If/ElseIf Statement Inequality Not Resolving Correctly

I'm trying to plot the angular position of a robotic arm whose equation of motion changes over time. Ideally the plot of the position should have this shape:

but instead looks like this:

I have an if/elseif/else statement to handle the change in equation. The problem is that "else" part is being tripped for all values of t, which is why the plot is linear. I cannot seem to figure out why this is, but I can only assume it's because I've made some mistake with my if conditions. Below is a copy of my code. Any help would be appreciated. Thank you!

vm1 = 0.41415;
theta01 = -0.57982;
thetaf1 = 0.57982;
hold on

t = linspace(0,3);
    if (t < 0.5)
        theta1 = theta01 + (vm1 .* (t .^ 2));  
    elseif (t > 2.5)
        theta1 = thetaf1 - (vm1 .* (9 - (6 .* t) + (t .^ 2)));  
    else
        theta1 = vm1 .* (t - 1.5);  
    end
plot(t, theta1)

Answer 1

[Cris LaPierre]

If statements only work on one value at a time. You can't have it check the entire vector all at the same time. You can put the if statement inside a for loop and loop through each value of t one by one:

for i = 1:length(t)
    if (t(i) < 0.5)
        theta1(i) = theta01 + (vm1 .* (t(i) .^ 2));  
    elseif (t(i) > 2.5)
        theta1(i) = thetaf1 - (vm1 .* (9 - (6 .* t(i)) + (t(i) .^ 2)));  
    else
        theta1(i) = vm1 .* (t(i) - 1.5);  
    end
end

or create a piecewise function:

theta1 = (theta01 + (vm1 .* (t .^ 2))).*(t<0.5) + ...
    (thetaf1 - (vm1 .* (9 - (6 .* t) + (t .^ 2)))).*(t>2.5) + ...
    (vm1 .* (t - 1.5)).*(t>=0.5).*(t<=2.5);

The actual functions may not be quite right yet, but at least now you can visualize it.

[Sarah Ten Eyck]

This is exactly what I needed, thank you so much!

Quick followup question, is there a way to have i increment by very small amounts? Say, 0.001? I think that might fix the weird disjunction at 0.5 and 2.5.

[Cris LaPierre]

You have two ways to do that. Either increase the number of points created by linspace (100 is default):

t = linspace(0,3,500);

or use the colon operator instead and specify the increment:

t = 0:0.001:3;

[Sarah Ten Eyck]

I figured it out, I just needed to adjust the value of vm. Thank you again for your help!

[Cris LaPierre]

I don't think that making the increments smaller will help, though. It looks to me like the slope of the middle line is off, so it is not aligning with the tails. I calculated what the slope between the inner most points of the tails is and I get vm1 = 0.476188. It's still not perfect, but play around with that.

[Sarah Ten Eyck]

There's a specific equation for vm values that I didn't use the first time, it should be vm1 = 0.464. The final result comes out looking like this:

[Cris LaPierre]

Nice! Love when the math works!

I must have been writing my last comment the same time you were writing yours. What I said was in reference to decreasing the point interval spacing.

[Sarah Ten Eyck]

You were right on that front, there was still the weird discontinuity when I decreased the interval. Cheers!