Derivative

Filtered derivative du/dt.

signal
Gradara equations
2 ports
1 parameter

BlockDerivativeKindderivativeLibraryContinuous

Description

Approximates the time derivative of its input, filtered by a first-order lag with Filter time τ. Smaller τ comes closer to the true derivative but amplifies noise and fast edges more.

Example

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 Derivative block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:Limited integrator Step Low-pass filter Ramp Second-order Transport delay

Ports

Inputs 1

usignal

Input signal.

Outputs 1

ysignal

Filtered derivative of u, in units of u per second.

Parameters

Filter timetau0.01 s

≥ 0.00001

Filter time constant τ, in seconds. At least 1e-5 s.

Equations

Modelica

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

Implementation

The block’s Modelica model

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

Assumptions and limitations

The internal state starts at 0, not at the input, so a nonzero input at time 0 gives an initial spike of u(0)/tau that decays with time constant τ.
A step in the input gives a spike of height step/tau rather than an impulse.