A closed loop system is shown in the figure where  and . The steady state error due to a ramp input  is given by

Two linear time-invariant systems with transfer functions

have unit step responses  and , respectively. Which of the following statements is/are true?

The block diagram of a closed-loop control system is shown in the figure. , and  are the Laplace transforms of the time-domain signals , and , respectively. Let the error signal be defined as . Assuming the reference input  for all , the steady state error , due to a unit step disturbance , is __________(rounded off to two decimal places).

Consider the following closed loop control system

where  and . If the steady state error for a unit ramp input is 0.1 , then the value of  is __________.

Let Y(s) be the unit step response of a casual system having a transfer function                                                

That is ,. The forced response of the system is

Consider a casual second-order system with the transfer function

With a unit stepas an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady state value, rounded off to two decimal places, is

For a unity feedback control system with the forward path transfer function  

The peak resonant magnitudeof the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _______

The open loop transfer function

Where p is an integer, is connected in unity feedback configuration as shown in the figure.                        

Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is ________________.

A second-order LTI system is described by the following state equations.

Where  and  are the two state variables and r(t) denotes the input. The output. The system is

The transfer function of a causal LTI system  H(s) = 1/s. If the input to the system is , where u (t) is a unit step function, the system output __________.  

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

For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is_____.

In the feedback system shown below. The step response of the closed loop system should have minimum settling time and have no overshoot.

The required value of gain k to achieve this is  ________.

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as . The steady state error due to a unit step input is

A unity negative feedback system has an open-loop transfer function. The gain K for the system to have a damping ratio of 0.25 is ________.

The output of a standard second-order system for a unit step input is given as

 .

The transfer function of the system is

The transfer function of a mass-spring-damper system is given by  . The frequency response data for the system are given in the following table.

The unit step response of the system approaches a steady state value of

The forward path transfer function of a unity negative feedback system is given by. The value of K which will place both the poles of the closed-loop system at the same location is ______.

The natural frequency of an un-damped second-order system is 40rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ____.

The steady state error of the system shown in the figure for a unit step input is _________.

For the second-order closed-loop system shown in the figure, the natural frequency (in rad/s) is

The position control of a DC servo-motor is given in the figure.

The values of the parameters are

N-m/(rad/sec) and . The steady-state position response (in radians) due to unit impulse disturbance torque  is _______.

The open-loop transfer function of a dc motor is given as . When connected in feedback as shown below, the approximate value of  that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

Given.

If , then the value of K is

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has these properties?

Step responses of a set of three second-order under-damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.

Group I

Group II

(1)

(2)

(3)

(4)

A control system with a PD controller is shown in the figure. If the velocity error constant  and the damping ratio ζ =0.5, then the values of  and  are

The unit impulse response of a system is: , . For this system, the steady-state value of the output for unit step input is equal to

In the derivation of the expression for peak percent overshoot,  , which one of the following conditions is NOT required?

A unit ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively.

A second-order system has the transfer function With r(t) as the unit-step function, the response c(t) of the system is represented by

(a)

(b)

(c)

(d)

Consider a system with the transfer function.

Its damping ratio will be 0.5 when the value of k is

The transfer function of a system is . For a unit step input to the system the approximate settling time for 2% criterion is

If the characteristic equation of a closed-loop system is , then the system is

The block diagram of a feedback system is shown in Fig (a).

(a) Find the closed-loop transfer function.

(b) Find the minimum value of G for which the step response of the system would exhibit an overshoot, as shown in Fig (b).

(c) For G equal to twice this minimum value, find the time period T indicated in Fig(b).

For a second-order system with the closed-loop transfer function.

The settling time for a 2-per cent band, in seconds, is

If the closed-loop transfer function T(s) of a unity negative feedback system is given by

.

Then the steady-state error for a unit ramp input is

Consider a unity feedback control system with an open-loop transfer function. The steady state error of the system due to a unit step input is

Consider a feedback control system with an open-loop transfer function .

The type of the closed-loop system is

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

The characteristic equation of the closed system is

Consider the system shown in the figure. Determine the value of ‘a’ such that the damping ratio is 0.5. Also obtain the values of the rise time  and maximum overshoot  in its step response.

The step input error coefficient of a system  with unity feedback is

The final value theorem is used to find the

For a second-order system, the damping ratio,  is , then the roots of the characteristic polynomial are

Match the following

(A) Very low response at very high frequencies

(B) Overshoot

(C) Synchro-control transformer output

(1) Low-pass systems

(2) Velocity damping

(3) Natural frequency

(4) Phase-sensitive modulation

(5) Damping ratio

A block diagram model of a position control system is shown in the figure.

1.  In the absence of derivative feedback, determine damping ratio of the system for amplifier gain .

Also, find the steady state error to a unit ramp input.

2.  Find suitable values of the parameters  and  so that the damping ratio of the system is increased to 0.7 without affecting the steady-state error as obtained in part (a).

A second order system has a transfer function given by . If the system, initially at rest is subjected to a unit step input at , the second peak in response will occur at

A unity feedback control system has the open loop transfer function. If the input to the system is a unit ramp, the steady state error will be