ode45 - plotting issue for two functions

Khalilullah Mayar

2019 9 6

0 个回答

7 次查看（30 天）

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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!

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Khalilullah Mayar 2019-9-6

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;

Khalilullah Mayar 2019-9-6

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.

Khalilullah Mayar 2019-9-6

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.