Consider the standard second-order system of the form  with the poles  and  having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:

System 1:  and

System 2:  and

Which one of the following statements is correct?

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as  and ωn, respectively. The values of  and  are

Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

The output response of a system is denoted as y(t), and its Laplace transform is given by   the steady state value of y(t)  is

Consider a unity feedback system with forward transfer function given by

The steady-state error in the output of the system for a unit-step input is______(up to 2 decimal places).

Match the transfer functions of the second-order systems with the nature of the systems given below.

The unit step response y(t) of a unity feedback system with open loop transfer function is shown in the figure.

The value of K is ________ (up to decimal places).

For a system having transfer function, a unit step input is applied at time t= 0.  The value of the response of the system at t = 1.5 sec. (rounded off to three decimal places) is

When a unit ramp input is applied to the unity feedback system having closed loop transfer function , the steady rate error will be

Which of the following systems has maximum peak overshoot due to a unit step input?

A second-order real system has the following properties: 

(a) the damping ratio  and undamped natural frequency ,

(b) the steady state value of the output, to a unit step input, is 1.02

The transfer function of the system is

An open loop control system results in a response of  for a unit impulse input. The DC gain of the control system is ___________.

The unit step response of a system with the transfer function  is given by which one of the following waveforms?

The closed-loop transfer function of a system is . The steady state error due to unit step input is_____________.

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) 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

The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is         

For the system , the approximate time taken for a step response to reach 98% of its final value is

The unit-step response of a unity feedback system with open loop transfer function  is shown in the figure.  The value of K is

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

The steady state value of the output of this system for a unit impulse input applied at time instant t = 1 will be

The transfer function of a system is given as         

This system is        

Consider the feedback control system shown below which is subjected to a unit step input. The system is stable and has the following parameters and         

The steady state value of z is

Consider the R-L-C circuit shown in figure.

For a step-input, the overshoot in the output will be

Consider the R-L-C circuit shown in figure.

If the above step response is to be observed on a non-storage CRO, then it would be best to have the , as a

When subjected to a unit step input, the closed loop control system shown in Figure will have a steady state error of

Consider the function , where F(s) is the Laplace transform of the function f(t). The initial value of f(t) is equal to

The block diagram of a closed loop control system is given by figure. The values of K and P such that the system has a damping ratio of 0.7 and an un-damped natural frequency  of 5rad/sec, are respectively equal to                 

The unit impulse response of a second order under-damped system starting from rest is given by

The steady-state value of the unit step response of the system is equal to

A control system is defined by the following mathematical relationship

The response of the system as t →∞ is

A control system with certain excitation is governed by the following mathematical equation         

The natural time constants of the response of the system are

The block diagram shown in Figure gives a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is

The roots of the closed loop characteristic equation of the system shown in above figure are

Given the relationship between the input u(t) and the output y(t) to be, the transfer function  is

A unity feedback system has open loop transfer function G(s). The steady-state error is zero for

A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response,. The transfer function of the system is:

A unity feedback system has open loop transfer function. The peak overshoot in the step-input response of the system is approximately equal to:

The output of a linear time invariant control system is c(t) for a certain input r(t). If r(t) modified by passing it through a block whose transfer function is  and then applied to the system, the modified output of the system would be

The Laplace transform of  is:

A first order system is initially at rest and excited by a step input at time t=0. Its output becomes 1.1V is in 4 seconds and eventually reacts a steady state value of 2V. Determine its time constant

The unit-impulse response of a unit-feedback control system is given by

The open loop transfer function is equal to

Consider the unit-step response of a unity-feedback control system whose open-loop transfer functions is . The maximum overshoot is equal to

For a feedback control system of type 2, the steady state error for a ramp input is

For the system shown in figure, with a damping ratio  of 0.7 and an undamped natural frequency

 of 4 rad/sec, the values of K and a are         

The unit impulse response of a system is given as . The step response of the same system for  is equal to

The impulse response of an initially relaxed linear system is . To produce a response of , the input must be equal to         

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

For a unit step input the output is

The Laplace transform of f(t) is F(s). Given , the final value of f(t) is :

The steady state error due to a step input for type 1 system is _______________

Root locations of the characteristic unit step responses of second order of second equations order systems        

If f(t) is the step-response of a linear-time invariant system, then its impulse response is given by .
(True=1, False=0)

For what values of ‘a’ does the system shown in figure have a zero steady state error  for a step input?                 

Match the following transfer functions and impulse responses

A first order system and its response to a unit step input are shown in figure. The system parameters are

a= _______________

K= _______________