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I have an exercise that gives me the following transfer function
$$ \frac{0.5}{s+0.5} $$
and an assumed step change in the target of 20
I am asked to calculate the maximum input for the assumed step change.
I know the answer is 500 but can't figure out how to get there. I have seen this which gives me the following but I don't know where to go from there.
$$40\,{\delta }\left(t\right)+20$$
This is an application of the Final Value Theorem for the Laplace Transform combined with knowing what the Laplace Transform of a unit step is. With The Final Value Theorem and given a description of the output in Laplace (which is the product of the Laplace of a unit step and the OP’s transfer function), we can easily determine the final value of the related time domain function at $t=\infty$.
I recommend studying the Final Value Theorem and related examples and you will find it to be a very easy way to determine the final value! With that you can back out what the step value needs to be to reach a final value of 500.
