Time Response Analysis · Control Systems · GATE ECE

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Marks 1

GATE ECE 2022
Two linear time-invariant systems with transfer functions $${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10...
GATE ECE 2022
The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r...
GATE ECE 2017 Set 1
The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\ri...
GATE ECE 2016 Set 2
The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit step input u(t) is y(t). The v...
GATE ECE 2016 Set 3
For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;...
GATE ECE 2015 Set 2
A unity negative feedback system has an open–loop transfer function $$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The gain K for the system to have a...
GATE ECE 2014 Set 4
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is ...
GATE ECE 2014 Set 3
The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer fu...
GATE ECE 2014 Set 2
The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency i...
GATE ECE 2011
The differential equation $$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\mathrm x\left(\mathrm t\right)...
GATE ECE 2008
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents t...
GATE ECE 2007
If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final value is:
GATE ECE 2002
Consider a system with the transfer function $$$G\left(s\right)=\frac{s+6}{Ks^2+s+6}$$$ Its damping ratio will be 0.5 when the value of K is
GATE ECE 2001
If the characteristic equation of a closed-loop system is s2 + 2s + 2 =0, then the system is
GATE ECE 1999
For a second-order system with the closed-loop transfer function $$$T\left(s\right)=\frac9{s^2+4s+9}$$$ the settling time for 2% band in seconds is
GATE ECE 1998
Consider a unity feedback control system with open-loop transfer function $$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ . The steady state er...
GATE ECE 1998
If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\l...
GATE ECE 1998
Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+...
GATE ECE 1995
For a second order system, damping ratio $$\left(\xi\right)$$ , is 0 < $$\xi$$ < 1 ,then the roots of the characteristic polynomial are
GATE ECE 1995
The final value theorem is used to find the
GATE ECE 1995
If $$L\left(f\left(t\right)\right)=\frac{2\left(s+1\right)}{s^2+2s+5}$$ then f(0+) and f($$\infty$$) are given by [Note: 'L' stands for 'Laplace Trans...
GATE ECE 1995
The step error coefficient of a system G(s)=$$\frac1{\left(s+6\right)\left(s+1\right)}$$ with unity feedback is
GATE ECE 1994
The poles of a continuous time oscillator are ___________.

Marks 2

GATE ECE 2016 Set 2
In the feedback system shown below $$$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$ The step response of the closed-loop system should have minimum settl...
GATE ECE 2016 Set 1
The open-loop transfer function of a unity-feedback control system is $$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For the peak overshoot of the close...
GATE ECE 2015 Set 2
The output of a standard second–order system for a unit step input is given as $$$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}\cos\left(\sqrt3t\;-\;\frac{\m...
GATE ECE 2015 Set 1
The damping ratio of a series RLC circuit can be expressed as
GATE ECE 2014 Set 3
The steady state error of the system shown in the figure for a unit step input is _______. ...
GATE ECE 2014 Set 1
For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of the step response is required t...
GATE ECE 2013
The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when connected in fee...
GATE ECE 2009
The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these pro...
GATE ECE 2008
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=...
GATE ECE 2008
Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding...
GATE ECE 2007
The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the s...
GATE ECE 2007
The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order approximation of T (s) using d...
GATE ECE 2006
The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state value of the output for unit st...
GATE ECE 2006
The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm ...
GATE ECE 2005
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 respectiv...
GATE ECE 2005
In the derivation of expression for peak percent overshoot,$$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\times100\%$$$ .Which one of the ...
GATE ECE 2004
A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$ is excited with 10u(t). The time at which the output reaches 99% ...
GATE ECE 2004
A system described by the following differential equation $$$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is initially at rest. For input x(...
GATE ECE 2003
A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) as the unit-step function, the...
GATE ECE 2002
The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For a unit step input to the syste...
GATE ECE 1999
If the closed-loop transfer function T(s) of a unity negative feedback system is given by $$$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1s^{n-1}+.....+...
GATE ECE 1998
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e-...
GATE ECE 1994
The response of an LCR circuit to a step input is (a) Over damped (b) Critically damped (c) Oscillatory If the transfer function has (1) poles on the...
GATE ECE 1994
Match the following with List-1 with List-2 List-1 (a) Very low response at very high frequencies. (b) Overshoot (c) Synchro-control transformer outp...
GATE ECE 1991
A unity feedback control system has the open loop transfer function $$G\left(s\right)\;=\;\frac{4\left(1\;+\;2s\right)}{s^2\left(s\;+\;2\right)}$$ .I...
GATE ECE 1991
A second order system has a transfer function given by $$\mathrm G\left(\mathrm s\right)\;=\;\frac{25}{\mathrm s^2\;+\;8\mathrm s\;+\;25}$$ .If the sy...
GATE ECE 1990
The steady state error of a stable 'type 0' unity feedback system for a unit step function is
GATE ECE 1988
A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)

Marks 5

GATE ECE 2000
The block diagram of a feedback system is shown in Figure. (a) Find the closed loop transfer function. (b) Find the minimum value of G for which the...
GATE ECE 1997
Following fig. shows the block diagram representation of control system. The system in block A has an impulse response h(t ) = e−t u(t ). The system i...

Marks 8

GATE ECE 2000
For the linear, time-invariant system whose block diagram is shown in Fig. with input x(t) and output y(t), (a) Find the transfer function. (b) For ...
GATE ECE 1992
Block diagram model of a position control system is shown in figure. (a) In absence of derivative feedback (Kt=0) , determine damping ratio of the sy...

Marks 10

GATE ECE 1998
Consider the system shown in Fig. Determine the value of 'a' such that the damping ratio is 0.5. Also obtain the values of the rise time 'tr' and ma...
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