The magnitude plot of a rational transfer function G (s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot?

Which one of the following polar diagrams corresponds to a lag network?

The pole-zero given below corresponds to a

The feedback system shown below oscillates at 2 rad/s when

Given G(s) H(s) = $\dfrac{K}{s(s+1)(s+3)}$. The point of intersection of the asymptotes of the root loci with the real axis is

Direction: The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

Which of the following statements is true?

The transfer function of a phase-lead compensator is given by G_c = ^{$\dfrac{1+3T_s}{1+T_s}$}, where T > 0. What is the maximum phase shift of the compensator?

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the conditions R₂C₂ > R₁C_1. The transfer functions $\dfrac{V_0}{V_i}$represents a kind of controller.

Match the impedances in Group I with the type of controllers in Group II.

The signal flow graph of a system is shown in figure. The transfer function $\dfrac{C(s)}{R(s)}$ of the system is

Consider the Bode magnitude plot shown in the fig. The transfer function H(s) is

The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G(s) corresponding to this Bode plot is

A control system with a PD controller is shown in the figure. If the velocity error constant K_V = 1000 and the damping ratio $\xi$= 0.5, the values of K_P and K_D are

Consider a linear system whose state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =$ \left[ \begin{array} \ 1 \\ -2 \end{array} \right] $, the system response is x (t) = $ \left( \begin{array} \ e^{-2t} \\ -2 e^{-2t} \end{array} \right) $. If the initial state vector of the system changes, the system response becomes x(t) = $ \left[ \begin{array} \ e^{-t} \\

• e^{-6} \end{array} \right] $.

The system matrix A is

The open loop transfer function of a unity feedback is given by $G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

Based on the above results, the gain and phase margins of the system will be

Consider two transfer functions:

G₁ (s) = ^{$\dfrac{1}{s^2 + as +b}$} and G₂ (s) = ^{$\dfrac{1}{s^2 + as +b}$}

The 3 dB bandwidths of their frequency responses respectively are

A unity negative feedback closed loop system has a plant with the transfer function G(s) = ^{$\dfrac{1}{s^2 + 2s +2}$} and a controller G_c(S) in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is

A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively

Consider a linear system with state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =^{$ \left[ \begin{array} \ 1 \\ -2 \end{array} \right] $}, the system response is x (t) = ^{$ \left( \begin{array} \ e^{-2t} \\ -2 e^{-2t} \end{array} \right) $}. If the initial state vector of the system changes, the system response becomes x(t) = ^{$ \left[ \begin{array} \ e^{-t} \\}

• e^{-6} \end{array} \right] $.

The eigen value and eigen vector pairs (^{$\lambda_i, V_i$}) for the system are

The open loop transfer function of a unity feedback is given by $G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

The gain and phase crossover frequencies in rad/sec are respectively

Directions : The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

The gain and phase margins of G (s) for closed loop stability are