The system just becomes unstable when it is marginally stable, which occurs when the Routh array has a row of zeros or when an element in the first column becomes zero, leading to poles on the imaginary axis. The characteristic equation is $s^3 + 6s^2 + 8s + k = 0$. Using the Routh-Hurwitz criterion, the condition for marginal stability is when the coefficient of $s^1$ in the Routh array is zero. This leads to $\frac{48-k}{6} = 0$, which gives $k=48$.
The loop gain $GH$ of a closed-loop system is given by the following expression : $\frac{k} {s(s+2)(s+4)}$ The value of $k$ for which the system just becomes unstable is
Asked in GS&EI ElectEngg 14 2024 1601 2025 · Topic: Computer and Information Technology (Computational Physics: Numerical methods and algorithms for physical problems)
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