Modelica.Blocks.MathBoolean

Library of Boolean mathematical functions as input/output blocks

Information

This package contains basic mathematical operations on Boolean signals.

Package MathBoolean is a new design that shall replace in the future the Logical package. The new features are:

If useful, blocks may have an arbitrary number of inputs (e.g., "And" block with 2,3,4,... Boolean inputs). This is based on the "connectorSizing" annotation which allows a tool to conveniently handle vectors of connectors.
The blocks are smaller in size, so that the diagram area is better utilized for trivial blocks such as "And" or "Or".

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name Description

MultiSwitch Set Boolean expression that is associated with the first active input signal

And Logical 'and': y = u[1] and u[2] and ... and u[nu]

Or Logical 'or': y = u[1] or u[2] or ... or u[nu]

Xor Logical 'xor': y = oneTrue(u) (y is true, if exactly one element of u is true, otherwise it is false)

Nand Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )

Nor Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )

Not Logical 'not': y = not u

RisingEdge Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))

FallingEdge Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))

ChangingEdge Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))

OnDelay Delay a rising edge of the input, but do not delay a falling edge.

Name	Description
MultiSwitch	Set Boolean expression that is associated with the first active input signal
And	Logical 'and': y = u[1] and u[2] and ... and u[nu]
Or	Logical 'or': y = u[1] or u[2] or ... or u[nu]
Xor	Logical 'xor': y = oneTrue(u) (y is true, if exactly one element of u is true, otherwise it is false)
Nand	Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )
Nor	Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )
Not	Logical 'not': y = not u
RisingEdge	Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))
FallingEdge	Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))
ChangingEdge	Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))
OnDelay	Delay a rising edge of the input, but do not delay a falling edge.

Modelica.Blocks.MathBoolean.MultiSwitch

Set Boolean expression that is associated with the first active input signal

Modelica.Blocks.MathBoolean.MultiSwitch

Information

The block has a vector of Boolean input signals u[nu] and a vector of (time varying) Boolean expressions expr[:]. The output signal y is set to expr[i], if i is the first element in the input vector u that is true. If all input signals are false, y is set to parameter "y_default" or the previous value of y is kept if parameter use_pre_as_default = true:

  // Conceptual equation (not valid Modelica)
  i = 'first element of u[:] that is true';
  y = if i==0 then (if use_pre_as_default then pre(y)
                                          else y_default)
      else expr[i];

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Parameters

Type Name Default Description

Boolean expr[nu] fill(false, nu) y = if u[i] then expr[i] else y_default (time varying)

Boolean use_pre_as_default true set true to hold last value as default (y_default = pre(y))

Boolean y_default false Default value of output y if all u[i] = false

Type	Name	Default	Description
Boolean	expr[nu]	fill(false, nu)	y = if u[i] then expr[i] else y_default (time varying)
Boolean	use_pre_as_default	true	set true to hold last value as default (y_default = pre(y))
Boolean	y_default	false	Default value of output y if all u[i] = false

Connectors

Type Name Description

input BooleanVectorInput u[nu] Set y = expr[i], if u[i] = true

output BooleanOutput y Output depending on expression

Type	Name	Description
input BooleanVectorInput	u[nu]	Set y = expr[i], if u[i] = true
output BooleanOutput	y	Output depending on expression

Modelica definition

block MultiSwitch 
  "Set Boolean expression that is associated with the first active input signal"

  input Boolean expr[nu]=fill(false, nu) 
    "y = if u[i] then expr[i] else y_default (time varying)";
  parameter Boolean use_pre_as_default=true 
    "set true to hold last value as default (y_default = pre(y))";
  parameter Boolean y_default=false 
    "Default value of output y if all u[i] = false";

  parameter Integer nu(min=0) = 0 "Number of input connections";

  Modelica.Blocks.Interfaces.BooleanVectorInput u[nu] 
    "Set y = expr[i], if u[i] = true";
  Modelica.Blocks.Interfaces.BooleanOutput y(start=y_default,fixed=true) 
    "Output depending on expression";

protected 
  Integer firstActiveIndex;
equation 
    firstActiveIndex =
      Modelica.Math.BooleanVectors.firstTrueIndex(
                                   u);
   y = if firstActiveIndex == 0 then (if use_pre_as_default then pre(y) else y_default) else 
                                     expr[firstActiveIndex];
end MultiSwitch;

