Simulink^®

Derivative

Output time derivative of input

Library

Continuous

Description

The Derivative block approximates the derivative of its input by computing

where du is the change in input value and dt is the change in time since the previous simulation time step. The block accepts one input and generates one output. The initial output for the block is zero.

The accuracy of the results depends on the size of the time steps taken in the simulation. Smaller steps allow a smoother and more accurate output curve from this block. Unlike blocks that have continuous states, the solver does not take smaller steps when the input changes rapidly.

When the input is a discrete signal, the continuous derivative of the input is an impulse when the value of the input changes, otherwise it is 0. You can obtain the discrete derivative of a discrete signal using

and taking the z-transform

See Circuit Model in Using Simulink^® for an example on choosing the best-form mathematical model to avoid using Derivative blocks in your models.

Using linmod to linearize a model that contains a Derivative block can be troublesome. To improve the accuracy of linearizations of this block, use the optional linearization parameter within the block dialog box. Additionally, for more information about how to avoid problems linearizing Derivative blocks, see Linearizing Models.

Data Type Support

The Derivative block accepts and outputs a real signal of type double.

Parameters and Dialog Box

The exact linearization of the Derivative block is difficult due to the fact that the block cannot be represented as a state space system since the dynamic equation for the block is . However, it is possible to approximate the linearization by adding a pole to the Derivative to create a proper transfer function. The addition of the pole has the effect of filtering the signal before differentiating it, to remove the effect of noise. The approximated linearization of the Derivative block is then . You can change the Linearization Time Constant, N, to more accurately approximate the linearization for your system. Its default value is Inf, corresponding to a linearization of 0, but it is common practice to change it to , where is the break frequency for the filter.

Characteristics