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The root locus method can also be used for the analysis of sampled data systems by computing the root locus in the z-plane, the discrete counterpart of the s-plane. The equation z = e sT maps continuous s -plane poles (not zeros) into the z -domain, where T is the sampling period.
Walter Richard Evans (January 15, 1920 – July 10, 1999) was a noted American control theorist and the inventor of the root locus method and the Spirule device in 1948. He was the recipient of the 1987 American Society of Mechanical Engineers Rufus Oldenburger Medal [1] and the 1988 AACC's Richard E. Bellman Control Heritage Award.
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Root locus plot of Wien bridge oscillator pole positions for R 1 = R 2 = 1 and C 1 = C 2 =1 versus K = (R b + R f)/R b. The numerical values of K are shown in a purple font. The trajectory of the poles for K=3 is perpendicular to the imaginary (β) axis. For K >> 5, one pole approaches the origin and the other approaches K. [34]
In 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
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:
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Root locus; Transfer function; Liénard–Chipart criterion (variant requiring fewer computations) Kharitonov's theorem (variant for unknown coefficients bounded within intervals) Jury stability criterion (analog for discrete-time LTI systems) Bistritz stability criterion (analog for discrete-time LTI systems)