Try to plot position vs time

I have bug in delerating phase in my code, I have attached two picture (one on paper is what i am trying to get)

Thanks

%% Intialization
vmax=300;
v0=0;
a=100;
y0=130;
ymax=10;
dt=0.02;
%% Create Position signal (y)
%Lead in 1 second at a constant position
t=dt:dt:1;
y(1:length(t))=y0;
v(1:length(t))=v0;
%% accelerating phase
i=length(t);
while v(i)<vmax
    i=i+1;
    t(i)=t(i-1)+dt;
    v(i)=v(i-1)+a*dt;
    y(i)=y(i-1)-v(i)*dt+1/2*a*dt.^2;
end
%% constant velocity phase phase
for i=1:10 %need to determine how long the costant velocity phase would need to be 10 to 12 secs 
    t(i)=t(i-1)+dt;
    v(i)=vmax;
    y(i)=y(i-1)-v(i)*dt;
    %end
    
    %% delerating phase
    % To do list 
    A=-a;
    i=length(t);
    while v(i)>-30
        i=i+1;
        t(i)=t(i-1)+dt;
        v(i)=v(i-1)+a*dt;
        y(i)=y(i-1)-v(i)*dt+1/2*a*dt.^2;
    end 
    yDeac=y(i)-y0;
    v(k)=-30;
    ideac=i;

[dpb]

...
    
%% delerating phase
% To do list 
A=-a;
i=length(t);
while v(i)>-30
    i=i+1;
    t(i)=t(i-1)+dt;
    v(i)=v(i-1)+a*dt;    
    ...

HINT: You set A to -a but are still using a in the while...end loop...

[Kiran Isapure]

Ahh,Thanks. I am tryig to have y(i)<ymax- number of degrees for deleration phase, Do I need a seprate for loop for this ?

[dpb]

You have the loop; but if decelerating then the acceleration in the integration expression has to be negative. You set a new variable to be negative, but then continue to use the old one that is still positive.

You don't have to have separate loops even though you've used one here; you could use one loop and just change the acceleration value inside that loop. The decision/magnitude could be based on either time, velocity, or position, depending upon the problem specification.

[Kiran Isapure]

Yes, I continued to use the old varible.I made those changes, my decision are based on position, for acceleration phase my position varible should be y <ymax - number of degrees for deleration phase.

Should I need to use if statement after foor loop (acceleration phase).?

[Jan]

This is strange:

t(i) = t(i-1) + dt;
v(i) = v(i-1) + a*dt;
y(i) = y(i-1) - v(i)*dt + 1/2*a*dt.^2;

The acceleration is considered twice. a/2*t^2 is the integrated velocity already.

Answer 1

[nick]

Hi Kiran,

I understand that you are facing an issue with debugging the decelerating phase in your code and in obtaining the desired position vs time plot.

In the constant velocity phase there is array indexing error. MATLAB array indices must be positive integer, i.e. greater than or equal to 1. Also the following section of code rewrites the intital velocity which is incorrect. Furthermore, in the acceleration phase as well as the constant velocity phase, I have infered from the position vs time plot, the equation of motion for distance is incorrect.

%% accelerating phase 
i=length(t); 
while v(i)<vmax 
    i=i+1; 
    t(i)=t(i-1)+dt; 
    v(i)=v(i-1)+a*dt; 
    y(i)=y(i-1)-v(i)*dt+1/2*a*dt.^2; 
end 
 
%% constant velocity phase 
for i=1:10 %need to determine how long the constant velocity phase would need to be 10 to 12 secs  
t(i)=t(i-1)+dt; 
v(i)=vmax; 
y(i)=y(i-1)-v(i)*dt; 
end

Instead, the code should look like,

%% accelerating phase 
i=length(t); 
while v(i)<vmax 
i=i+1; 
t(i)=t(i-1)+dt; 
v(i)=v(i-1)+a*dt; 
y(i)=y(i-1)+v(i)*dt+1/2*a*dt.^2; 
end 
 
%% constant velocity phase 
for m = 1:10 %need to determine how long the constant velocity phase would need to be 10 to 12 secs  
i=i+1; 
t(i) = t(i-1)+dt; 
v(i) = vmax; 
y(i) = y(i-1)+v(i)*dt; 
end 

Also as @dpb mentioned the acceleration should be 'A' instead of '-a' so as to decelerate the object. Furthermore, like in the acceleration phase, in this phase also the equation of motion for distance is incorrect. I have attached sample code for the deceleration phase for your reference

  %% decelerating phase
    A=-a;
    while v(i)>-30
        i=i+1;
        t(i)=t(i-1)+dt;
        v(i)=v(i-1)+A*dt;
        y(i)=y(i-1)+v(i)*dt+1/2*A*dt.^2;
    end 

I have obtained the distance vs time plotlike the desired result and attached the figure for your reference :

Hope this helps,

Regards,

Neelanshu