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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 the Simulink User's Guide for an example of choosing the best-form mathematical model to avoid using Derivative blocks in your models.

Improved Linearization with Switched Derivative Blocks

Using linmod to linearize a model that contains a Derivative block can be troublesome. Before linearizing your model, replace each Derivative block with a block that avoids the problems. In the Library Browser, go to the Simulink Extras library and open the Linearization sublibrary. For each instance of the Derivative block in your model, use the Switched derivative for linearization block.

For more information, see the linmod reference page and Linearizing Models in the Simulink documentation.

Improved Linearization with Transfer Fcn Blocks

To improve linearization, you can also try to incorporate the derivative term in other blocks. For example, if you have a Derivative block in series with a Transfer Fcn block, try using a single Transfer Fcn block of the form

For example, you can replace the blocks on the left of this figure by using the block on the right.

Data Type Support

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

Parameters and Dialog Box

Linearization Time Constant s/(Ns + 1)

Specify the time constant N to approximate the linearization of your system.

Settings

Default: inf

The default value inf corresponds to a linearization of 0.
The exact linearization of the Derivative block is difficult, because the dynamic equation for the block is , which you cannot represent as a state-space system. However, you can approximate the linearization by adding a pole to the Derivative to create a transfer function . The addition of a pole filters the signal before differentiating it, which removes the effect of noise.