Control theory

Angle condition

In mathematics, the angle 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 magnitude 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 factored form, and representing each factor and by their vector equivalents, and , respectively, may be rewritten. Simplifying the characteristic equation, from which we derive the angle condition: for , are the angles of zeros 1 to n, and are the angles of poles 1 to m. The magnitude condition is derived similarly. (Wikipedia).

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Related pages

Root locus | Magnitude condition | Closed-loop pole | Factorization