GATE ECE
Control Systems
Time Response Analysis
Previous Years Questions

## Marks 1

Two linear time-invariant systems with transfer functions $${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10... The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r... The open loop transfer function$$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\ri... The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit step input u(t) is y(t). The v... For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;... A unity negative feedback system has an open–loop transfer function$$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The gain K for the system to have a... For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is ... The input$$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer fu... The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency i... The differential equation$$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\mathrm x\left(\mathrm t\right)...
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents t...
If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final value is:
Consider a system with the transfer function $$G\left(s\right)=\frac{s+6}{Ks^2+s+6}$$$Its damping ratio will be 0.5 when the value of K is If the characteristic equation of a closed-loop system is s2 + 2s + 2 =0, then the system is For a second-order system with the closed-loop transfer function $$T\left(s\right)=\frac9{s^2+4s+9}$$$ the settling time for 2% band in seconds is
Consider a unity feedback control system with open-loop transfer function $$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ . The steady state er...
If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\l... Consider a feedback control system with loop transfer function$$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+... For a second order system, damping ratio $$\left(\xi\right)$$ , is 0 < $$\xi$$ < 1 ,then the roots of the characteristic polynomial are The final value theorem is used to find the If $$L\left(f\left(t\right)\right)=\frac{2\left(s+1\right)}{s^2+2s+5}$$ then f(0+) and f($$\infty$$) are given by [Note: 'L' stands for 'Laplace Trans... The step error coefficient of a system G(s)=$$\frac1{\left(s+6\right)\left(s+1\right)}$$ with unity feedback is The poles of a continuous time oscillator are ___________. ## Marks 2 In the feedback system shown below $$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$ The step response of the closed-loop system should have minimum settl...
The open-loop transfer function of a unity-feedback control system is $$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$For the peak overshoot of the close... The output of a standard second–order system for a unit step input is given as $$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}\cos\left(\sqrt3t\;-\;\frac{\m... The damping ratio of a series RLC circuit can be expressed as The steady state error of the system shown in the figure for a unit step input is _______. ... For the following feedback system$$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of the step response is required t... The open-loop transfer function of a dc motor is given as$$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when connected in fee... The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these pro... A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=... Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding... The frequency response of a linear, time-invariant system is given by$$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$.The step response of the s... The transfer function of a plant is$$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$The second-order approximation of T (s) using d... The unit impulse response of a system is:$$$h\left(t\right)\;=\;e^{-t},\;t\geq0$$For this system, the steady-state value of the output for unit st... The unit-step response of a system starting from rest is given by$$$\mathrm c\left(\mathrm t\right)=1-\mathrm e^{-2\mathrm t}\;\mathrm{for}\;\mathrm ...
A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectiv...
In the derivation of expression for peak percent overshoot,$$M_p=exp\left(\frac{-\mathrm{πξ}}{\sqrt{1-\xi^2}}\right)\times100\%$$$.Which one of the ... A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$ is excited with 10u(t). The time at which the output reaches 99% ... A system described by the following differential equation $$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is initially at rest. For input x(...
A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) as the unit-step function, the...
The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For a unit step input to the syste...
If the closed-loop transfer function T(s) of a unity negative feedback system is given by $$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1s^{n-1}+.....+... The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e-... The response of an LCR circuit to a step input is (a) Over damped (b) Critically damped (c) Oscillatory If the transfer function has (1) poles on the... Match the following with List-1 with List-2 List-1 (a) Very low response at very high frequencies. (b) Overshoot (c) Synchro-control transformer outp... A unity feedback control system has the open loop transfer function$$G\left(s\right)\;=\;\frac{4\left(1\;+\;2s\right)}{s^2\left(s\;+\;2\right)}$$.I... A second order system has a transfer function given by$$\mathrm G\left(\mathrm s\right)\;=\;\frac{25}{\mathrm s^2\;+\;8\mathrm s\;+\;25} .If the sy...
The steady state error of a stable 'type 0' unity feedback system for a unit step function is
A critically damped, continuous-time, second order system, when sampled, will have ( in Z domain)

## Marks 5

The block diagram of a feedback system is shown in Figure. (a) Find the closed loop transfer function. (b) Find the minimum value of G for which the...
Following fig. shows the block diagram representation of control system. The system in block A has an impulse response h(t ) = e−t u(t ). The system i...

## Marks 8

For the linear, time-invariant system whose block diagram is shown in Fig. with input x(t) and output y(t), (a) Find the transfer function. (b) For ...
Block diagram model of a position control system is shown in figure. (a) In absence of derivative feedback (Kt=0) , determine damping ratio of the sy...

## Marks 10

Consider the system shown in Fig. Determine the value of 'a' such that the damping ratio is 0.5. Also obtain the values of the rise time 'tr' and ma...
EXAM MAP
Joint Entrance Examination