Stability · Control Systems · GATE ECE

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...

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(...

Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane? ...

A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$...

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 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...

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...

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...

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 characteristic polynomial of a system is q(s) = 2s5 + s4 + 4s3 + 2s2 + 2s + 1. The system is

The system shown in Figure remains stable when ...

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

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...