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Improved Linearization with Transfer Fcn Blocks

The Laplace domain transfer function for the operation of differentiation is:

\frac{Y(s)}{X(s)} = s

This equation is not a proper transfer function, nor does it have a state-space representation. As such, the Simulink software linearizes this block as an effective gain of 0 unless you explicitly specify that a proper first-order transfer function should be used to approximate the linear behavior of this block.

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

$$ \frac{s}{s+a} $$

For example, you can replace the first set of blocks in this figure with the blocks below them:

See Also