters below:

load mytrafficdata5;
someidmm(Time_t,Distance_n,Velocity_n)
function someidmm(Time_t,Distance_n,Velocity_n)
% y is velocity
% t is time
% Using interpolant for distance and velocity 
close all;
time_vector = Time_t;
init_speed = 0.2;
vel_vector = Velocity_n;
Dist_vector= Distance_n;
F_time = time_vector(end);
figure (1);
[T,Y] = ode45(@(t,y)idm5(t,y),[0,F_time],init_speed);
plot(T,Y(:,1),'b-',time_vector,vel_vector,'r--')
legend('By IDM','Real Velocity')
xlabel('Time')
ylabel('Velocity (m/sec)')
legend('Location','best')
function dy = idm5(t,y)
% parameters
x0_dot =30; % unit is m/sec
delta =4;
a=0.3;
b= 3;
s0=2;
Th=1.5; %time headway=1.5 sec
k = 1/(2*sqrt(a*b));
lc=5;
dist_interp = interp1(time_vector, Dist_vector, t);
vel_interp = interp1(time_vector, vel_vector, t);
xn = dist_interp;
Delta_v = y-vel_interp;
Dis = int(y,[0 F_time]) % integratoin of y (velocity) to get distance 
s = xn-Dis - lc;
s_star = s0 + max(0,y*Th + y*Delta_v*k);
%-main system-- %
dy = a*(1 - (y/x0_dot).^delta - (s_star/s).^2);
end
end

Data for the leader car is attached (mytrafficdata5.mat)

Note: I believe there might an issue with the integration line (Dis = int(y,[0 F_time]) % integratoin of y (velocity) to get distance).

[Khalilullah Mayar]

Following is an alternative version of the code with some fixings:

load mytrafficdata5;
someidmm(Time_t,Distance_n,Velocity_n)
function someidmm(Time_t,Distance_n,Velocity_n)
% y is distance for follower car
% t is time
% Using interpolant for distance and velocity 
close all;
time_vector = Time_t;
y0=[2;2];
tspan=[0 100];
vel_vector = Velocity_n;
Dist_vector= Distance_n;
[t,y] = ode45(@idm8,tspan,y0);
plot(t,y(:,2),'b-',time_vector,vel_vector,'r--')
legend('By IDM','Real Velocity')
xlabel('Time')
ylabel('Velocity (m/sec)')
legend('Location','best')
function dydt = idm8(t,y)
dydt= zeros(2,1)
dydt(1)= y(2);
dydt(2)= a*(1 - (y(2)/x0_dot).^delta - (s_star/s).^2);
% parameters
x0_dot =30; % unit is m/sec
delta =4;
a=0.3;
b= 3;
s0=2;
Th=1.5; %time headway=1.5 sec
k = 1/(2*sqrt(a*b));
lc=5;
dist_interp = interp1(time_vector, Dist_vector, t);
vel_interp = interp1(time_vector, vel_vector, t);
xn = dist_interp;
Delta_v = y(2)-vel_interp;
s = xn-y(1) - lc;
s_star = s0 + max(0,y(2)*Th + y(2)*Delta_v*k);
end
end

Answer 1

[Ni Tao]

load mytrafficdata5;
someidmm(Time_t,Distance_n,Velocity_n)
function someidmm(Time_t,Distance_n,Velocity_n)
% y is distance for follower car
% t is time
% Using interpolant for distance and velocity 
close all;
time_vector = Time_t;
y0=[2;2];
tspan=[0 100];
vel_vector = Velocity_n;
Dist_vector= Distance_n;
[t,y] = ode45(@idm8,tspan,y0);
plot(t,y(:,2),'b-',time_vector,vel_vector,'r--')
legend('By IDM','Real Velocity')
xlabel('Time')
ylabel('Velocity (m/sec)')
legend('Location','best')
function dydt = idm8(t,y)
dydt= zeros(2,1)
dydt(1)= y(2);
a=0.3;
x0_dot =30; % unit is m/sec
delta =4;
b= 3;
s0=2;
Th=1.5; %time headway=1.5 sec
k = 1/(2*sqrt(a*b));
lc=5;
dist_interp = interp1(time_vector, Dist_vector, t);
vel_interp = interp1(time_vector, vel_vector, t);
xn = dist_interp;
Delta_v = y(2)-vel_interp;
s = xn-y(1) - lc;
s_star = s0 + max(0,y(2)*Th + y(2)*Delta_v*k);
dydt(2)= a*(1 - (y(2)/x0_dot).^delta - (s_star/s).^2);
% parameters
end
end

[Anirudh]

If I were to do this in Simulink, how can I go about it?

Answer 2

[Mouncef]

can you explain this simulation ?