Time Response Analysis · Control Systems · GATE ECE

In the feedback control system shown in the figure below $G(s) = \dfrac{6}{s(s+1)(s+2)}$. $R(s), Y(s),$ and $E(s)$ are the Laplace transforms of $r(t)...

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

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+...

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...

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 ___________.

Consider a unity negative feedback control system with forward path gain $G(s) = \frac{K}{(s + 1)(s + 2)(s + 3)}$ as shown. The impulse response of t...

A closed loop system is shown in the figure where $$k>0$$ and $$\alpha > 0$$. The steady state error due to a ramp input $$(R(s) = \alpha /{s^2}...

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...

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...

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...

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=...

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 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 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 ...

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...

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 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...

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-...

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...

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...

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...

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...

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)

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...

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...

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...