GATE ECE

Stability

Control Systems

(Past Years Questions)

Marks 1

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Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Rou...
GATE ECE 2016 Set 1
A unity negative feedback system has the open-loop transfer function $$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right...
GATE ECE 2015 Set 1
The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left...
GATE ECE 2014 Set 1
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
GATE ECE 2013
A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has
GATE ECE 2013
An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The ampl...
GATE ECE 2000
A system described by the transfer function $$$H\left(s\right)=\frac1{s^3+\alpha s^2+ks+3}$$$ is stable. The constraints...
GATE ECE 2000
The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are
GATE ECE 1998
The open loop transfer function of a unity feedback open-loop system is $$\frac{2s^2+6s+5}{\left(s+1\right)^2\left(s+2\r...
GATE ECE 1998

Marks 2

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A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left...
GATE ECE 2017 Set 2
Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the...
GATE ECE 2017 Set 1
The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given ...
GATE ECE 2016 Set 3
The transfer function of a linear time invariant system is given by $$H\left(s\right)\;=\;2s^4\;-\;5s^3\;+\;5s\;-\;2$$. ...
GATE ECE 2016 Set 1
The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 +3s3 + 6s2 - 4s - 8 = 0.The number of roots tha...
GATE ECE 2015 Set 3
A plant transfer function is given as $$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\rig...
GATE ECE 2015 Set 1
Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ wit...
GATE ECE 2014 Set 4
The feedback system shown below oscillates at 2 rad/s when ...
GATE ECE 2012
The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$
GATE ECE 2008
A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter....
GATE ECE 2008
The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec r...
GATE ECE 2006
For the polynomial P(s) = s5 + s4 + 2s3 + 2s2 + 3s + 15 ,the number of roots which lie in the right half of the s-plane ...
GATE ECE 2004
The open-loop transfer function of a unity feedback system is $$$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\...
GATE ECE 2003
The system shown in Figure remains stable when ...
GATE ECE 2002
The characteristic polynomial of a system is q(s) = 2s5 + s4 + 4s3 + 2s2 + 2s + 1. The system is...
GATE ECE 2002
The feedback control system in Figure is stable ...
GATE ECE 2001
If G(s) is a stable transfer function, then $$F\left(s\right)=\frac1{G\left(s\right)}$$ is always a stable transfer func...
GATE ECE 1994
If $$s^3+\;3s^2\;+\;4s\;+A\;=\;0$$ ,then all the roots of this equation are in the left half plane provided that
GATE ECE 1993
An electromechanical closed-loop control system has the following characteristic equation $$s^3+6Ks^2+\left(K+2\right)s+...
GATE ECE 1990
In order to stabilize the system shown in fig. Ti should satisfy: ...
GATE ECE 1989
Consider a characteristic equation given by s4 + 3s3 + 5s2 + 6s + K + 10 = 0. The condition for stability is...
GATE ECE 1988

Marks 5

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Consider the feedback control system shown in figure. (a) Find the transfer function of the system and its characterist...
GATE ECE 2001
The loop transfer function of a feedback control system is given by $$$G\left(s\right)H\left(s\right)=\frac{K\left(s+1\r...
GATE ECE 1999
The characteristic equation of a feedback control system is $$$s^4+20s^3+15s^2+2s+K\;=\;0$$$ (i) Determine the range of ...
GATE ECE 1998
A system having an open loop transfer function $$G\left(s\right)=\frac{K\left(s+3\right)}{s\left(s^2+2s+2\right)}$$ is u...
GATE ECE 1996

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