List of top Control Systems Questions

Consider a unity-gain negative feedback system consisting of the plant $G(s)$ and a proportional-integral (PI) controller. \[ G(s) = \frac{1}{s-1} \] PI controller: $C(s) = K_p + \frac{K_i}{s} = \frac{K_p s + K_i}{s}$. Given $K_p = 3, K_i = 1$. For a unit step reference input, the final values of the controller output and the plant output are asked.

In the Nyquist plot of the open-loop transfer function \[ G(s)H(s) = \frac{3s+5}{s-1} \] corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in the $s$-plane is mapped into a point at: \begin{center} \includegraphics[width=0.5\textwidth]{05.jpeg} \end{center}

The open-loop DC gain of a unity negative feedback system with closed-loop transfer function $\frac{S+3}{ 2s^2+5s +8} $ is

The overall transmittance for the signal flow graph shown in figure is

The first two rows in the Routh table for characteristics equation of a certain closed loop control system are given as:-

S³	1	(2K+3)
S²	K	4

The range of K for which the system is stable is-

For the closed-loop control system shown, with $r(t)=0$, the steady-state error $e(\infty)$ due to a unit step disturbance $d(t)$ is ____________ (rounded off to two decimal places).

Two linear time-invariant systems with transfer functions \[ G_1(s) = \frac{10}{s^2 + s + 1}, \qquad G_2(s) = \frac{10}{s^2 + s\sqrt{10} + 10} \] have unit step responses $y_1(t)$ and $y_2(t)$, respectively. Which of the following statements is/are true?

Consider an even polynomial $p(s)$ given by \[ p(s) = s^4 + 5s^2 + 4 + K, \] where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is ________________.

Consider a closed-loop control system with unity negative feedback and $K G(s)$ in the forward path, where the gain $K = 2$. The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume $G(s)$ has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ____________.

The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied from 0 to $\infty$. Select the transfer function $G(s)$ that results in the shown root-locus.

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 damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $ \zeta $ and $ \omega_n $, respectively. The values of $ \zeta $ and $ \omega_n $ are

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:

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is -180°. This system has

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

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 _________

In the given figure, plant $G_p(s)=\dfrac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)}$ and compensator $G_c(s)=K \left\{ \dfrac{1+T_1 s}{1+T_2 s} \right\}$. The disturbance input is $D(s)$. The disturbance is a unit step, and the steady-state error must not exceed 0.1 unit. Find the minimum value of $K$. (Round off to 2 decimal places.)

For the closed-loop system with $G_p(s) = \frac{14.4}{s(1 + 0.1s)}$ and $G_c(s) = 1$, the unit-step response shows damped oscillations. The damped natural frequency is $\underline{\hspace{2cm}}$ rad/s. (Round off to 2 decimal places.)

For the given Bode magnitude plot of the transfer function, the value of R is $\underline{\hspace{2cm}}$ Ω. (Round to 2 decimals).

For the feedback system shown, the transfer function $\dfrac{E(s)}{R(s)}$ is: