equations

Define component or domain equations

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Parent Section: component | domain

Syntax

equations
   Expression1 == Expression2;
end

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 equations section establishes the mathematical relationships between the component 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 equations section.

Similarly, the equations section in a domain file establishes 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 equations 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 equations 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

Note

The total number of equation expressions, their dimensionality, and their order must be the same for every branch of the if-elseif-else statement.

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.

Note

The end keyword is required at the end of a let-in-end statement.

The following rules apply to the equations section:

  • EquationList is one or more objects of class EquationExpression, separated by a comma, semicolon, or newline.

  • EquationExpression can be one of:

    • Expression

    • Conditional expression (if-elseif-else statement)

    • Let expression (let-in-end statement)

  • Expression is any valid MATLAB expression. It may be formed with the following operators:

  • In the equations section, Expression may not be formed with the following operators:

  • The colon operator only accepts constants or end as its operands.

  • All members of the component are accessible in the equations section, but none are writable.

Supported Functions

You can use these MATLAB functions in the equations section. The table contains additional restrictions that pertain only to the equations section. It also indicates whether a function is discontinuous. If the function is discontinuous, it introduces a zero-crossing when used with one or more continuous operands.

All arguments that specify size or dimension must be unitless constants or unitless compile-time parameters. For array operations, two operands must be of the same size, or one must be a scalar.

Supported Functions

NameRestrictionsDiscontinuous
ones  
zeros  
cat  
horzcat  
vertcat  
length  
ndims  
numel  
size  
isempty  
isequal Possibly, if arguments are real and have the same size and commensurate units
isinf Yes
isfinite Yes
isnan Yes
plus  
uplus  
minus  
uminus  
mtimes  
times  
mpower  
power  
mldivideFirst argument must be a scalar 
mrdivideSecond argument must be a scalar 
ldivide  
rdivide  
mod Yes
sum  
cumsumdirection and nanflag arguments are not supported 
movsumnanflag and Name=Value arguments are not supported 
prod  
floor Yes
ceil Yes
fix Yes
round Yes
eqDo not use with continuous variables 
neDo not use with continuous variables 
lt  
gt  
le  
ge  
and Yes
or Yes
logical Yes
sin  
cos  
tan  
asin  
acos  
atan  
atan2 Yes
sinh  
cosh  
tanh  
asinh  
acosh  
atanh  
log  
log10  
expLimiting applied during initialization and simulation to avoid nonfinite (Inf or NaN) values. Limiting is not applied when exp is used as an argument inside functions such as isinf, isnan, or isfinite, to ensure the correct predicate evaluation.  
sqrt  
abs Yes
sign Yes
any Yes
all Yes
min Yes
max Yes
double  
int32 Yes
uint32 Yes
erf  
erfc  
repmat  
reshapeExpanded empty dimension is not supported 
dot  
cross  
diff  

Initial Equations

The (Initial=true) attribute lets you specify equations that are executed during model initialization only:

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

The default value of the Initial attribute for equations is false, therefore you can omit this attribute when declaring regular equations.

For more information on when and how to specify initial equations, see Initial Equations.

Examples

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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 a component where x and y are declared as 1x1 variables, specify a piecewise equation:

y={xfor −1<= x<=1x2otherwise 

This equation, written in the Simscape language, looks 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

Version History

Introduced in R2009a

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See Also

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