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UPRVUNL AE EC 2014 Official Paper

Option 4 : Bode-Asymptotic plots, Evans-Roots-locus technique, Nyquist-Polar plots

Hindi Subject Test 1

4248

10 Questions
10 Marks
10 Mins

**Bode plot:**

- In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift.
- The Bode magnitude plot is the graph of the function |H(s=jω)| of frequency ω (with j being the imaginary unit). The ω -axis of the magnitude plot is logarithmic and the magnitude is given in decibels, i.e., a value for the magnitude |H| is plotted on the axis at 20\log
_{10}|H| - The Bode phase plot is the graph of the phase, commonly expressed in degrees, of the transfer function (H(s=jω )\right as a function of ω . The phase is plotted on the same logarithmic ω -axis as the magnitude plot, but the value for the phase is plotted on a linear vertical axis.
- For many practical problems, the detailed Bode plots can be approximated with straight-line segments that are
**asymptotes of the precise response. Hence Bode plot is an asymptotic plot.**

**Root locus Technique:**

- This is a technique used as a stability criterion in the field of classical control theory
**developed by****Walter R. Evans**which can determine the stability of the system. - In the root locus diagram, we can observe the path of the closed-loop poles. Hence, we can identify the nature of the control system.
- In this technique, we will use an open-loop transfer function to know the stability of the closed-loop control system.

**Nyquist plot:**

**Nyquist plots are an extension of polar plots **for finding the stability of the closed-loop control systems. This is done by varying ω from −∞ to ∞, i.e. Nyquist plots are used to draw the complete frequency response of the open-loop transfer function.

Method of drawing Nyquist plot:

- Locate the poles and zeros of open-loop transfer function G(s)H(s) in ‘s’ plane.
- Draw the polar plot by varying ω from zero to infinity.
- Draw the mirror image of the above polar plot for values of ω ranging from −∞ to zero.
- The number of infinite radii half circles will be equal to the number of poles at the origin.
- The infinite radius half-circle will start at the point where the mirror image of the polar plot ends. And this infinite radius half-circle will end at the point where the polar plot starts.