issue generating triangular wave function in Modelica

Question

I'm trying to create a model where one Modelica variable is a triangular wave of another variable. First I tried the floor() function as below:

model test1
  final constant Real pi=2*Modelica.Math.asin(1.0);
  parameter Real b = 1;
  parameter Real a = 1;
  Real x,p,u;
equation
  if sign(sin(x*pi/b))>=0 then 
    p=a*(x-b*floor(x/b));
  else 
    p=a*(b-(x-b*floor(x/b)));
  end if;
  x=time;
  u = floor(x/b);
end test1

(x=time; is arbitrary so the model compiles)

but the result is weird, as you can see below

zoom in:

somehow 0.005 seconds before the next step floor function behaves unexpectedly and becomes a linear function ending by the next value.

then I tried the ceil() function. everything seemed right till I realised the same problem happens with ceil() function at other values (e.g. x=13)

I would appreciate if you could:

1. help me understand why this "glitch" happens and if it is intentional by design or a bug?
2. how I can fix this?
3. are there any alternatives to create a triangular wave function?

P.S. I am using this "wave function" to model the interaction between two jagged bodies"

Answer 1

If you are allowed to utilize the Modelica Standard Library, you can build up a parametrized, time-based zigzag signal using the CombiTimeTable block with linear interpolation and periodic extrapolation. For example,

model Test4
  parameter Real a=2 "Amplitude";
  parameter Real b=3 "Period";
  Real y=zigzag.y[1] "Zigzag";
  Modelica.Blocks.Sources.CombiTimeTable zigzag(
    table=[0,0;b/4,a;b/4,a;b/2,0;b/2,0;3*b/4,-a;3*b/4,-a;b,0],
    extrapolation=Modelica.Blocks.Types.Extrapolation.Periodic)
    annotation(Placement(transformation(extent={{-80,60},{-60,80}})));
  Modelica.Blocks.Sources.Trapezoid trapezoid(
    amplitude=2*a,
    rising=b/2,
    width=0,
    falling=b/2,
    period=b,
    offset=-a)
    annotation(Placement(transformation(extent={{-80,25},{-60,45}})));
  annotation(uses(Modelica(version="3.2.2")));
end Test4;

Answer 2

I don't have an explanation for the glitches in your simulation.

However, I would take another approach to the sawtooth function: I see it as an integrator integrating +1 and -1 upwards and downwards. The integration time determines the amplitude and period of the sawtooth function.

The pictures below show an implementation using MSL blocks and one using code. The simulation results below are the same for both implementations.

Best regards, Rene Just Nielsen

Block diagram: Code:

model test3
  parameter Real a=2 "amplitude";
  parameter Real b=3 "period";

  Real u, y;
initial equation 
  u = 1;
  y = 0;
equation 
  4*a/b*u = der(y);
  when y > a then
    u = -1;
  elsewhen y < -a then
    u = 1;
  end when;
end test3;

Simulation result: