Closed-loop pole: Difference between revisions

Revision as of 18:44, 16 December 2009

Revision as of 17:56, 15 May 2010

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==Closed-loop poles in control theory==

The response of a system to any input can be derived from its [[impulse response]] and [[step response]]. The eigenvalues of the system determine completely the [[natural response]] ([[unforced response]]). In control theory, the response to any [[input]] is a combination of a [[transient response]] and [[steady-state response]]. Therefore, a crucial design parameter is the ___location of the eigenvalues, or closed-loop poles.

In [[root-locus|root-locus design]], the [[gain]], K, is usually parameterized. Each point on the locus satisfies the [[angle condition]] and [[magnitude condition]] and corresponds to a different value of K. For [[negative feedback]] systems, the closed-loop poles move along the [[root-locus]] from the [[open-loop poles]] to the [[open-loop zeroes]] as the gain is increased. For this reason, the root-locus is often used for design of [[proportional control]], i.e. those for which <math>\textbf{G}_c = K</math>.