What is the stability of the system s³ + s² + s + 4 = 0 using Hurwitz criteria?

Question

Question

This question was previously asked in

MPPKVVCL Jabalpur JE Electrical 16 August 2018 Official Paper

Answer 1

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 s^n-1 + a₂s^n-2 + __________a_n-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.

Calculation:

With the help of the

Routh table explains the concept we can extend the calculation.

So in the first column, there are two sign changes, the system is unstable