GATE EE
Control Systems
Polar Nyquist and Bode Plot
Previous Years Questions

## Marks 1

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, i...
An LTI system is shown in the figure where $$G(s) = {{100} \over {{s^2} + 0.1s + 100}}$$. The steady state output of the system, to the input r(t), is...
The open loop transfer function of a unity gain negative feedback system is given as $$G(s) = {1 \over {s(s + 1)}}$$ The Nyquist contour in the s-plan...
The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$ Let the output of...
Consider the unity feedback control system shown. The value of $$K$$ that results in a phase margin of the system to be $${30^0}$$ is ____________. (...
The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\... The phase cross-over frequency of the transfer function$$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$in$$rad/s$$is A Bode magnitude plot for the transfer function$$𝐺(𝑠)$$of a plant is shown in the figure. Which one of the following transfer functions best descr... Nyquist plots of two functions$${G_1}\left( s \right)$$and$${G_2}\left( s \right)$$are shown in figure. Nyquist plot of the product of$${G_1}\...
The Bode plot of a transfer function $$G(s)$$ is shown in the figure below. The gain is $$\left( {20\log \left| {G\left( s \right)} \right|} \right... A system with transfer function$$\,G\left( s \right) = {{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3...
The frequency response of a linear system $$G\left( {j\omega } \right)$$ is provided in the tubular form below. The gain margin and phase margin of t...
An open loop system represented by the transfer function $$G\left( s \right) = {{\left( {s - 1} \right)} \over {\left( {s + 2} \right)\left( {s + 3} \... The polar plot of an open loop stable system is shown below. The closed loop systems is ... A system with zero initial conditions has the closed loop transfer function$$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s ...
The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {s + 1} \right)} \over {{s^2}}}... The Nyquist plot of loop transfer function$$G(s) H(s)$$of a closed loop control system passes through the point$$(-1,j0)$$in the$$G(s) H(s)$$pla... The polar plot of a type-$$1, 3$$-pole, open-loop system is shown in Fig. below. The closed loop system is ... The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig. Its tr... The closed - loop transfer function of a control system is given by$${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \righ...
A unity feedback system has the open loop transfer function $$G\left( s \right) = {1 \over {\left( {s - 1} \right)\left( {s + 2} \right)\left( {s + 3}... The system having the Bode magnitude plot shown in Fig. below has the transfer function ... Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below. ... ## Marks 2 Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$is in$$rad/s$$) Which one of the following transfer functions is best rep... Loop transfer function of a feedback system is$$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$Take the Nyquis... The Bode magnitude plot of the transfer function$$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \right)} \over {s\left( {1 + {s \ov...
The magnitude Bode plot of a network is shown in the figure The maximum phase angle $${\phi _m}$$ and the corresponding gain $${G_m}$$ respectively ...
For the transfer function $$G\left( s \right) = {{5\left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {{s^2} + 4s + 25} \right)}}.$$ The ...
The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( ... The open loop transfer function of a unity feedback system is given by$$G\left( s \right) = \left( {{e^{ - 0.1s}}} \right)/s.$$The gain margin of t... The asymptotic approximation of the log magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function i... The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure: This transfer function has... If$$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$and$$y = {\rm I}mG\left( {j\omega } \right)$$then for$$\omega \to {0^ + },\,...
The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {... Consider the following Nyquist plots of loop transfer functions over$$\omega = 0$$to$$\omega = \infty .$$Which of these plots represents a stabl... In the$$GH(s)$$plane, the Nyquist plot of the loop transfer function$$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$passe... If the compensated system shown in the figure has a phase margin of$${60^ \circ }$$at the crossover frequency of$$1 rad/sec,$$the value of the gai... The open loop transfer function of a unity feedback control system is given as$$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of$$‘a’$$... In the system shown in figure, the input$$x(t)=sint.$$In the steady-state, the response$$y(t)$$will be ... The asymptotic Bode plot of the transfer function$${K \over {1 + {s \over a}}}$$. The error in phase angle and$$dB$$gain at a frequency of$$\omega...
The function corresponding to the Bode plot of Figure, is ...
A unity feedback system with the open loop transfer function $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}$$ has gai...
An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + ... ## Marks 5 A unity feedback system has an open-loop transfer function of$$G\left( s \right) = {{10000} \over {s{{\left( {s + 10} \right)}^2}}}$$(a) Determine t... Open-loop transfer function of a unity - feedback system is$$\$G\left( s \right) = {G_1}\left( s \right).{e^{ - s{\tau _D}}} = {{{e^{ - s{\tau _D}}}}...
The asymptotic magnitude Body plot of a system is given in Figure. Find the transfer function of the system analytically. It is known that the system ...
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