Polar Nyquist and Bode Plot · Control Systems · GATE EE

In the Nyquist plot of the open-loop transfer function $$G(s)H(s) = {{3s + 5} \over {s - 1}}$$ corresponding to the feedback loop shown in the figure,...

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...

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...

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 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...

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 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 polar plot of a type-$$1, 3$$-pole, open-loop system is shown in Fig. below. The closed loop system is ...

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. ...

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20$ dB/decade at le...

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $G(s)$ are given in the table....

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is ...

Consider a lead compensator of the form $$K(s) = {{1 + {s \over a}} \over {1 + {s \over {\beta a}}}},\beta > 1,a > 0$$ The frequency at which this co...

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...

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 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 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 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 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 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 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^ + },\,...

Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of these plots represents a stabl...

The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {...

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...

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...

In the system shown in figure, the input $$x(t)$$ $$=$$ $$sin$$ $$t.$$ In the steady-state, the response $$y(t)$$ will be ...

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 $$‘a’$$...

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 + ...

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 ...