Stability · Control Systems · GATE ECE

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Marks 1

GATE ECE 2018
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identi...
GATE ECE 2018
Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The nu...
GATE ECE 2016 Set 1
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system chara...
GATE ECE 2015 Set 1
A unity negative feedback system has the open-loop transfer function $$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)\left(s\;+\;3\right)}$$$ The ...
GATE ECE 2014 Set 1
The forward path transfer function of a unity negative feedback system is given by $$$G\left(s\right)\;=\;\frac k{\left(s\;+\;2\right)\left(s\;-\;1\r...
GATE ECE 2013
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
GATE ECE 2013
A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has
GATE ECE 2000
An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier
GATE ECE 2000
A system described by the transfer function $$$H\left(s\right)=\frac1{s^3+\alpha s^2+ks+3}$$$ is stable. The constraints on $$\alpha$$ and k are,
GATE ECE 1998
The number of roots of $$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\right)}$$. The characteristic e...

Marks 2

GATE ECE 2022
Consider an even polynomial p(s) given by $$p(s) = {s^4} + 5{s^2} + 4 + K$$ where K is an unknown real parameter. The complete range of K for which p(...
GATE ECE 2017 Set 1
Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane? ...
GATE ECE 2017 Set 2
A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$...
GATE ECE 2016 Set 3
The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which t...
GATE ECE 2016 Set 1
The transfer function of a linear time invariant system is given by $$H\left(s\right)\;=\;2s^4\;-\;5s^3\;+\;5s\;-\;2$$. The number of zeros in the rig...
GATE ECE 2015 Set 3
The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 +3s3 + 6s2 - 4s - 8 = 0.The number of roots that lie strictly in the left hal...
GATE ECE 2015 Set 1
A plant transfer function is given as $$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\right)$$$ . When the plant operat...
GATE ECE 2014 Set 4
Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ with 'p' a positive real paramete...
GATE ECE 2012
The feedback system shown below oscillates at 2 rad/s when ...
GATE ECE 2008
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. Consider the standard negativ...
GATE ECE 2006
The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are ...
GATE ECE 2004
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 is ...
GATE ECE 2003
The open-loop transfer function of a unity feedback system is $$$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\right)}$$$ the range of 'k' fo...
GATE ECE 2002
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 2001
The feedback control system in Figure is stable ...
GATE ECE 1994
If G(s) is a stable transfer function, then $$F\left(s\right)=\frac1{G\left(s\right)}$$ is always a stable transfer function.
GATE ECE 1993
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 1990
An electromechanical closed-loop control system has the following characteristic equation $$s^3+6Ks^2+\left(K+2\right)s+8\;=\;0$$, where K is the forw...
GATE ECE 1989
In order to stabilize the system shown in fig. Ti should satisfy: ...
GATE ECE 1988
Consider a characteristic equation given by s4 + 3s3 + 5s2 + 6s + K + 10 = 0. The condition for stability is

Marks 5

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