File Name: root locus examples and solutions .zip
This is a section in the chapter on classic control analysis methods.
The root locus is a graphical representation in s-domain and it is symmetrical about the real axis. Because the open loop poles and zeros exist in the s-domain having the values either as real or as complex conjugate pairs. In this chapter, let us discuss how to construct draw the root locus.
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A computer-aided root-locus method Abstract: An efficient computer-aided root-locus method is described The approach is based on the concept of continuation methods in which the solution of a parameterized family of algebraic problems is converted into the solution of a differential equation.
The root-locus plot is obtained in a systematic manner by numerical integration. Singularities are analyzed and classified according to the properties of higher order derivatives. Depending on their classification, singular points on the root loci are taken care of accordingly. Article :. Date of Publication: Oct Need Help?
Documentation Help Center Documentation. The root locus returns the closed-loop pole trajectories as a function of the feedback gain k assuming negative feedback. Root loci are used to study the effects of varying feedback gains on closed-loop pole locations. In turn, these locations provide indirect information on the time and frequency responses. You can use rlocus to plot the root locus diagram of any of the following negative feedback loops by setting sys as shown below:.
Root locus plots show the roots of the systems characteristic equation, i. By examining these graphs it is possible to determine the stability of different values of the control variable. In other words, after factorization the poles are the roots of the denominators and the zeros are the roots of the numerator. Stability only depends on the value of the poles. The system is stable for all values of the control variables that result in the value of the real part of every pole value being less than zero.
The open loop poles of a third order unity feedback system are at 0,-1, Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact.
Several root locus examples are provided. Click on the transfer function to get to an explanation of how the root locus would be drawn by hand. The page also lets you enter your own transfer functions. The root locus is obviously a very powerful technique for design and analysis of control systems, but it must be used with some care, and results obtained with it should always be checked.
Marcelo C. Silva, Erica R. This paper addresses the root locus locus of positive gain and the complementary root locus locus of negative gain of biproper transfer functions transfer functions with the same number of poles and zeros.
This book contains mathematical formulae that look better rendered as PNG. Consider a system like a radio. The radio has a "volume" knob, that controls the amount of gain of the system. High volume means more power going to the speakers, low volume means less power to the speakers. As the volume value increases, the poles of the transfer function of the radio change, and they might potentially become unstable.
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