Closed-loop pole: Difference between revisions

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In [[systems theory]], '''closed-loop poles''' are the positions of the [[Zeros and poles|poles]] (or [[eigenvalue]]s) of a [[closed-loop transfer function]] in the [[s-plane]]. The [[open-loop controller|open-loop]] transfer function is equal to the product of all transfer function blocks in the [[forward path]] in the [[block diagram]]. The closed-loop transfer function is obtained by dividing the open-loop transfer function by the sum of one and the product of all transfer function blocks throughout the negative [[feedback loop]]. The closed-loop transfer function may also be obtained by algebraic or block diagram manipulation. Once the closed-loop transfer function is obtained for the system, the closed-loop poles are obtained by solving the characteristic equation. The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function to zero.

In [[control theory]] there are two main methods of analyzing feedback systems: the [[transfer function]] (or frequency ___domain) method and the [[state space (controls)|state space]] method. When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is [[Singularity (mathematics)|undefined]] (the '''poles''') or zero (the '''zeroes'''; see [[Zeroes and poles]]). Two different transfer functions are of interest to the designer. If the feedback loops in the system are opened (that is prevented from operating) one speaks of the '''[[open-loop transfer function']]'', while if the feedback loops are operating normally one speaks of the '''[[closed-loop transfer function']]''. For more on the relationship between the two, see [[root-locus]].

==Closed-loop poles in control theory==

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: <math>\det(\textbf{I}+\textbf{G}(s)\textbf{K}(s))=0. \, </math>

==References==

{{reflist}}

{{DEFAULTSORT:Closed-Loop Pole}}