how to integrate angle in matlab

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.

Answer 1

[JMP Phillips]

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: http://au.mathworks.com/help/simulink/slref/saturation.html

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.

[Bhargav Jha]

Hello, I used wrapto2Pi function in matlab function block and that solved my problem.