equations

Define component equations

Syntax

equations
   Expression1 == Expression2;
end

Description

equations begins the equation section in a component file; this section is terminated by an end keyword. The purpose of the equation 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.

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

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 equation 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 equation section, Expression may not be formed with the following operators:

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

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

The following MATLAB functions can be used in the equation section. The table contains additional restrictions that pertain only to the equation 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.

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  
mldivideNonmatrix denominator 
mrdivideNonmatrix denominator 
ldivide  
rdivide  
mod Yes
sum  
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  
log  
log10  
sinh  
cosh  
tanh  
exp  
sqrt  
abs Yes
sign Yes
any Yes
all Yes
min Yes
max Yes
double  
int32 Yes
uint32 Yes
repmat  
reshapeExpanded empty dimension is not supported 
dot  
cross  
diffIn the two argument overload, the upper bound on the second argument is 4, due to a Simscape limitation 

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

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:

y={xfor 1<= x<=1x2otherwise 

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

Introduced in R2009a