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# Component Equations

Write equations to represent custom component behavior

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. Topics on this page provide detailed information on defining component equations and the related tasks.

## Language Syntax

 `assert` Program customized run-time errors and warnings `delay` Return past value of operand `der` Return time derivative of operand `equations` Define component equations `function` Reuse expressions in component equations and in member declarations of domains and components `integ` Perform time integration of expression `intermediates` Define intermediate terms for use in equations `tablelookup` Return value based on interpolating set of data points `time` Access global simulation time `value` Convert variable or parameter to unitless value with specified unit conversion

## Topics

• Defining Component Equations

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.

• Simple Algebraic System

This example shows implementation for a simple algebraic system.

• Use Simulation Time in Equations

This example shows how you can access global simulation time from the equation section.

• Using Conditional Expressions in Equations

You can specify conditional equations by using `if` statements.

• Using Intermediate Terms in Equations

Textbooks often define certain equation terms in separate equations, and then substitute these intermediate equations into the main one.

• Using Lookup Tables in Equations

You can use the `tablelookup` function in the `equations` section of the Simscape™ file to interpolate input values based on a set of data points in a one-dimensional, two-dimensional, or three-dimensional table.

• Programming Run-Time Errors and Warnings

Use the `assert` construct to implement run-time error and warning messages for a custom block.

• Initial Equations

Specify additional equations to be executed during model initialization only.

• Simscape Functions

Use Simscape functions to reuse expressions in equations and member declarations of multiple components.

• Import Symbolic Math Toolbox Equations

Example of using Symbolic Math Toolbox™ software to solve the physical equations, generate code in the format appropriate for the Simscape language equation section, and incorporate the generated code into the equation section of a component file.