GATE ECE

Time Response Analysis

Control Systems

(Past Years Questions)

Marks 1

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The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\ma...
GATE ECE 2017 Set 1
For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\r...
GATE ECE 2016 Set 3
The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit ...
GATE ECE 2016 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 g...
GATE ECE 2015 Set 2
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is ...
GATE ECE 2014 Set 4
The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applie...
GATE ECE 2014 Set 3
The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, ...
GATE ECE 2014 Set 2
The differential equation $$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\...
GATE ECE 2011
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the f...
GATE ECE 2008
If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final v...
GATE ECE 2007
Consider a system with the transfer function $$$G\left(s\right)=\frac{s+6}{Ks^2+s+6}$$$ Its damping ratio will be 0.5 wh...
GATE ECE 2002
If the characteristic equation of a closed-loop system is s2 + 2s + 2 =0, then the system is
GATE ECE 2001
For a second-order system with the closed-loop transfer function $$$T\left(s\right)=\frac9{s^2+4s+9}$$$ the settling ti...
GATE ECE 1999
If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\lef...
GATE ECE 1998
Consider a unity feedback control system with open-loop transfer function $$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\r...
GATE ECE 1998
Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\rig...
GATE ECE 1998
For a second order system, damping ratio $$\left(\xi\right)$$ , is 0 ...
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:...
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 1995
The poles of a continuous time oscillator are ___________.
GATE ECE 1994

Marks 2

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In the feedback system shown below $$$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$ The step response of the closed-loop sy...
GATE ECE 2016 Set 2
The open-loop transfer function of a unity-feedback control system is $$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For t...
GATE ECE 2016 Set 1
The output of a standard second–order system for a unit step input is given as $$$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}...
GATE ECE 2015 Set 2
The damping ratio of a series RLC circuit can be expressed as
GATE ECE 2015 Set 1
The steady state error of the system shown in the figure for a unit step input is _______. ...
GATE ECE 2014 Set 3
For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of t...
GATE ECE 2014 Set 1
The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1...
GATE ECE 2013
The unit step response of an under-damped second order system has steady state value of -2. Which one of the following t...
GATE ECE 2009
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and 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 re...
GATE ECE 2008
The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}...
GATE ECE 2007
The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order ...
GATE ECE 2007
The unit impulse response of a system is: $$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$$ For this system, the steady-state v...
GATE ECE 2006
The unit-step response of a system starting from rest is given by $$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mat...
GATE ECE 2006
A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency ga...
GATE ECE 2005
In the derivation of expression for peak percent overshoot,$$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\ti...
GATE ECE 2005
A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$ is excited with 10u(t). The time at...
GATE ECE 2004
A system described by the following differential equation $$$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is i...
GATE ECE 2004
A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) ...
GATE ECE 2003
The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For ...
GATE ECE 2002
If the closed-loop transfer function T(s) of a unity negative feedback system is given by $$$T\left(s\right)=\frac{a_{n-...
GATE ECE 1999
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the...
GATE ECE 1998
The response of an LCR circuit to a step input is (a) Over damped (b) Critically damped (c) Oscillatory If the transfer...
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) Sy...
GATE ECE 1994
A second order system has a transfer function given by $$\mathrm G\left(\mathrm s\right)\;=\;\frac{25}{\mathrm s^2\;+\;8...
GATE ECE 1991
A unity feedback control system has the open loop transfer function $$G\left(s\right)\;=\;\frac{4\left(1\;+\;2s\right)}...
GATE ECE 1991
The steady state error of a stable 'type 0' unity feedback system for a unit step function is
GATE ECE 1990
A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)
GATE ECE 1988

Marks 5

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The block diagram of a feedback system is shown in Figure. (a) Find the closed loop transfer function. (b) Find the mi...
GATE ECE 2000
Following fig. shows the block diagram representation of control system. The system in block A has an impulse response h...
GATE ECE 1997

Marks 8

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

Marks 10

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Consider the system shown in Fig. Determine the value of 'a' such that the damping ratio is 0.5. Also obtain the value...
GATE ECE 1998

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