GATE ECE
Control Systems
Stability
Previous Years Questions

## Marks 1

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(...
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identi...
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...
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...
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 ... The forward path transfer function of a unity negative feedback system is given by $$G\left(s\right)\;=\;\frac k{\left(s\;+\;2\right)\left(s\;-\;1\r... Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? A polynomial$$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$with all coefficients positive has An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier A system described by the transfer function$$$H\left(s\right)=\frac1{s^3+\alpha s^2+ks+3}$$is stable. The constraints on$$\alpha$$and k are, The number of roots of$$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$in the left half of the s-plane are The open loop transfer function of a unity feedback open-loop system is$$\frac{2s^2+6s+5}{\left(s+1\right)^2\left(s+2\right)}$$. The characteristic e... ## Marks 2 A unity feedback control system is characterized by the open-loop transfer function$$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$... Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane? ... The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which t... The transfer function of a linear time invariant system is given by$$H\left(s\right)\;=\;2s^4\;-\;5s^3\;+\;5s\;-\;2$$. The number of zeros in the rig... The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 +3s3 + 6s2 - 4s - 8 = 0.The number of roots that lie strictly in the left hal... A plant transfer function is given as$$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\right)$$. When the plant operat... Consider a transfer function$$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$with 'p' a positive real paramete... The feedback system shown below oscillates at 2 rad/s when ... The number of open right half plane poles of$$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$A certain system has transfer function$$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where$$\alpha$$is a parameter. Consider the standard negativ... The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are ... For the polynomial P(s) = s5 + s4 + 2s3 + 2s2 + 3s + 15 ,the number of roots which lie in the right half of the s-plane is ... The open-loop transfer function of a unity feedback system is$$$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\right)}$$the range of 'k' fo... The system shown in Figure remains stable when ... The characteristic polynomial of a system is q(s) = 2s5 + s4 + 4s3 + 2s2 + 2s + 1. The system is The feedback control system in Figure is stable ... If G(s) is a stable transfer function, then$$F\left(s\right)=\frac1{G\left(s\right)}$$is always a stable transfer function. If$$s^3+\;3s^2\;+\;4s\;+A\;=\;0$$,then all the roots of this equation are in the left half plane provided that An electromechanical closed-loop control system has the following characteristic equation$$s^3+6Ks^2+\left(K+2\right)s+8\;=\;0$$, where K is the forw... In order to stabilize the system shown in fig. Ti should satisfy: ... Consider a characteristic equation given by s4 + 3s3 + 5s2 + 6s + K + 10 = 0. The condition for stability is ## Marks 5 Consider the feedback control system shown in figure. (a) Find the transfer function of the system and its characteristic equation. (b) Use the Routh... The loop transfer function of a feedback control system is given by$$$G\left(s\right)H\left(s\right)=\frac{K\left(s+1\right)}{s\left(1+Ts\right)\left... 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....
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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