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A linear, time - invarient, casual continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$.A unit step $u\left(t\right)$ is applied at the input of the system. At steady state, the output has constant value of $1$. The impulse response of this system is

A signal flow graph of a system is given below



The set of equations that correspond to this signal flow graph is

A unity negative feedback system has the open-loop transfer function $G\left(s\right)=\frac{K}{s(s+1)(s+3)}$

The value of the gain $K(>0)$ at which the root locus crosses the imaginary axis is

1. 12

The transfer function of a Zero-Order-Hold system with sampling interval T is

For the following feedback system $G\left(s\right)=\frac{1}{(s+1)(s+2)}.$ The 2%-setting time of the step response is required to be less than $2seconds$.



Which one of the following compensators

$C\left(s\right)$ acheives this?

An unity feedback system is given as,

$G\left(s\right)=\frac{K(1-s)}{s(s+3)}$

Indicate the correct root locus diagram

Group I gives two possible choices for the impedance $Z$ in the diagram. The circuit elemets in $Z$ satisfy the condition $R_2{C}_2>R_1{C}_1$. The tranfser function $\frac{V_0}{V_i}$ represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II.



Group -I



Group-II

1.PID controller

2. Lead compensator

3. Lag compensator

The open loop transfer function of a unity gain feedback system is given by:

$G\left(s\right)=\frac{k(s+3)}{(s+1)(s+2)}$

The range of positive values of k for which the closed loop system will remain stable is

The asymptotic magnitude Bode plot of an open loop system G(s) with K > 0 and all poles and zeros on the left hand side of the s-plane is shown in the figure. It is completetly sysmmetric about ${\omega }_c$. The minimum absolute angle contribution by G(s) is given by

The transfer function of a compensator is given as $G_c\left(s\right)=\frac{s+1}{s+2}$

The phase of the above lead compensator is maximum at

A unity feedback control system has an open-loop transfer function $G\left(s\right)=\frac{K}{s(s^2+7s+12)}.$ The gain $K$ for which $s=-1+j1$ will lie on the root locus of the system is

The number of times the Nyquist plot of

$G\left(s\right)=\frac{s-1}{s+1}$

will encircle the origin clockwise is

1. 1

A second -order system has the transfer function $\frac{C\left(s\right)}{R\left(s\right)}=\frac{4}{s^2+4s+4}$. With $r\left(t\right)$ as the unit-step function, the response $c\left(t\right)$ of the system is represented by

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function

$\frac{Y\left(s\right)}{X_2\left(s\right)}{|}_{x_1\left(s\right)=0}$?

The gain margin and the phase margin of a feedback system with $G\left(s\right)H\left(s\right)=\frac{s}{(s+100{)}^3}$ are

For the signal flow graph show in figure, the transfer function is C(s)/R(s)=

Group I lists a set of your transfer functions

Group II gives a list of possible step responses $y\left(t\right)$. Match the step responses with the corresponding transfer functions.



Group I

$P=\frac{25}{s^2+25}$ ; $Q=\frac{36}{s^2+20s+36}$

$R=\frac{36}{s^2+12s+36}$ ; $S=\frac{36}{s^2+7s+49}$



Group II

Which of the following figure(s) represent valid root loci in the s-plane for positive K? Assume that the system has transfer function with real coefficient.

Given

$A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$,

the state transition matrix $e^{At}$ is given by

The transfer function of the open loop system G(s) which is represented by the singal flow graph shown in the figure below is

Consider the system shown in the figure below:



$\text{The transfer function}\frac{C}{R}\text{of this system is}$

Consider the signal flow graph shown in the figure.

The gain $x_5/x_1$ is

The state space equation of a system is described by $\dot{x}=Ax+Bu$, $y=Cx$ where $x$ is state vector, $u$ is input, $y$ is output and $A=\left[\begin{array}{cc}0& 1\\ 0& -2\end{array}\right]$, $B=\left[\begin{array}{c}0\\ 1\end{array}\right],C=\left[10\right]$



The transfer function G(s) if this system will be

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

A lead compenstor used for a closed loop controller has the following transfer function

$\frac{K(1+\frac{s}{a})}{(1+\frac{s}{b})}$

For such a lead compensator

The OLTF of a feedback control system is $G\left(s\right)H\left(s\right)=\frac{-1}{2s(1-20s)}$, the Nyquist plot of the system is

Consider a stable system with transfer function

$G\left(s\right)=\frac{s^p+b_1{s}^{p-1}+...+b_p}{s^q+a_1{s}^{q-1}+...+a_q}$

where $b_1,.....,b_{p}and{a}_1,....a_q$ are real valued constant. the slope of the Bode log magnitude curve of $G\left(s\right)$ converges to $-60dB/decadeas\omega \to \infty$. A possible pair of values for $pandq$ is

Which of the options is an equivalent representation of the signal flow graph shown here?

