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...

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 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...

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 magnitude Bode plot of a network is shown in the figure The maximum phase angle $${\phi _m}$$ and the corresponding gain $${G_m}$$ respectively ...

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 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...

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 ...