What is the stability of the system s3+ s2+ s + 4 = 0 using Hurwitz criteria?a)Unstableb)Stablec)Critically stabled)Marginally stableCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Hurwitz Criteria Analysis for Stability:
Hurwitz criteria is a method used to determine the stability of a system based on the coefficients of its characteristic equation.

Characteristic Equation:
The characteristic equation for the given system is:
s^3 + s^2 + s + 4 = 0

Hurwitz Criteria:
To apply the Hurwitz criteria, we need to check the coefficients of the characteristic equation.

Step 1:
Check the first column of the Hurwitz matrix for all coefficients of s starting from the highest power of s down to the constant term.
Coefficient for s^3 = 1
Coefficient for s^2 = 1
Coefficient for s^1 = 1
Coefficient for s^0 = 4

Step 2:
Check if all coefficients are positive.
In this case, all coefficients are positive.

Step 3:
Apply the Hurwitz criteria:
For a polynomial of degree 3, the system is stable if and only if all upper left submatrices have positive determinants.

Result:
Since not all upper left submatrices have positive determinants, the system is unstable according to the Hurwitz criteria.
Therefore, the correct answer is option 'A' - Unstable.

Answer

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 explained in the concept we can extend the calculation.

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

Top Courses for Electrical Engineering (EE)View all

Network Theory (Electric Circuits)

GATE Electrical Engineering (EE) Mock Test Series 2025

General Aptitude for GATE

GATE Notes & Videos for Electrical Engineering

Engineering Mathematics

Top Courses for Electrical Engineering (EE)

Top Courses for Electrical Engineering (EE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company