Transfer Function

The asymptotic Bode magnitude plot of a system is shown. Which one of the following options best represents the transfer function of the system?

A system is characterized by the following state equation and output equation (U: input, X: state vector, y: output) $\dot{x} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}x + \be...

The open-loop transfer function of the system shown in the figure, is $G(s) = \frac{Ks(s + 2)}{(s + 5)(s + 7)}$ For $K \ge 0$, which of the following real axis point(s) is/are on t...

For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is

For the block diagram shown in the figure, the transfer function $\frac{Y(s)}{R(s)}$ is

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 t...

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

Consider the state-space description of an LTI system with matrices A = $\begin{bmatrix} 0 & 1 \ -1 & -2 \end{bmatrix}$, B = $\begin{bmatrix} 0 \ 1 \end{bmatrix}$, C = $\begin{bmat...

Consider the state-space description of an LTI system with matrices $$A = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 2} \cr } } \right],B = \left[ {\matrix{ 0 \cr 1 \cr } } \right],C...

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

A system transfer function is H(s) = $\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}$. If $a_1 = b_1 = 0$, and all other coefficients are positive, the transfer function represents a

The open loop transfer function of a unity feedback system is given by $G(s) = \frac{\pi e^{-0.25s}}{s}$. In G(s) plane, the Nyquist plot of G(s) passes through the negative real a...

The asymptotic Bode magnitude plot of a minimum phase transfer function G(s) is shown below. Consider the following two statements. Statement I: Transfer function G(s) has three po...

The transfer function of a system is given by, $V_o(s) / V_i(s) = (1-s) / (1+s)$. Let the output of the system be $v_o(t) = V_m sin(\omega t + \phi)$ for the input, $v_i(t) = V_m s...

When a unit ramp input is applied to the unity feedback system having closed loop transfer function $\frac{C(s)}{R(s)} = \frac{Ks+b}{s^2+as+b}$, $(a>0, b>0, K>0)$, the steady state...

Match the transfer functions of the second-order systems with the nature of the systems given below. Transfer functions P: 15 / (s² + 5s + 15) Q: 25 / (s² + 10s + 25) R: 35 / (s² +...

Consider a unity feedback system with forward transfer function given by G(s) = 1 / ((s+1)(s+2)) The steady-state error in the output of the system for a unit-step input is _______...

In the system whose signal flow graph is shown in the figure, $U_1(s)$ and $U_2(s)$ are inputs. The transfer function $\frac{Y(s)}{U_1(s)}$ is

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: $\begin{bmatrix} \dot{x_1}(t) \\ \dot{x_2}(t) \end{bmatrix} = \begin{bmatrix} 1 & 2 \\...

The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s) = \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ________ (...

For a system having transfer function G(s) = $\frac{-s+1}{s+1}$, a unit step input is applied at time t = 0. The value of the response of the system at t = 1.5 sec (rounded off to...

Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H(1) = $\frac{5}{4}$. The poles of...

The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is: $$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits...

The transfer function $$C(s)$$ of a compensator is given below: $$C\left( s \right) = {{\left( {1 + {s \over {0.1}}} \right)\left( {1 + {s \over {100}}} \right)} \over {\left( {1 +...

The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$ Let the output of the system be $${v_0}\left( t...

The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$ in $$rad/s$$ is

For the system governed by the set of equations: $$$\eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = - 2{x_1} + u \cr & \,\,\,\,\,\,y = 3{x_1} \cr} $$$ the transfer fun...

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $$\left( {2 - j3} \right).$$ List all the poles and zeros.

The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given by which one of the following waveforms?

An open loop control system results in a response of $${e^{ - 2t}}\left( {\sin 5t + \cos 5t} \right)$$ for a unit impulse input. The DC gain of the control system is __________.

Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system is cos(3t) and the steady state output is $$A\sin\left(3t+\al...

Consider the system described by the following state space equations $$$\eqalign{ & \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 1...

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$ $${G_c}\left( s \right)$$ is a lead compensator if

A system with transfer function $$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right...

An open loop system represented by the transfer function $$G\left( s \right) = {{\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$ is

A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t \right) + 2u\left( t \right)$$...

The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input, $$Y$$ is output and $$$A = \lef...

The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is

The transfer function of two compensators are given below: $${C_1} = {{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}},\,{C_2} = {{s + 10} \over {10\left( {s + 1} \right...

For a system with the transfer function $$H\left( s \right) = {{3\left( {s - 2} \right)} \over {{s^3} + 4{s^2} - 2s + 1}},\,\,$$ the matrix $$A$$ in the state space form $$\mathop...

A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s + 4} \right)}}.$$ The system o...

For a tachometer if $$\theta \left( t \right)$$ is the rotor displacement is radians, $$e\left( t \right)$$ is the output voltage and $${K_t}$$ is the tachometer constant in V/rad/...

A lead compensator used for a closed loop controller has the following transfer function $${\textstyle{{K\left( {1 + {s \over a}} \right)} \over {\left( {1 + {s \over b}} \right)}}...

For the system $$\mathop X\limits^ \bullet = \left[ {\matrix{ 2 & 0 \cr 0 & 4 \cr } } \right]X + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u;\,\,\,y = \left[ {\matrix{ 4 & 0 \cr } }...

The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is

A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage transfer function of the filter i...

Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be $$y\left( t \right) = \int\limits_0^t {\left( {2 + t - \tau } \right){e^{ - 3\left( {t - \tau } \rig...

A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response $$y\left( t \right) = t{e^{ - t}},\,\,t > 0.$$ The transfer function of the...

The output of a linear time invariant control system is $$c(t)$$ for a certain input $$r(t).$$ If $$r(t)$$ is modified by passing it through a block whose transfer function is $${e...

Determine the transfer function of the system having the following state variable representation: $$\eqalign{ & X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 40} & { - 44} &...

The impulse response of an initially relaxed linear system is $${e^{ - 2t}}u\left( t \right).$$ To produce a response of $${te^{ - 2t}}u\left( t \right),$$ the input must be equal...

A system is described by the state equation $$\mathop X\limits^ \bullet = AX + BU$$ , The output is given by $$Y=CX$$ Where $$A = \left( {\matrix{ { - 4} & { - 1} \cr 3 & { - 1} \c...

The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)} \over {\left( {s + 2} \right)...

A differentiator has transfer function whose

The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ is given by

Signal flow graph is used to obtain the