A Stable plan

Computer Science Level 2

For what value of n n will the system presented in the image be stable for a k > n ? k > n? Consider n n to be the smallest possible value of n . n.


The answer is 1.

João Areias by João Areias , 24, Brazil

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1 solution

João Areias
Jan 16, 2018

One can multiply the two transfer functions to get the system below.

The transfer function H ( s ) H(s) of the sistem is then given by:

H ( s ) = k s − 1 1 + k s − 1 = k s − 1 + k H(s) = \frac{\frac{k}{s-1}}{1 + \frac{k}{s-1}} = \frac{k}{s-1+k}

For the system to be stable all the poles have to be on the left half plane, so k − 1 > 0 ⇒ k > 1 k-1 > 0 \Rightarrow k > 1

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This is a topic related to Control Systems Engineering, not Computer Science per se.

A Former Brilliant Member - 3 years, 4 months ago

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Is just that signals and systems are under computer science in Brilliant's practice, that's why I put it there, even though it's more related to Control Systems Engineering.

João Areias - 3 years, 4 months ago

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