## 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...