Low-pass filter

First-order continuous filter.

BlockLow-pass filterKindfilterLibraryContinuous

Description

A first-order low-pass filter with unity DC gain. The output follows the input with time constant τ, reaching about 63% of a step after τ.

Step responses A unit step through a first-order filter, a second-order system, an integrator, and a delay; a ramp through a derivative.

Step at 0.1 sFirst orderSecond orderIntegratorDelay 0.3 sRamp, slope 2Derivative

In Gradara, select a Low-pass filter block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Time constanttau0.05 s

≥ 0.00001

Time constant τ, in seconds. At least 1e-5 s. The corner frequency is 1/(2π · tau) Hz.

Modelica

dx/dt = (u − x) / tau
y = x, with x = 0 at time 0
Transfer function: 1 / (tau · s + 1)

The block’s Modelica model

Real x(start=0, fixed=true);
der(x) = (u-x)/tau;
y = x;

The output always starts at 0, so a nonzero input at time 0 gives a start-up transient.

These larger examples use it too. Open them from Examples in the app.