ode45 - plotting issue for two functions

Hi everyone,

Could anyone help how to get a continuous plot of ode45 results for two different tspans of [0 10] and [10 20] for two slightly different functions.

The two functions are for linear kinematic motion with linear varying acceleration and constant acceleration scenarios as follows.

Linear varying acceleration motion function

function dxdt = vdp6(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 2;

Constant acceleration motion function

function dxdt = vdp7(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= 2;
dxdt(3)= 0;

The part I struggle with is the second section of the code to get a continous graph for the behavior variables over the entire [0 20] tspane:

tspan=[0 10];
x0=[0;0;4];
[t,x] = ode45(@vdp6,tspan,x0);

subplot(3,1,1);
plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');


subplot(3,1,3);  
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');

% 2nd part 

hold on;
tspan=[10 20];
x0=[0;0;0];
[t,x] = ode45(@vdp7,tspan,x0);

plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');


subplot(3,1,3); % Notes 
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');

hold off;

Thank you!

[Walter Roberson]

You forgot subplot(3,1,1) before plotting for 2nd part

[Khalilullah Mayar]

Added. Still the subplot(3,1,1) displaying tspan of [10 20] not [0 20]?

[Torsten]

Constant acceleration motion function

function dxdt = vdp7(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 0;

Linear varying acceleration motion function

function dxdt = vdp6(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 2;

[Khalilullah Mayar]

Corrected but still only the [10 20] tspan is displlayed:

functions:

function dxdt = vdp6(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 2;


function dxdt = vdp7(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 0;

code:

tspan=[0 10];
x0=[0;0;4];
[t,x] = ode45(@vdp6,tspan,x0);
subplot(3,1,1);
plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');

subplot(3,1,3);  
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');

tspan=[10 20];
x0=[0;0;0];
[t,x] = ode45(@vdp7,tspan,x0);

hold on;

subplot(3,1,1);
plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');


subplot(3,1,3); 
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');
hold off;

[Walter Roberson]

hold on

Only applies to the Current Axes. You need on for each subplot.

[Khalilullah Mayar]

Thanks that worked well. One last thing, the 2nd graph doesn't pick up from the point where the 1st one ends (t=10sec). Although I did it manually by selecting the initial condition for the 2nd graph as the end point for 1st one: x0=[333.3;100;20]. Is there any way this could be coded?

tspan=[10 20];
x0=[333.3;100;20];
[t,x] = ode45(@vdp7,tspan,x0);

[Torsten]

x0 = [x(end,1);x(end,2);x(end,3)]

[Khalilullah Mayar]

Thank you!

[Khalilullah Mayar]

Back with another issue. Consider the first component of motion with constant acceleration and then the 2nd one with constant velocity.

I revised the function as follows:

Constant acceleration:

function dxdt = vdp7(t,x)
dxdt= zeros(3,1)
dxdt(1)= x(2);
dxdt(2)= x(3);
dxdt(3)= 0;

Constant velocity:

function dxdt = vdp8(t,x)
dxdt= zeros(3,1);
dxdt(1)= x(2);
dxdt(2)= 0;
dxdt(3)= 0;

Code:

tspan=[0 10];
x0=[0;0;2];
[t,x] = ode45(@vdp7,tspan,x0);
hold on;
subplot(3,1,1);
plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

hold on;
subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');

hold on;
subplot(3,1,3);  
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');

tspan=[10 20];
x0=[x(end,1);x(end,2);x(end,3)];
[t,x] = ode45(@vdp8,tspan,x0);

hold on;

subplot(3,1,1);
plot(t,x(:,1),'-',t,x(:,2),'-',t,x(:,3),'-')
title('Behaviour Variables vs Time');
xlabel('Time t');
ylabel('x, v, a');
legend('x_1(x)','x_2(v)','x_3(a)')

hold on;
subplot(3,1,2);
plot(x(:,1),x(:,2),'-')
title('Distance vs Velocity');
xlabel('Distance');
ylabel('Velocity');

hold on;
subplot(3,1,3); 
plot(x(:,2),x(:,3),'-')
title('Velocity vs Acceleration');
xlabel('Velocity');
ylabel('Acceleration');
hold off;

Now at point t=10 sec the acceleratoin plot should drop to 0 which didn't apear so (plot enclosed) rather continues with its previous value of 2.

[Torsten]

Why should x(3) drop to 0 if you specify x0(3) = x(end,3) ( = 2) and dx3/dt = 0 ?

x(3) will remain at its value at t=10, namely x(3) = 2.

But since position only depends on velocity and velocity is kept constant, the value you prescribe for acceleration is irrelevant for the result.

[Khalilullah Mayar]

I did manually set x0(3) to zero, now the graph got fixed for subplot(1) but for subplot (3) none of the changes reflects - still a horizontal line at value 2 all the way long.

[Khalilullah Mayar]

Hi Torsten,

Any help on following is highly appreciated:

https://www.mathworks.com/matlabcentral/answers/481828-idm-car-following-microspoic-model?s_tid=prof_contriblnk