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GATE EE 2019 Set 1 — Question 41

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MCQ+2 / -0.67EasyState-Space ModelState-Space AnalysisControl SystemsFirst & Second-Order ResponseTime-Domain Analysis

Control Systems → State-Space Analysis → First & Second-Order Response

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Question

Consider a state-variable model of a system[x˙1x˙2]=[01−α−2β][x1x2]+[0α]r\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -\alpha & -2\beta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ \alpha \end{bmatrix} ry=[10][x1x2]y = \begin{bmatrix} 1 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}where yy is the output, and rr is the input. The damping ratio ξ\xi and the undamped natural frequency ωn\omega_n (rad/sec) of the system are given by
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