Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Control system - Question Paper

Routh condition states that the necessary and sufficient condition for stability is that all of the elements in the 1st column of routh array be positive. If this condition is not met,the system is unstable and the number of of sign modifications in the elements of the 1st column of routh array corresponds to number of roots of characteristic formula in the right half of s-plane.
12.) What is auxiliary polynomial?
In the construction of routh array a row of all zero shows the existence of an even polynomial as a factor of the provided characteristic formula.In an even polynomial the exponents of s are even integers or 0 only.This even polynomial factor is called auxiliary polynomial.
13.) What is quadrantal symmetry?
The symmetry of roots with respect to both real and imaginary axis is called quadrantal symmetry.
14.) In routh array what conclusion can you make when there is a row of all zeros?
All zero row shows that the existence of an even polynomial as a factor of provided characteristic formula.
15.) What is limitedly stable system?
For a bounded input signal,if the output has constant amplitude oscillations the the system may be stable or unstable under a few limited constraints.Such a system is called Limitedly stable system.
16.) What is Nyquist stability criterion?
If G(s) H(s) contour in the G(s) H(s) palne corresponding to Nyquist contour in s-plane encircles the point -1+j0 in the anticlockwise direction as many times as the number of right half s-planes poles of G(s) H(s).Then the closed loop system is stable.
17.) What is root locus?
The path taken by a root of characteristic formula when open loop gain K is varied from 0 to infinity is called root locus.
18.) What is magnitude direction?
The magnitude direction condition states that s=sa will be a point on root locus if for the value of s ,magnitude of G(s) H(s) if equal to 1.
19.) What is angle direction?
The angle direction states that s=sa will be point on the root locus if for that value os s the argument or phase of G(s) H(s) if equal to an odd multiple of 180.
20.) How will you obtain gain K at a point on root locus?
K=Product of length of vector from open loop poles to the point sa Product of length of vector from open loop zeros to the point sa
21.) How will you obtain root locus on real axis?
select a test point on real axis.If the total number of poles and zeros on the real axis to the right of this test point is odd number then the test point lies on the root locus.
22.) elaborate asymptotes?How do u obtain the angle of asymptotes?

Earning:   Approval pending.