List of top Control Systems Questions on Transfer function asked in GATE EE

The open loop transfer function of a unity gain negative feedback system is given as \[ G(s) = \frac{1}{s(s+1)}. \] The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point \( (-1 + j0) \) by the Nyquist plot of \( G(s) \), corresponding to the Nyquist contour, is denoted as \( N \). Then \( N \) equals to

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 transfer function of a real system, \( H(s) \), is given as:
\[ H(s) = \frac{As + B}{s^2 + Cs + D} \] where \( A \), \( B \), \( C \), and \( D \) are positive constants. This system cannot operate as: