Time Response Analysis · Control Systems · GATE EE

Marks 1

The Laplace transform of the step response of a system is given by

$$ Y(s)=\frac{100}{s(s+100)} $$

The rise time is defined as the time taken for the response to go from 0.1 to 0.9 of its final value. The settling time is defined as the time taken for the response to reach 0.98 of its final value.

For this system, the rise time ( $T_r$ ), settling time ( $T_s$ ), and time constant ( $T_c$ ), all expressed in seconds, are

GATE EE 2026

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

$$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Time (sec) } & 0.6 & 1.6 & 2.6 & 10 & \infty \\ \hline \text { Output } & 0.78 & 1.65 & 2.18 & 2.98 & 3 \\ \hline \end{array} $$

GATE EE 2025

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

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

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

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

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

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

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

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

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

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

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

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

GATE EE 2000

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

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

GATE EE 1997

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

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

GATE EE 1996

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

GATE EE 1996

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

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 $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 1} \right)}}$$ for a unit step input the output is

GATE EE 1995

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

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

Consider a closed loop system as shown.

$$ G_p(s)=\frac{14.4}{s(1+0.1 s)} $$

is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}$. (Round off to 2 decimal places).