Root Locus - Electrical Engineering (EE) PDF Download


ROOT LOCUS

  • The Routh's criterion gives a satisfactory answer to the question of stability but its adoption to determine the relative stability is not satisfactory and requires trial and error procedure even in the analysis problem.
  • A simple technique, known as the root locus technique, for finding the roots of the characteristic equation, introduced by W.R.Evens, is extensively used in control engineering practice.
  • This technique provides a graphical method of plotting the locus of the roots in the s-plane as a given system parameter is varied over the complete range of values (may be from zero to infinity).
  • The roots corresponding to a particular value of the system parameter can then be located on the locus or the value of the parameter for a desired root location can be determined from the locus.
  • Root locus is drawn with the help of spirule

Advantages

  • The roots locus is a powerful technique as it brings into focus the complete dynamic response of the system and further, being a graphical technique, an approximate root locus sketch can be made quickly and the designer can easily visualize the effects of varying various system parameters on root locations.
  • The root locus also provides a measure of sensitivity of roots to the variation in the parameter being considered.
  • The root locus also provides a measure of sensitivity of roots to the variation in the parameter being considered.
  • It may further be pointed out here that the root locus technique is applicable for single as well as multiple-loop system.
  • In short it is defined as the locus of the roots of the characteristic equation as the gain parameter 'K' varies from 0 to ∞

ANGLE & MAGNITUDE CONDITIONS
Angle condition

  • The angle condition is used for checking whether particular points are lying on root locus or not

1 + G(s)H(s) = 0

G(s)H(s) = -1

 G(s)H(s) = -1 +10

∠G(s)H(s) = 1800

∠G(s)H(s) = +- (2q + 1)1800

Root Locus - Electrical Engineering (EE)

  • The angle condition may be stated as for a point to lie on root locus, the angle evaluated at that point must be an odd multiple of ±180º . Magnitude Condition
  • This condition is used for finding the value of system gain K at that point on root locus.

G(s)H(s) =1

 

RULES OF DRAWING THE ROOT LOCUS

  • Root locus starts from open loop poles with K= 0 (although practically it never happens as practically we have number of poles greater then number of zeros); and ends on open loop zeros with K = ∞
  • Root locus is always symmetrical about real axis.
  • A point on real axis lies on the root locus if number of poles + zeros to the right of the point are odd.

Steps of Drawing the Root Locus
 Let, Number of poles = n (open loop poles)
 Number of open loop zeros = m

  • Number of root loci ending on infinite = n - m, n > m
  • Root locus on real axis 

Root Locus - Electrical Engineering (EE)

 

  • Here the root locus on real axis confirms above mentioned rule.
  • Root locus moves always away from open loop poles and towards zero or infinity.
  •  Number of asymptotes = (n – m)
  •  Asymptotes are the paths along which root locus moves towards ∞ .
  •  Angle of asymptotes

  Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

r = Number of incoming branch of root locus

Root Locus - Electrical Engineering (EE)

q = 0, 1, 2, ......, n – m – 1

(e) Centroid

Root Locus - Electrical Engineering (EE)

(f) Determination of Breakaway or breaking point put Root Locus - Electrical Engineering (EE) and find out the value of 's'.

(g) Angle of departure or Angle of arrival

Root Locus - Electrical Engineering (EE)

  • Angle made by root locus with real axis when it departs from a complex open loop pole is called angle of departure.

Root Locus - Electrical Engineering (EE)

∠GH' = angle of the function excluding the concerned poles at the poles itself

  Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

  • Just calculate for one (s1, or s2) and you can write for the other by putting negative sign.
  • Crossover at imaginary axis.
  • The roots of the auxiliary equation in Routh array at K = Kmar determines the intersection of rootlocus with imaginary axis.
  • Determination of 'K' from root-locus:

Root Locus - Electrical Engineering (EE)

i.e for the following root locus

Root Locus - Electrical Engineering (EE)

Table: Open-loop pole-zero configurations and the corresponding Root loci.

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

Root Locus - Electrical Engineering (EE)

The document Root Locus - Electrical Engineering (EE) is a part of Electrical Engineering (EE) category.
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

Top Courses for Electrical Engineering (EE)

FAQs on Root Locus - Electrical Engineering (EE)

1. What is the root locus in electrical engineering?
Ans. The root locus is a graphical representation of the possible locations of the roots of a characteristic equation as a parameter, such as the gain, is varied. It is commonly used in control systems analysis and design to determine the stability and performance of a system.
2. How is the root locus used in electrical engineering?
Ans. The root locus is used to analyze the stability and performance of control systems. By plotting the possible locations of the roots of the characteristic equation, engineers can determine the range of parameter values that will result in a stable system. It also helps in identifying the gain values that will result in desired system response.
3. What information can be obtained from the root locus plot in electrical engineering?
Ans. The root locus plot provides information about the stability of a control system. It shows the regions of the parameter space where the system is stable, unstable, or marginally stable. It also helps in identifying the gain values that will result in certain system characteristics, such as overshoot, settling time, and steady-state error.
4. How can the root locus be used to design a control system in electrical engineering?
Ans. The root locus can be used for control system design by selecting the desired system characteristics, such as settling time and overshoot, and finding the corresponding gain values from the root locus plot. Engineers can then design a controller that will achieve the desired system response based on the identified gain values.
5. What are the limitations of using the root locus in electrical engineering?
Ans. The root locus assumes a linear time-invariant system and does not consider nonlinearities or time-varying parameters. It also assumes that the system transfer function is known and that the gain is the only parameter being varied. Additionally, the root locus does not provide information about the transient response of the system, such as the response to a step input.
Download as PDF
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Free

,

Extra Questions

,

pdf

,

Sample Paper

,

Root Locus - Electrical Engineering (EE)

,

Objective type Questions

,

MCQs

,

Summary

,

ppt

,

study material

,

shortcuts and tricks

,

Viva Questions

,

Exam

,

Important questions

,

practice quizzes

,

Root Locus - Electrical Engineering (EE)

,

past year papers

,

mock tests for examination

,

Semester Notes

,

Previous Year Questions with Solutions

,

video lectures

,

Root Locus - Electrical Engineering (EE)

;