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Trapezoidal function

#9415  Permalink Top

Trapezoidal function

Oct-14-19 09:02:57

I am building a BLDC motor model with 6-step drive. I am having numerical errors in the transitions due to trapezoidal back-emf functions. I tried to use smooth operator but that does not generate a continous differentiable intersections. Is there a way to obtain a trapezoidal shape that is differentiable even in the intersection points (given with a tolerance) to prevent numerical errors in the simulation?

My current shape functions;

Code:

function ShapeFunc

extends Modelica.Icons.Function;

input SI.Angle phi_e;

output Real y;

protected SI.Angle phi_e_wrapped;



algorithm

phi_e_wrapped := Modelica.Math.wrapAngle(phi_e,true) ;



y := smooth(1 ,if (phi_e_wrapped < 2*pi/3) then 1 else 

     if (phi_e_wrapped < pi) then 1 - 6/pi*(phi_e_wrapped - 2*pi/3) else 

     if (phi_e_wrapped < 5*pi/3) then -1 else 

     if (phi_e_wrapped < 2*pi) then -1 + 6/pi*(phi_e_wrapped - 5*pi/3) else 0);



end ShapeFunc;

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