Control theory

Magnitude condition

Within engineering control theory, the magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the angle condition, these two mathematical expressions fully determine the root locus. Let the characteristic equation of a system be , where . Rewriting the equation in polar form is useful. where are the only solutions to this equation. Rewriting in , and representing each factor and by their vector equivalents, and , respectively, may be rewritten. Simplifying the characteristic equation, from which we derive the magnitude condition: The angle condition is derived similarly. (Wikipedia).

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Related pages

Control theory | Root locus | Angle condition