Consider the polynomial

. Let  be defined as follows.

 is the number of roots of  with negative real parts.

 is the number of roots of  that are purely imaginary.

 is the number of roots of  with positive real parts.

Which one of the following options is correct?

In the feedback control system shown in the figure below .

R(s), Y(s) and E(s) are the Laplace transforms of r(t), y(t), and e(t), respectively. If the input r(t) is a unit step function, then ________.

Consider a unity negative feedback control system with forward path gain  as shown.

The impulse response of the closed-loop system decays faster than  if

Consider an even polynomial  given by

where  is an unknown real parameter. The complete range of  for which  has all its roots on the imaginary axis is

The loop transfer function of a negative feedback system is

The value of , for which the system is marginally stable, is________.

Consider a unity feedback system, as in the figure shown, with an integral compensator  and open-loop transfer function 

Where. The positive value of K for which there are exactly two poles of the unity feedback system on the  axis is equal to __________ (rounded off to two decimal places).

Which one of the following options correctly describes the locations of the roots of the equation on the complex plane?

A unity feedback control system is characterized by the open-loop transfer function

. The value of k for which the system oscillates at 2 rad/s is ___________

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 characteristic equation

X: The system is stable ...            

Y: The system is unstable ...

Z: The test breaks down ...          

P: ... when all elements are positive

Q: ... when any one element is zero

R: ... when there is a change in sign of coefficient

The transfer function of a linear time invariant system is given by

The number of zeros in the right half of the s-plane is_______________

The first two rows in the Routh table for the characteristics equation of a certain closed-loop control system are given as

The range of K for which the system is stable is

A plant transfer function is given as

. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

The feedback system shown below oscillates at 2rad/s when

Consider a transfer function   with p a positive real parameter. The maximum value of p until which  remains stable is _____.

The characteristic equation of an LTI system is given by. The number of roots that lie strictly in the left half s-plane is ______.

A certain system has transfer function, where  is a parameter. Consider the standard negative unity feedback configuration as shown below.  

Which of the following statements is true?

The number of open right half plane poles of  is

The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2rad/sec respectively are

The open loop transfer function of a unity feedback system is .

The range of K for which the system is stable is

For the polynomial

, the number of roots which lie in the right half of the s-plane is

The system shown in Figure remains stable when

The characteristic polynomial of a system is . The system is

The feedback control system in Figure is stable

Consider the feedback control system in Figure.

A system described by the transfer function  is stable. The constraints on  and k are.

The loop transfer function of a feedback control system is given by

,

Using Routh-Hurwitz criterion, determine the region of K-T plane in which the closed-loop system is stable.

The number of roots of  in the left half of the s-plane is

The characteristic equation of a feedback control system is

(i) Determine the range of K for the system to be stable.

(ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation.

The figure shows the block diagram representation of control system. The system in block A has an impulse response. The system in block B has an impulse response. The block ‘K’ amplifies its inputs by a factor k. For the overall system with input  and output

If , then all the roots of this equation are in the left half plane provided that