equations

Description

equations begins the equation section in a component or domain file; this section is terminated by an end keyword.

In a component file, the purpose of the equations section is to establish the mathematical relationships among a component’s variables, parameters, inputs, outputs, time and the time derivatives of each of these entities. All members declared in the component are available by their name in the equation section.

Similarly, the equations section in a domain file serves to establish the mathematical relationships between the domain Across variables, parameters, and intermediates. Use the domain equations when your custom domain has more Across variables than Through variables. For more information, see Domain Equations.

The equation section of a Simscape™ file is executed throughout the simulation. You can also specify equations that are executed during model initialization only, by using the (Initial=true) attribute. For more information, see Initial Equations.

The following syntax defines a simple equation.

equations
   Expression1 == Expression2;
end

The statement Expression1 == Expression2 is an equation statement. It specifies continuous mathematical equality between two objects of class Expression. An Expression is a valid MATLAB^® expression. Expression may be constructed from any of the identifiers defined in the model declaration.

The equation section may contain multiple equation statements. You can also specify conditional equations by using if statements as follows:

equations
   if Expression 
       EquationList 
   { elseif Expression 
       EquationList } 
   else 
       EquationList 
   end
end

You can declare intermediate terms in the intermediates section of a component or domain file and then use these terms in any equations section in the same component file, in an enclosing composite component, or in a component that has nodes of that domain type.

You can also define intermediate terms directly in equations by using let statements as follows:

equations
   let 
      declaration clause
   in 
      expression clause 
   end 
end

The declaration clause assigns an identifier, or set of identifiers, on the left-hand side of the equal sign (=) to an equation expression on the right-hand side of the equal sign:

  LetValue = EquationExpression

The expression clause defines the scope of the substitution. It starts with the keyword in, and may contain one or more equation expressions. All the expressions assigned to the identifiers in the declaration clause are substituted into the equations in the expression clause during parsing.

The following rules apply to the equation section:

equations (Initial=true)
   Expression1 == Expression2;
end

Examples

For a component where x and y are declared as 1x1 variables, specify an equation of the form y = x²:

equations
  y == x^2;
end

For the same component, specify the following piecewise equation:

This equation, written in the Simscape language, would look like:

equations
  if x >= -1 && x <= 1
    y == x;
  else
    y == x^2;
  end
end

If a function has multiple return values, use it in a let statement to access its values. For example:

equations
  let 
    [m, i] = min(a);
  in
    x == m;
    y == i;
  end
end