List of top Control Systems Questions asked in GATE IN

In a unity-gain feedback control system, the plant \[ P(s) = \frac{0.001}{s(2s + 1)(0.01s + 1)} \] is controlled by a lag compensator \[ C(s) = \frac{s + 10}{s + 0.1} \] The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain at \( \omega = 3 \, \text{rad/s} \) is _________ (in integer).

The signal flow graph of a system is shown. The expression for \( Y(s)/X(s) \) is _________

The Nyquist plot of a stable open-loop system \( G(j\omega) \) is plotted in the frequency range \( 0 \leq \omega>\infty \) as shown. It is found to intersect a unit circle with center at the origin at the point \( P = -0.77 - 0.64j \). The points \( Q \) and \( R \) lie on \( G(j\omega) \) and assume values \( Q = 14.40 + 0.00j \) and \( R = -0.21 + 0.00j \). The phase margin (PM) and the gain margin (GM) of the system are _________

A proportional-integral-derivative (PID) controller is employed to stably control a plant with transfer function \[ P(s) = \frac{1}{(s + 1)(s + 2)}. \] Now, the proportional gain is increased by a factor of 2, the integral gain is increased by a factor of 3, and the derivative gain is left unchanged. Given that the closed-loop system continues to remain stable with the new gains, the steady-state error in tracking a ramp reference signal_________

The transfer function of a system is: \[ \frac{(s + 1)(s + 3)}{(s + 5)(s + 7)(s + 9)}. \] In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________.

A unity-gain negative-feedback control system has a loop-gain \( L(s) \) given by \[ L(s) = \frac{6}{s(s-5)} \] The closed-loop system is _________

Taking \( N \) as positive for clockwise encirclement, otherwise negative, the number of encirclements \( N \) of \( (-1, 0) \) in the Nyquist plot of \( G(s) = \frac{3}{s-1} \) is \(\underline{\hspace{2cm}}\).

Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. \( G(s) = \dfrac{1}{(s+1)(s+3)} \text{ and } C(s) = \dfrac{K(s+3-j)(s+3+j)}{s} \) with \( K \) being scalar. The closed loop is

A sinusoid \( (\sqrt{2} \sin t) \mu(t) \), where \( \mu(t) \) is the step input, is applied to a system with transfer-function \( G(s) = \frac{1}{s+1} \). The amplitude of the steady-state output is \(\underline{\hspace{2cm}}\).

Consider a system with transfer-function \( G(s) = \frac{2}{s+1} \). A unit step function \( \mu(t) \) is applied to the system, which results in an output \( y(t) \). If \( e(t) = y(t) - \mu(t) \), then \( \lim_{t \to \infty} e(t) \) is \(\underline{\hspace{2cm}}\).

The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are

For u(t) input find out Steady state error in term of k