# Time Response Analysis · Control Systems · GATE EE

Start Practice## Marks 1

GATE EE 2022

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $$\xi$$ and $$\omega$$n are
...

GATE EE 2017 Set 2

When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} ...

GATE EE 2014 Set 2

The closed-loop transfer function of a system is $$T\left( s \right) = {4 \over {\left( {{s^2} + 0.4s + 4} \right)}}.$$ The steady state error due to ...

GATE EE 2011

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 inpu...

GATE EE 2010

For the system $${2 \over {\left( {s + 1} \right)}},$$ the approximate time taken for a step response to reach $$98$$% of its final value is

GATE EE 2008

A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$...

GATE EE 2004

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f...

GATE EE 2004

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f...

GATE EE 2004

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f...

GATE EE 2003

A control system is defined by the following mathematical relationship
$$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - ...

GATE EE 2000

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

GATE EE 1998

The output of a linear time invariant control system is $$c(t)$$ for a certain input $$r(t).$$ If $$r(t)$$ is modified by passing it through a block w...

GATE EE 1997

Introduction of integral action in the forward path of a unity feedback system result in a

GATE EE 1996

The unit - impulse response of a unity - feedback control system is given by $$c\left( t \right) = - t{e^{ - t}} + 2\,\,{e^{ - t}},\,\left( {t \ge 0}...

GATE EE 1996

Consider the unit step response of a unity feedback control system whose open loop transfer function is $$G\left( s \right) = {1 \over {s\left( {s + 1...

GATE EE 1996

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

GATE EE 1995

The Laplace transformation of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ i...

GATE EE 1995

The steady state error due to a step input for type $$1$$ system is ______________.

GATE EE 1995

The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)}...

GATE EE 1992

For what values of $$'a'$$ does the system shown in figure have a zero steady state error $$\left[ {i.e.,\mathop {Lim}\limits_{t \to \infty } \,\,E\le...

## Marks 2

GATE EE 2015 Set 2

The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given by which one of the following ...

GATE EE 2013

The open-loop transfer function of a $$dc$$ motor is given as $${{\omega \left( s \right)} \over {{V_a}\left( s \right)}} = {{10} \over {1 + 10s}}.$$ ...

GATE EE 2011

A two-loop position control system is shown below.
The gain $$k$$ of the Tacho-generator influences mainly the...

GATE EE 2011

The response $$h(t)$$ of a linear time invariant system to an impulse $$\delta \left( t \right),$$ under initially relaxed condition is $$h\left( t \r...

GATE EE 2009

The unit - step response of a unity feedback system with open loop transfer function $$G\left( s \right) = {K \over {\left( {s + 1} \right)\left( {s +...

GATE EE 2008

The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$
The steady state value of the ...

GATE EE 2008

The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is

GATE EE 2007

$$R-L-C$$ circuit shown in figure
For a step input $${e_{i,}}$$ the overshoot in the output $${e_{0,}}$$ will be ...

GATE EE 2007

Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters $${k_p} = 4,\,\,{k...

GATE EE 2007

$$R-L-C$$ circuit shown in figure
If the above step response is to be observed on a non - storage $$CRO,$$ then it would be best have the $${e_i}$...

GATE EE 2005

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

GATE EE 2005

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

GATE EE 2004

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$...

GATE EE 2004

The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \g...

GATE EE 2003

The block diagram shown in fig given is a unity feedback closed loop control system. The steady state error in the response of the above system to un...

GATE EE 2003

A control system with certain excitation is governed by the following mathematical equation
$$${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}...

GATE EE 2003

The roots of the closed loop characteristic equation of the system shown in fig is
...

GATE EE 2000

A unity feedback system has open-loop transfer function $$G\left( s \right) = {{25} \over {s\left( {s + 6} \right)}}.$$ The peak overshoot in the step...

GATE EE 1996

The unit impulse response of a system is given as $$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$ The step response of the same system fo...

GATE EE 1996

For the system shown in Figure, with a damping ratio $$\xi $$ of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$4$$ rad/sec, the value...

GATE EE 1991

A first order system and its response to a unit step input are shown in Fig. below. The system parameters are
$$a=$$ ____________
$$K=$$ ___________...