Integrate physical signal

**Library:**Simscape / Foundation Library / Physical Signals / Linear Operators

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

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

where

`u` | Physical signal at the input port I |

`y` | Initial condition |

`y` | Physical signal at the output port O |

`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:

$$x=y(t)$$

$${x}_{0}={y}_{0}$$

$$\dot{x}=u(t)$$

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 s. You can specify another value for the initial condition as a parameter on the block dialog box.

The block performs integration of the input signal over time, therefore the unit of the
output signal equals the unit of the input signal multiplied by the unit of time, s. For
example, if the input signal is in `m/s`

, then the output signal is in
`m`

. The unit specified for the **Initial condition**
parameter must be commensurate with the unit of the output signal.