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how to integrate angle in matlab

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Hi! I have these three state equations:
x_dot = v*cos(alpha);
y_dot = v*sin(alpha);
alpha_dot = lateralAcceleration/v;
I have to integrate these states to get x,y and alpha. I am implementing this on simulink. But I am facing a problem that while integrating the angle alpha goes to a very large number. I need it to be in a certain range such as range of atan2. Is there a way to do it?
I have attached the image which shows my current implementation.

Accepted Answer

JMP Phillips
JMP Phillips on 19 Aug 2015
If alpha_dot is going very large, you could consider filtering or smoothing out the large jumps.
You can put a saturation block in to limit your alpha_dot between lower and upper values:
Alternatively or additionally you can insert a gain block: alpha_dot = k*lateralAcceleration/v where k is a proportional gain that you can tune such that alpha_dot is within an acceptable range.
After you integrate alpha_dot to get alpha you need to wrap it between -pi and pi or 0 and 2 pi, whatever convention you are using, using mod, e.g.
angle_wrapped = ( mod( (angle-angle_min),(angle_max-angle_min)) +angle_min);
I don't remember if Simulink already has a wrap block, but there is already a wrapToPi function in the mapping toolbox if you have that.
  1 Comment
Bhargav Jha
Bhargav Jha on 20 Aug 2015
Hello, I used wrapto2Pi function in matlab function block and that solved my problem.

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