List of top Control Systems Questions asked in GATE IN

A linear time invariant (LTI) system has a transfer function \[ G(s)=\frac{10(s+1)}{s(s^2+2s+5)} \] The system is placed in unity negative feedback configuration.
For a unit ramp reference, the steady state error is ________. (rounded off to two decimal places)

The system \[ G(s)=\frac{K}{(s+1)^4} \] has a gain margin of 20 dB. The value of \(K\) is ________. (rounded off to two decimal places)

A linear time invariant (LTI) system is described by:
\[ \begin{bmatrix}\dot{x}_1\\ \dot{x}_2\end{bmatrix}=\begin{bmatrix}0 & 1\\ -10 & -7\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}+\begin{bmatrix}1\\ 1\end{bmatrix}u \]
\[ y=\begin{bmatrix}1 & 1\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix} \]
The poles of the system are ______.

Among the following, the differential equation(s) not representative of a linear dynamical system is/are ____.
(i) \[ \frac{d^2x}{dt^2} + 2t\frac{dx}{dt} + x(t) = u(t) \]
(ii) \[ \left(\frac{dx}{dt}\right)^2 + 2\frac{dx}{dt} + x(t) = u(t) \]
(iii) \[ \frac{d^2x}{dt^2} + 2\frac{dx}{dt} + x(t) = u(t) \]