Buildings.Utilities.Math.Functions.BaseClasses

Information

This package contains base classes that are used to construct the models in Buildings.Utilities.Math.Functions.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
der_2_regNonZeroPower	Power function, regularized near zero, but nonzero value for x=0
der_polynomial	Derivative for polynomial function
der_regNonZeroPower	Power function, regularized near zero, but nonzero value for x=0
der_spliceFunction	Derivative of splice function

Buildings.Utilities.Math.Functions.BaseClasses.der_2_regNonZeroPower

Information

Implementation of the second derivative of the function Buildings.Utilities.Math.Functions.regNonZeroPower.

Inputs

Type	Name	Default	Description
Real	x		Abscissa value
Real	n		Exponent
Real	delta	0.01	Abscissa value where transition occurs
Real	der_x
Real	der_2_x

Outputs

Type	Name	Description
Real	der_2_y	Function value

Modelica definition

function der_2_regNonZeroPower 
  "Power function, regularized near zero, but nonzero value for x=0"
 input Real x "Abscissa value";
 input Real n "Exponent";
 input Real delta = 0.01 "Abscissa value where transition occurs";
 input Real der_x;
 input Real der_2_x;
 output Real der_2_y "Function value";
protected 
  Real a1;
  Real a3;
  Real delta2;
  Real x2;
  Real y_d "=y(delta)";
  Real yP_d "=dy(delta)/dx";
  Real yPP_d "=d^2y(delta)/dx^2";
algorithm 
  if abs(x) > delta then
   der_2_y := n*(n-1)*abs(x)^(n-2);
  else
   delta2 :=delta*delta;
   x2 :=x*x;
   y_d :=delta^n;
   yP_d :=n*delta^(n - 1);
   yPP_d :=n*(n - 1)*delta^(n - 2);
   a1 := -(yP_d/delta - yPP_d)/delta2/8;
   a3 := (yPP_d - 12 * a1 * delta2)/2;
   der_2_y := 12*a1*x2+2*a3;
  end if;
end der_2_regNonZeroPower;

Buildings.Utilities.Math.Functions.BaseClasses.der_polynomial

Information

y = a₁ + a₂ x + a₃ x² + ...

This function computes new coefficients

b₁ = a₂, b₂ = 2 a₃, ...

and then calls recursively Buildings.Utilities.Math.polynomial

Inputs

Type	Name	Default	Description
Real	x
Real	a[:]
Real	dx

Outputs

Type	Name	Description
Real	y

Modelica definition

function der_polynomial "Derivative for polynomial function"
    input Real x;
    input Real a[:];
    input Real dx;
    output Real y;
protected 
 parameter Integer n = size(a, 1)-1;
 Real b[n] "Coefficients of derivative polynomial";
algorithm 
  for i in 1:n loop
     b[i] :=a[i+1]*i;
  end for;
  y := Buildings.Utilities.Math.Functions.polynomial(
                                           a=b, x=x);
end der_polynomial;

Buildings.Utilities.Math.Functions.BaseClasses.der_regNonZeroPower

Information

Implementation of the first derivative of the function Buildings.Utilities.Math.Functions.regNonZeroPower.

Inputs

Type	Name	Default	Description
Real	x		Abscissa value
Real	n		Exponent
Real	delta	0.01	Abscissa value where transition occurs
Real	der_x

Outputs

Type	Name	Description
Real	der_y	Function value

Modelica definition

function der_regNonZeroPower 
  "Power function, regularized near zero, but nonzero value for x=0"
  annotation(derivative=der_2_regNonZeroPower);
 input Real x "Abscissa value";
 input Real n "Exponent";
 input Real delta = 0.01 "Abscissa value where transition occurs";
 input Real der_x;
 output Real der_y "Function value";
protected 
  Real a1;
  Real a3;
  Real delta2;
  Real x2;
  Real y_d "=y(delta)";
  Real yP_d "=dy(delta)/dx";
  Real yPP_d "=d^2y(delta)/dx^2";
algorithm 
  if abs(x) > delta then
   der_y := sign(x)*n*abs(x)^(n-1);
  else
   delta2 :=delta*delta;
   x2 :=x*x;
   y_d :=delta^n;
   yP_d :=n*delta^(n - 1);
   yPP_d :=n*(n - 1)*delta^(n - 2);
   a1 := -(yP_d/delta - yPP_d)/delta2/8;
   a3 := (yPP_d - 12 * a1 * delta2)/2;
   der_y := x * ( 4 * a1 * x * x + 2 * a3);
  end if;
end der_regNonZeroPower;

Buildings.Utilities.Math.Functions.BaseClasses.der_spliceFunction

Information

Implementation of the first derivative of the function Buildings.Utilities.Math.Functions.spliceFunction.

Inputs

Type	Name	Default	Description
Real	pos
Real	neg
Real	x
Real	deltax	1
Real	dpos
Real	dneg
Real	dx
Real	ddeltax	0

Outputs

Type	Name	Description
Real	out

Modelica definition

function der_spliceFunction "Derivative of splice function"
    input Real pos;
    input Real neg;
    input Real x;
    input Real deltax=1;
    input Real dpos;
    input Real dneg;
    input Real dx;
    input Real ddeltax=0;
    output Real out;
protected 
    Real scaledX;
    Real scaledX1;
    Real dscaledX1;
    Real y;
    constant Real asin1 = Modelica.Math.asin(1);
algorithm 
    scaledX1 := x/deltax;
    if scaledX1 <= -0.99999999999 then
      out := dneg;
    elseif scaledX1 >= 0.9999999999 then
      out := dpos;
    else
      scaledX := scaledX1*asin1;
      dscaledX1 := (dx - scaledX1*ddeltax)/deltax;
      y := (Modelica.Math.tanh(Modelica.Math.tan(scaledX)) + 1)/2;
      out := dpos*y + (1 - y)*dneg;
      out := out + (pos - neg)*dscaledX1*asin1/2/(
        Modelica.Math.cosh(Modelica.Math.tan(scaledX))*Modelica.Math.cos(
        scaledX))^2;
    end if;

end der_spliceFunction;