The Nyquist plot of a system is given in the figure below. Let , and  be the positive frequencies at the points , and , respectively.

Which one of the following statements is TRUE?

In the context of Bode magnitude plots. . decade is the same as

The open loop transfer function of a unity negative feedback system is , where   and  are positive constants. The phase cross-over frequency, in rad/s, is

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is , where  and c are positive constants. The value of  is __________. (rounded off to the nearest integer).

Consider a closed-loop control system with unity negative feedback and  in the forward path, where the gain . The complete Nyquist plot of the transfer function  is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume  has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ________.

The complete Nyquist plot of the open-loop transfer function  of a feedback control system is shown in the figure.        

If  has one zero in the right-half of the splane, the number of poles that the closed-loop system will have in the right-half of the s-plane is

The pole-zero map of a rational function  is shown below. When the closed contour  is mapped into the -plane, then the mapping encircles.

A system with transfer function

is subjected an input . The steady state output of the system is .

The value of “a” is __________.

For the LTI system, the Bode plot for its gain is illustrated in the figure shown. The number of system poles and the number of system zerosin the frequency range is

The Nyquist stability criterion and the Routh criterion both are powerful analyst’s tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

The figure below shows the Bode magnitude and phase plots of a stable transfer function  

Consider the negative unity feedback configuration with gain k in the feed forward path. The closed loop is stable for. The maximum value of is ______.

Consider a stable system with transfer function

where are real valued constants. The slope of the Bode log magnitude curve of G (s) converges to – 60 dB/decade as . A possible pair of values for p and q is  

The Nyquist plot of the transfer function

does not encircle the point  for K = 10 but does encircle  the point for K = 100. Then the closed loop system (having unity gain feedback) is  

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

.

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.

If , then the number of poles of the closed-loop transfer function that lie in the right-half of the s-plane is

A closed-loop control system is stable if the Nyquist plot of the corresponding open loop transfer function

The number and direction of encirclements around the point in the complex plane by the Nyquist plot of is

In the feedback system shown below .

The positive value of k for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is   ________.

The asymptotic Bode phase plot of  , with k and  both positive, is shown below.

The value of  is ________.

The polar plot of the transfer function  for 0 ≤ ω < ∞ will be in the

Consider the feedback system shown in the figure. The Nyquist plot G(s) is also shown. Which one of the following conclusions is correct?

The phase margin in degrees of . Calculated using the asymptotic Bode plot is ________.

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.

If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________.        

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.

The value of(in Hz) is ___________.

The phase margin (in degrees) of the system is _______.

The bode plot of a transfer function G(s) is shown in the figure below.

The gain  is 32 dB and -8 dB at 1rad/s and 10rad/s respectively. The phase is negative for all. Then G(s) is

For the transfer function, the corresponding Nyquist plot for positive frequency has the form

The input-output transfer function of a plant .

The plant is placed in a unity negative feedback configuration as shown in the figure below.

The signal flow graph that DOES NOT model the plant transfer function H(s) is

The input-output transfer function of a plant .

The plant is placed in a unity negative feedback configuration, as shown in the figure below.

The gain margin of the system under closed loop unity negative feedback is

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.

Which of the following statements is true?

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed-loop system in the feedback configuration shown.

The gain and phase margins of G(s) for closed loop stability are

The pole-zero plot given below corresponds to a

The magnitude of frequency response of an under-damped second order system is 5 at 0 rad/sec and peaks to  at rad/sec. The transfer function of the system is

If the closed-loop transfer function of a control system is given as  then it is

The transfer function of a plant is .

The second-order approximation of T(s) using dominant pole concept is

The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G(s) corresponding to this Bode plot is

The open-loop transfer function of a unity-gain feedback control system is given by .

The gain margin of the system in dB is given by

Consider two transfer functions   and.

The 3-dB bandwidths of their frequency responses are, respectively,

The Nyquist plot of  for a closed loop control system, passes through (-1, j0) point in the GH plane. The gain margin of the system in dB is equal to

Consider a unity-gain feedback control system whose open-loop transfer function is:

The value of “a” so that the system has a phase margin equal to is approximately equal to

Consider a unity-gain feedback control system whose open-loop transfer function is:

with the value of “a” set for a phase-margin of, the value of unit-impulse response of the open-loop system at t = 1 second is equal to

The open loop transfer function of a unity feedback is given by .

The gain and phase crossover frequencies in rad/sec are, respectively

The open loop transfer function of a unity feedback is given by .

Based on the above results, the gain and phase margins of the system will be

The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in the figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

The gain margin for the system with open-loop transfer function, is

Consider the Bode magnitude plot shown in Figure. The transfer function H(s) is

A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

Figure shows the Nyquist plot of the open-loop transfer function  of a system. If  has one right hand pole, the closed loop system is

The approximate Bode magnitude plot of a minimum-phase system is shown in figure. The transfer function of the system is

The gain margin and the phase margin of a feedback system with  are

The phase margin of a system with the open-loop transfer function  is

The system with the open loop transfer function  has a gain margin of

The Nyquist plot of an all-pole second order open-loop system is shown in Figure. Obtain the transfer function of the system.

The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in Figure. if G(s) has no pole in the right half of s-plane, the number of roots of the system characteristic equation in the right half of s-plane is

The gain margin (in dB) of a system having the loop transfer function is

The phase margin (in degrees) of a system having the loop transfer function   is

The asymptotic Bode plot of the minimum phase open-loop transfer function  in as shown in Figure. Obtain the transfer function

Consider a feedback system with the open-loop transfer function, given by

Find the stability of the closed loop system using Nyquist stability theory.

In the Bode-plot of a unity feedback control system, the value of phase of  at the gain cross over frequency is. The phase margin of the system is

The Nyquist plot of a phase transfer function  of a system encloses the  point. The gain margin of the system is.

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

Using the Nyquist criterion, the condition for the closed-loop system to be stable is T< K. Find the values of K.

Non-minimum phase transfer function is defined as the transfer function

The 3-dB bandwidth of a typical second-order system with the transfer function  is given by

The open loop frequency response of a system at two particular frequencies are given by:  and . The closed loop unity feedback control is then _________.

The poles of a continuous-time oscillator are pure imaginary. ( True=1, False=0)

Bode plot of a stable system is shown in figure. The transfer function of the system is ______.

A unity feedback system has open loop transfer function.

The pole-zero pattern of a certain filter is shown in the figure below. The filter must be of the following type.

The open loop transfer function of a feedback control system is: .

The gain margin of the system is:

The open loop transfer function of a feedback control system incorporating a dead time element is given by . Where , and are variable scalar parameters.

For a given value of T, find the value of k for which the closed-loop system is stable. is the smallest value of satisfying the equation