# PS Integrator

Integrate physical signal

## Library

Physical Signals/Linear Operators

## Description

The PS Integrator block outputs the integral of its input at the current time step. The following equation represents the output of the block:

`$y\left(t\right)=\underset{{t}_{0}}{\overset{t}{\int }}u\left(t\right)dt+{y}_{0}$`

where

 `u` Physical signal at the input port `y0` Initial condition `y` Physical signal at the output port `t` Time

The PS Integrator block is a dynamic system with one state, its output. The PS Integrator block's input is the state's time derivative:

`$x=y\left(t\right)$`
`${x}_{0}={y}_{0}$`
`$\stackrel{˙}{x}=u\left(t\right)$`

The solver computes the output of the PS Integrator block at the current time step, using the current input value and the value of the state at the previous time step. To support this computational model, the PS Integrator block saves its output at the current time step for use by the solver to compute its output at the next time step. The block also provides the solver with an initial condition for use in computing the block's initial state at the beginning of a simulation run. The default value of the initial condition is 0. You can specify another value for the initial condition as a parameter on the block dialog box.

## Dialog Box and Parameters

Initial Condition

Specify the initial condition for use in computing the block's initial state at the beginning of a simulation run. The default value is `0`.

## Ports

The block has one physical signal input port and one physical signal output port.