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Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh’s Table of the system characteristic equation. X: The system is stable … Y: The system is unstable … Z: The test breaks down … P: … when all elements are positive Q: … when any one element is zero R: … when there is a change in sign of coefficients

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh’s Table of the system characteristic equation. X: The system is stable … Y: The system is unstable … Z: The test breaks down … P: … when all elements are positive Q: … when any one element is zero R: … when there is a change in sign of coefficients Correct Answer X→P, Y→R, Z→Q

Concept:

To find the closed system stability by using RH criteria we require a  characteristic equation. Whereas in remaining all stability techniques we require open-loop transfer function.

The nth order general form of CE is

a0 sn + a1 sn-1 + a2sn-2 + __________an-1 s1 + an

RH table shown below

Necessary condition: 

All the coefficients of the characteristic equation should be positive and real.

Sufficient Conditions for stability:

1. All the coefficients in the first column should have the same sign and no coefficient should be zero.

2. If any sign changes in the first column, the system is unstable.

And the number of sign changes = Number of poles in right of s-plane.

Analysis:

i) If all the elements present in the first column of the RH table have a positive (+ve) sign then we can say that system is stable.

ii) If there is any change in the sign of the first column then we can say that system is Unstable and the number of sign changes indicates the Number of poles present on the right side of the S – plane.

iii) If any element is zero in the first column then it says the test breaks down.

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