Closed-loop pole: Difference between revisions

Revision as of 09:23, 27 May 2018

Revision as of 17:50, 15 September 2019

Line 5:

==Closed-loop poles in control theory==

The response of a linear and[[Linear time-invariant system | linear time-invariant 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 (electronics)|gain]] ''K'' is usually parameterized. Each point on the locus satisfies the [[angle condition]] and [[magnitude condition]] and corresponds to a different value of&nbsp;''K''. For [[negative feedback]] systems, the closed-loop poles move along the [[root-locus]] from the [[open-loop pole]]s to the [[open-loop zeroe]]s 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>.