I have tried using the Derivative block in Simulink and have generally found that it can lead to complications. I usually try to restructure my model to avoid the use of Derivative blocks, but that is sometimes difficult to do. In that case, what are some best practices for using the Derivative block, or should I consider using a different type of block or transfer function? If so, what are some possible alternatives?
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Here is a list of recommendations on the usage of the Derivative block:
1) Signals connected to the Derivative block should be continuous in time and amplitude
Derivative blocks amplify discontinuities when connected to a non-continuous signal. In example 'Example1_Discont.mdl', the slope of the input signal changes instantly. After being passed through a Derivative block, it becomes a peak.
2) Signals connected to the Derivative block should have a small derivative at t=0
‘Example2_Spike.mdl’ shows how a spike can occur in the second derivative after the first time step. This occurs because the Derivative block yields 0 by default at the initial time step, instead of 2*pi in this case. If this model is simulated again with a smaller time step, the spike amplitude increases.
3) Signals connected to the derivative should contain a low level of noise
In general, taking the derivative of a noisy signal tends to exacerbate the influence of that noise. Therefore, Derivative blocks in Simulink exhibit this behavior as well. In ‘Example3_Noise.mdl’, the noise gets amplified in the output, to the point where the derivative of the sine wave is not recognizable. By using a filtered derivative transfer function which filters out higher frequencies, a much better result can be obtained in the example.
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