Question:
The open loop transfer function of a unity gain negative feedback system is given by
\[
G(s) = \frac{k}{s^2 + 4s - 5}. \text{ The range of } k \text{ for which the system is stable, is}
\]
The open loop transfer function of a unity gain negative feedback system is given by
\[
G(s) = \frac{k}{s^2 + 4s - 5}. \text{ The range of } k \text{ for which the system is stable, is}
\]
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For a second-order system, the system is stable if the real parts of all poles are negative. The Routh-Hurwitz criterion helps in determining the stability conditions based on the system's coefficients.
Updated On: Nov 27, 2025
- ( k>3 \)
- ( k<3 \)
- ( k>5 \)
- ( k<5 \)
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The Correct Option is C
Solution and Explanation
Step 1: Analyzing the given transfer function.
The open-loop transfer function of a unity gain negative feedback system is given by \( G(s) = \frac{k}{s^2 + 4s - 5} \). Step 2: Stability criteria.
To determine the stability of the system, we analyze the poles of the system by solving the characteristic equation: \[ s^2 + 4s - 5 = 0. \] The roots of this quadratic equation will give us the pole locations, and we use the Routh-Hurwitz criterion to determine the range of \( k \) for stability. Step 3: Conclusion.
For stability, the roots must have negative real parts. Solving this, we find that \( k>5 \) ensures the system is stable.
The open-loop transfer function of a unity gain negative feedback system is given by \( G(s) = \frac{k}{s^2 + 4s - 5} \). Step 2: Stability criteria.
To determine the stability of the system, we analyze the poles of the system by solving the characteristic equation: \[ s^2 + 4s - 5 = 0. \] The roots of this quadratic equation will give us the pole locations, and we use the Routh-Hurwitz criterion to determine the range of \( k \) for stability. Step 3: Conclusion.
For stability, the roots must have negative real parts. Solving this, we find that \( k>5 \) ensures the system is stable.
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