Time Response Analysis · Control Systems · GATE EE
Marks 1
1
Consider the standard second-order system of the form $\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$ with the poles $p$ and $p^\ast$ 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: $\omega_n = 3$ rad/sec and $\theta = 60^{\circ}$
System 2: $\omega_n = 1$ rad/sec and $\theta = 70^{\circ}$
Which one of the following statements is correct?
GATE EE 2024
2
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?
GATE EE 2024
3
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as + b}},\,\left( {a > 0,\,b > 0,\,K > 0} \right),$$ the steady state error will be
GATE EE 2017 Set 2
4
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 unit step input is ________
GATE EE 2014 Set 2
5
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
GATE EE 2011
6
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 2010
7
A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
Where $$\delta \left( t \right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by $$u(t),y(t)$$ can be of the form
GATE EE 2008
8
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 $$f(t).$$ The initial value of $$f(t)$$ is equal to
GATE EE 2004
9
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 $$f(t).$$ The initial value of $$f(t)$$ is equal to
GATE EE 2004
10
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 $$f(t).$$ The initial value of $$f(t)$$ is equal to
GATE EE 2004
11
A control system is defined by the following mathematical relationship
$$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$
The response of the system as $$\,t \to \infty $$ is
GATE EE 2003
12
A unity feedback system has open loop transfer function $$G(s).$$ The steady-state error is zero for
GATE EE 2000
13
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 whose transfer function is $${e^{ - s}}$$ and then applied to the system, the modified output of the system would be
GATE EE 1998
14
Introduction of integral action in the forward path of a unity feedback system result in a
GATE EE 1997
15
Consider the unit step response of a unity feedback control system whose open loop transfer function is $$G\left( s \right) = {1 \over {s\left( {s + 1} \right)}}.$$ The maximum overshoot is equal to
GATE EE 1996
16
For a feedback control system of type $$2,$$ the steady state error for a ramp input is
GATE EE 1996
17
The unit - impulse response of a unity - feedback control system is given by $$c\left( t \right) = - t{e^{ - t}} + 2\,\,{e^{ - t}},\,\left( {t \ge 0} \right)$$ the open loop transfer function is equal to
GATE EE 1996
18
The steady state error due to a step input for type $$1$$ system is ______________.
GATE EE 1995
19
The Laplace transformation of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is
GATE EE 1995
20
The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 1} \right)}}$$ for a unit step input the output is
GATE EE 1995
21
For what values of $$'a'$$ does the system shown in figure have a zero steady state error $$\left[ {i.e.,\mathop {Lim}\limits_{t \to \infty } \,\,E\left( t \right)} \right]$$ for a step input?
GATE EE 1992
Marks 2
1
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 2022
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 waveforms?
GATE EE 2015 Set 2
3
The open-loop transfer function of a $$dc$$ motor is given as $${{\omega \left( s \right)} \over {{V_a}\left( s \right)}} = {{10} \over {1 + 10s}}.$$ When connected in feedback as shown below, the approximate value of $${K_a}$$ 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
GATE EE 2013
4
The response $$h(t)$$ of a linear time invariant system to an impulse $$\delta \left( t \right),$$ under initially relaxed condition is $$h\left( t \right) = \,{e^{ - t}} + {e^{ - 2t}}.$$ The response of this system for a unit step input $$u(t)$$ is
GATE EE 2011
5
A two-loop position control system is shown below.
The gain $$k$$ of the Tacho-generator influences mainly the
The gain $$k$$ of the Tacho-generator influences mainly the
GATE EE 2011
6
The unit - step response of a unity feedback system with open loop transfer function $$G\left( s \right) = {K \over {\left( {s + 1} \right)\left( {s + 2} \right)}}$$ is shown in the figure. The value of $$K$$ is
GATE EE 2009
7
The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is
GATE EE 2008
8
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 output of the system for a unit impulse input applied at time instant $$t=1$$ will be
GATE EE 2008
9
Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters $${k_p} = 4,\,\,{k_i} = 10,\,\,\omega = 500\,\,$$ and $$\xi $$ $$=0.7.$$ The steady state value of $$z$$ is
GATE EE 2007
10
$$R-L-C$$ circuit shown in figure
For a step input $${e_{i,}}$$ the overshoot in the output $${e_{0,}}$$ will be
GATE EE 2007
11
$$R-L-C$$ 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 $${e_i}$$ as a
GATE EE 2007
12
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
13
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
14
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 undamped natural frequency $${\omega _n}$$ of $$5$$ rad/sec, are respectively equal to
GATE EE 2004
15
The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \ge 0.$$
The steady-state value of the unit step response of the system is equal to
The steady-state value of the unit step response of the system is equal to
GATE EE 2004
16
A control system with certain excitation is governed by the following mathematical equation
$$${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$$
The natural time constants of the response of the system are
The natural time constants of the response of the system are
GATE EE 2003
17
The roots of the closed loop characteristic equation of the system shown in fig is
GATE EE 2003
18
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 unit step input is
GATE EE 2003
19
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-input response of the system is approximately equal to
GATE EE 2000
20
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 values of $$' K '$$ and $$' a '$$ are
GATE EE 1996
21
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 for $$\,t \ge 0$$ is equal to
GATE EE 1996
22
A first order system and its response to a unit step input are shown in Fig. below. The system parameters are
$$a=$$ ____________
$$K=$$ ___________
$$a=$$ ____________
$$K=$$ ___________
GATE EE 1991