A double integrator plant, $G\left(s\right)=\frac{K}{s^2},H\left(s\right)=1$ is to be compensated to acheive the damping ratio $\zeta =0.5$ and an undamped natural frequency, ${\omega }_n=5rad/sec$. Which one of the following compensator $G_c\left(s\right)$ will be suitable?

The transfer function of a position servo system is given as

$G\left(s\right)=\frac{1}{s(s+1)}.$



A first order compensator is designed in a unity feedback configuration so that poles of the compensated system are placed at $-1\pm j1$ and -4. The transfer function of the compensated system is

Valid state transition matrix $\varphi \left(t\right)$ is,

As shown in the figure, a negative feddback system has an amplifier of gain $100$ with $\pm 10\%$ tolerance in the forward path, and an attenuator of value $9/100$ in the feedback path. The overall system gain is approximately:

The state variable description of an LTI system given by

$\left[\begin{array}{c}\dot{x_1}\\ \dot{x_2}\\ \dot{x_3}\end{array}\right]=\left[\begin{array}{ccc}0& a_1& 0\\ 0& 0& a_2\\ a_3& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]u$



$y=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$



Where y is the ouput and u is the input. The system controllable for

The asymptotic Bode plot of the transfer function

$K/[1+(s/a\left)\right]$ is given in figure. The error in phase angle and dB gain at a frequency of $\omega =0.5$ are respectively.

Given figure shows a closed loop unity feedback system. The controller block has transfer function denoted by $G_c\left(s\right)$. The controller is cacaded to plant, which is denoted by $G_p\left(s\right)$







The loop transfer function $G_c\left(s\right)$ is

A system has poles at $0.01Hz,1Hz$ and $80Hz$ zeros at $5Hz,100Hz$ and $200Hz$. The approximate phase of the system response at$20Hz$ is

The following equation defines a separately excited dc motor in the form of a differential equation

$\frac{d^2\omega }{d{t}^2}+\frac{B}{J}\frac{d\omega }{dt}+\frac{K^2}{LJ}\omega =\frac{K}{LJ}{V}_a$

The above equation may be organized in the statespace form as follows

$\left[\begin{array}{c}\frac{d^2\omega }{d{t}^2}\\ \frac{d\omega }{dt}\end{array}\right]=P\left[\begin{array}{c}\frac{d\omega }{dt}\\ \omega \end{array}\right]+Q{V}_a$

Where the P matrix is given by

If the roots of a second order characteristic equation are given $s_{1,2}=-3\pm j2$, then the values of damping ratio $\xi$ and the damped natural frequency ${\omega }_d$ are respectively

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function

$G\left(s\right)=\frac{1}{s^2+3s+2}$

where $K>0$ . The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ is equal to (rounded off to two decimal places)

1. 6

A unity feedback control system is characterized by the open-loop transfer function

$G\left(s\right)=\frac{10K(s+2)}{s^3+3s^2+10}.$

The Nyquist path and the corresponding Nyquist plot of $G\left(s\right)$ are shown in the figures below.





If $0<K<1$, then the number of poles of the closed-loop transfer function that lie in the right -half of the s-plane is

In the system shown below, $x\left(t\right)=\left(\sin t\right)u\left(t\right)$. In steady-state, the response $y\left(t\right)$ will be

The unit impulse response of a unit feedback control system is given by: $c\left(t\right)=-t{e}^{-t}+2e^{-t},(t\ge 0)$ the open loop transfer funciton is equal to

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

If the transfer function of a control system is given below:

$\frac{Y\left(s\right)}{U\left(s\right)}=\frac{1}{s^3+4s^2+5s+3}$



The matrix [A] and [B] in state variable representation of the system will be

The unit impulse response of a linear time invarient system is the unit step function $u\left(t\right)$. For $t>0$, the response of the system to an excitation $e^{-at}u\left(t\right),a>0$ will be

In the system shown in figure, the input $x\left(t\right)=sint$. In the steady-state, the response $y\left(t\right)$ will be

The root locus of the system

$G\left(s\right)H\left(s\right)=\frac{K}{s(s+2)(s+3)}$

has the break-away point located at

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



The eigen-value and eigen-vector pairs $({\lambda }_i,v_i)$ for the system are

A second-order real system has the following properties:



(a) The damping ratio $\xi =0.5$ and undamped natural frequency ${\omega }_n=10rad/s.$



(b) The steady state value of the output to a unit step input is 1.02.



The transfer function of the system is