GATE EE
Control Systems
Time Response Analysis
Previous Years Questions

## Marks 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 ...
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} ... The closed-loop transfer function of a system is$$T\left( s \right) = {4 \over {\left( {{s^2} + 0.4s + 4} \right)}}.$$The steady state error due to ... The steady state error of a unity feedback linear system for a unit step input is$$0.1.$$The steady state error of the same system, for a pulse inpu... For the system$${2 \over {\left( {s + 1} \right)}},$$the approximate time taken for a step response to reach$$98$$% of its final value is A function$$y(t)$$satisfies the following differential equation :$${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$... 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 $$f... Consider the function$$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$Where$$F(s)$$is the Laplace transform of the function$$f... 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 $$f... A control system is defined by the following mathematical relationship$$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - ...
A unity feedback system has open loop transfer function $$G(s).$$ The steady-state error is zero for
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...
Introduction of integral action in the forward path of a unity feedback system result in a
The unit - impulse response of a unity - feedback control system is given by $$c\left( t \right) = - t{e^{ - t}} + 2\,\,{e^{ - t}},\,\left( {t \ge 0}... Consider the unit step response of a unity feedback control system whose open loop transfer function is$$G\left( s \right) = {1 \over {s\left( {s + 1...
For a feedback control system of type $$2,$$ the steady state error for a ramp input is
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...
The steady state error due to a step input for type $$1$$ system is ______________.
The closed loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}}\, = \,\,{{2\left( {s - 1} \right)}... For what values of$$'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

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 ...
The open-loop transfer function of a $$dc$$ motor is given as $${{\omega \left( s \right)} \over {{V_a}\left( s \right)}} = {{10} \over {1 + 10s}}.$$ ...
A two-loop position control system is shown below. The gain $$k$$ of the Tacho-generator influences mainly the...
The response $$h(t)$$ of a linear time invariant system to an impulse $$\delta \left( t \right),$$ under initially relaxed condition is $$h\left( t \r... The unit - step response of a unity feedback system with open loop transfer function$$G\left( s \right) = {K \over {\left( {s + 1} \right)\left( {s +...
The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is
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 ...
$$R-L-C$$ 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 $${e_i}...$$R-L-C$$circuit shown in figure For a step input$${e_{i,}}$$the overshoot in the output$${e_{0,}}$$will be ... Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters$${k_p} = 4,\,\,{k...
When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of ...
When subjected to a unit step input, the closed loop control system shown in the figure will have a steady state error of ...
The unit impulse response of a second order under-damped system starting from rest is given by $$c\left( t \right) = 12.5{e^{ - 6t}}\,\sin 8t,\,\,t \g... The block diagram of a closed loop control system is given by figure. The values of$$K$$and$$P$$such that the system has a damping ratio of$$0.7$... 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... The roots of the closed loop characteristic equation of the system shown in fig is ... A control system with certain excitation is governed by the following mathematical equation $${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}... A unity feedback system has open-loop transfer function$$G\left( s \right) = {{25} \over {s\left( {s + 6} \right)}}.$$The peak overshoot in the step... The unit impulse response of a system is given as$$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$The step response of the same system fo... For the system shown in Figure, with a damping ratio$$\xi $$of$$0.7$$and an undamped natural frequency$${\omega _n}$$of$$4$$rad/sec, the value... A first order system and its response to a unit step input are shown in Fig. below. The system parameters are$$a=$$____________$$K=$\$ ___________...
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