Step 1: Routh-Hurwitz Criterion Application.
The Routh-Hurwitz criterion is utilized to assess system stability. The Routh array is constructed from the characteristic equation's coefficients. For stability, the number of sign changes in the first column indicates the \(K_c\) value that ensures system stability.
Step 2: Conclusion.
Based on the Routh test, the system remains stable with a \(K_c\) value of (C) 13.5.
Given an open-loop transfer function \(GH = \frac{100}{s}(s+100)\) for a unity feedback system with a unit step input \(r(t)=u(t)\), determine the rise time \(t_r\).
Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is: