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Routh Array Stability

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a) Determine if the following characteristic equation represents a stable system?

S^3 + 4s^2 + 8s + 12 = 0

b) The characteristic equation of a given system is:

s^4 + 6s^3 + 11s^2 + 6s +K = 0

What restrictions must be placed upon the parameter K in order to ensure that the system is stable?

C-

A system is designed to give satisfactory performance when a particular amplifier gain K has the value 2. Determine how much this gain can vary before the system becomes unstable if the characteristic equation is:

S^3 + (4 + K)S^2 + 6S + 16 + 8K = 0

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The expert examines Routh array stability.

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a.

First we need to compute the Routh array [Reference 1] thus we form from the polynomial coefficients

This simplifies (after multiplying out the brackets and doing the sums within brackets) to

And simplifies again to

Therefore the system is stable since all values in the first column of the Routh array are positive (ie the same sign which is the ...

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