splane3

splane3 - Stability Design via Routh-Hurwitz Given the...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stability Design via Routh-Hurwitz Given the system below find the range of the gain K that will lead to stability, unstability and marginal stability. E(s) s(s+7)(s+11) K +- R(s) C(s) Closing the loop: T ( s ) = K s 3 + 18 s 2 + 77 s + K (1) 1 s 3 1 77 s 2 18 K s 1 1386- K 18 s K If K is positive (assumed) all the elements in the first column are positive except that the s 1 entry may be positive/nagative. If K &lt; 1386, the system will remain stable. If K &gt; 1386, the system will remain unstable. If K = 1386, a row of zeros, so using P ( s ) = 18 s 2 + 1386 (2) 2 dP ( s ) ds = 36 s + 0 (3) s 3 1 77 s 2 18 K s 1 6 36 s 1386 Since there are no sign change from s 2 to s the even polynomial has no unstable roots, only j roots, therefore the system is marginally stable when K = 1386. 3 Root locus techniques Root locus, a graphical representation of the closed loop poles as a system parameter is var- ied....
View Full Document

splane3 - Stability Design via Routh-Hurwitz Given the...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online