Modelica.Blocks.MathBoolean.And

Logical 'and': y = u[1] and u[2] and ... and u[nu]

Modelica.Blocks.MathBoolean.And

Information

The output is true if all inputs are true, otherwise the output is false.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

Connectors

Type Name Description

input BooleanVectorInput u[nu] Vector of Boolean input signals

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanVectorInput	u[nu]	Vector of Boolean input signals
output BooleanOutput	y	Boolean output signal

Modelica definition

block And 
  "Logical 'and': y = u[1] and u[2] and ... and u[nu]"
  extends Modelica.Blocks.Interfaces.PartialBooleanMISO;

equation 
  y = Modelica.Math.BooleanVectors.allTrue(
                            u);
end And;

Modelica.Blocks.MathBoolean.Or

Logical 'or': y = u[1] or u[2] or ... or u[nu]

Modelica.Blocks.MathBoolean.Or

Information

The output is true if at least one input is true, otherwise the output is false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

Connectors

Type Name Description

input BooleanVectorInput u[nu] Vector of Boolean input signals

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanVectorInput	u[nu]	Vector of Boolean input signals
output BooleanOutput	y	Boolean output signal

Modelica definition

block Or "Logical 'or': y = u[1] or u[2] or ... or u[nu]"
  extends Modelica.Blocks.Interfaces.PartialBooleanMISO;

equation 
  y = Modelica.Math.BooleanVectors.anyTrue(
                            u);
end Or;

Modelica.Blocks.MathBoolean.Xor

Logical 'xor': y = oneTrue(u) (y is true, if exactly one element of u is true, otherwise it is false)

Modelica.Blocks.MathBoolean.Xor

Information

The output is true if exactly one input is true, otherwise the output is false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

Connectors

Type Name Description

input BooleanVectorInput u[nu] Vector of Boolean input signals

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanVectorInput	u[nu]	Vector of Boolean input signals
output BooleanOutput	y	Boolean output signal

Modelica definition

block Xor 
  "Logical 'xor': y = oneTrue(u)  (y is true, if exactly one element of u is true, otherwise it is false)"
  extends Modelica.Blocks.Interfaces.PartialBooleanMISO;

equation 
  y = Modelica.Math.BooleanVectors.oneTrue(
                            u);
end Xor;

Modelica.Blocks.MathBoolean.Nand

Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )

Modelica.Blocks.MathBoolean.Nand

Information

The output is true if at least one input is false, otherwise the output is false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

Connectors

Type Name Description

input BooleanVectorInput u[nu] Vector of Boolean input signals

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanVectorInput	u[nu]	Vector of Boolean input signals
output BooleanOutput	y	Boolean output signal

Modelica definition

block Nand 
  "Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )"
  extends Modelica.Blocks.Interfaces.PartialBooleanMISO;

equation 
  y = not Modelica.Math.BooleanVectors.allTrue(
                                u);
end Nand;

Modelica.Blocks.MathBoolean.Nor

Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )

Modelica.Blocks.MathBoolean.Nor

Information

The output is false if at least one input is true, otherwise the output is true.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

Connectors

Type Name Description

input BooleanVectorInput u[nu] Vector of Boolean input signals

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanVectorInput	u[nu]	Vector of Boolean input signals
output BooleanOutput	y	Boolean output signal

Modelica definition

block Nor 
  "Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )"
  extends Modelica.Blocks.Interfaces.PartialBooleanMISO;

equation 
  y = not Modelica.Math.BooleanVectors.anyTrue(
                                u);
end Nor;

Modelica.Blocks.MathBoolean.Not

Logical 'not': y = not u

Modelica.Blocks.MathBoolean.Not

Information

The output is false if at least one input is true, otherwise the output is true.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

Connectors

Type Name Description

input BooleanInput u Boolean input signal

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanInput	u	Boolean input signal
output BooleanOutput	y	Boolean output signal

Modelica definition

block Not "Logical 'not': y = not u"
  extends Modelica.Blocks.Interfaces.PartialBooleanSISO_small;

equation 
  y = not u;
end Not;

Modelica.Blocks.MathBoolean.RisingEdge

Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))

Modelica.Blocks.MathBoolean.RisingEdge

Information

A rising edge of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

Parameters

Type Name Default Description

Boolean pre_u_start false Value of pre(u) at initial time

Type	Name	Default	Description
Boolean	pre_u_start	false	Value of pre(u) at initial time

Connectors

Type Name Description

input BooleanInput u Boolean input signal

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanInput	u	Boolean input signal
output BooleanOutput	y	Boolean output signal

Modelica definition

block RisingEdge 
  "Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))"
   parameter Boolean pre_u_start = false "Value of pre(u) at initial time";
   extends Modelica.Blocks.Interfaces.PartialBooleanSISO_small;
initial equation 
  pre(u) = pre_u_start;
equation 
  y = edge(u);
end RisingEdge;

Modelica.Blocks.MathBoolean.FallingEdge

Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))

Modelica.Blocks.MathBoolean.FallingEdge

Information

A falling edge of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

Parameters

Type Name Default Description

Boolean pre_u_start false Value of pre(u) at initial time

Type	Name	Default	Description
Boolean	pre_u_start	false	Value of pre(u) at initial time

Connectors

Type Name Description

input BooleanInput u Boolean input signal

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanInput	u	Boolean input signal
output BooleanOutput	y	Boolean output signal

Modelica definition

block FallingEdge 
  "Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))"
   parameter Boolean pre_u_start = false "Value of pre(u) at initial time";
   extends Modelica.Blocks.Interfaces.PartialBooleanSISO_small;
protected 
  Boolean not_u = not u;
initial equation 
  pre(not_u) = not pre_u_start;
equation 
  y = edge(not_u);
end FallingEdge;

Modelica.Blocks.MathBoolean.ChangingEdge

Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))

Modelica.Blocks.MathBoolean.ChangingEdge

Information

A changing edge, i.e., either rising or falling, of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

Parameters

Type Name Default Description

Boolean pre_u_start false Value of pre(u) at initial time

Type	Name	Default	Description
Boolean	pre_u_start	false	Value of pre(u) at initial time

Connectors

Type Name Description

input BooleanInput u Boolean input signal

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanInput	u	Boolean input signal
output BooleanOutput	y	Boolean output signal

Modelica definition

block ChangingEdge 
  "Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))"
   parameter Boolean pre_u_start = false "Value of pre(u) at initial time";
   extends Modelica.Blocks.Interfaces.PartialBooleanSISO_small;
initial equation 
  pre(u) = pre_u_start;
equation 
  y = change(u);
end ChangingEdge;

Modelica.Blocks.MathBoolean.OnDelay

Delay a rising edge of the input, but do not delay a falling edge.

Modelica.Blocks.MathBoolean.OnDelay

Information

A rising edge of the Boolean input u gives a delayed output. A falling edge of the input is immediately given to the output.

Simulation results of a typical example with a delay time of 0.1 s is shown in the next figure.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

Parameters

Type Name Default Description

Time delayTime Delay time [s]

Type	Name	Default	Description
Time	delayTime		Delay time [s]

Connectors

Type Name Description

input BooleanInput u Boolean input signal

output BooleanOutput y Boolean output signal

Type	Name	Description
input BooleanInput	u	Boolean input signal
output BooleanOutput	y	Boolean output signal

Modelica definition

block OnDelay 
  "Delay a rising edge of the input, but do not delay a falling edge."
      extends Modelica.Blocks.Interfaces.PartialBooleanSISO_small;
      parameter Modelica.SIunits.Time delayTime "Delay time";

protected 
      Boolean delaySignal(start=false,fixed=true);
      discrete Modelica.SIunits.Time t_next;
initial equation 
      pre(u) = false;
      pre(t_next) = time - 1;
algorithm 
      when u then
         delaySignal := true;
         t_next := time + delayTime;
      elsewhen not u then
         delaySignal := false;
         t_next := time - 1;
      end when;
equation 
      if delaySignal then
         y = time >= t_next;
      else
         y = false;
      end if;
end OnDelay;

Automatically generated Fri Nov 12 16:27:39 2010.