Frequency Response

In the context of Bode magnitude plots, 40 dB/decade is the same as ______.

The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The phase cross-over frequency, in rad/s, is

A system with transfer function $G(s)=\frac{1}{(s+1)(s+a)}, a>0$ is subjected to input $5 \cos 3 t$. The steady state output of the system is $\frac{1}{\sqrt{10}} \cos (3 t-1.892)$. The value of $a$ is

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE.

For a unity feedback control system with the forward path transfer function $$G(s) = {K \over {s\left( {s + 2} \right)}}$$ The peak resonant magnitude M r of the closed-loop frequency response is 2. The corresponding val...

The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then...

Consider a stable system with transfer function $$$G\left(s\right)=\frac{s^p+b_1s^{p-1}+....+b_p}{s^q+a_1s^{q-1}+....+a_q}$$$ Where $$b_1,.......,b_p$$ and $$a_1,.......,a_q$$ are real valued constants. The slope of the...

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is

The popular plot of the transfer function G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 \le \omega < \infty $$ will be in the

The phase margin (in degrees) of the system G(s)=$${{10} \over {\left( {s + 10} \right)}}$$ is ___________.

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4 th order all-pole system?

The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)}},$$ using the asymptotic Bode plot is ______

For the transfer function G$$\left( {j\omega } \right) = 5 + j\omega ,$$ the corresponding Nyquist plot for positive frequency has the form

The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain margin of the system in dB is equal to

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ The value of 'a', so that the system has a phase-margin equal to $$\pi $$/4 is approximately equal to

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$. With the value of "a" set for phase-margin of $$\pi $$/4, the value of unit-impulse response of the op...

The open-loop transfer function of a unity-gain feedback control system is given by $$G(s) = {K \over {(s + 1)(s + 2)}},$$ the gain margin of the system in dB is given by

Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their frequency responses are, respectively

The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ Based on the above results, the gain and phase margins of the system will be

The open loop transfer function of a unity feedback system is given by G(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ The gain and phase crossover frequencies in rad/sec are, respectively

Despite the presence of negative feedback, control systems still have problems of instability because the

A system has poles at 0.01 Hz, 1Hz and 80 Hz; zeroes at 5hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

The gain margin and the phase margin of a feedback system with G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ are

The gain margin for the system with open-loop transfer function G(s)H(s)=$${{2(1 + s)} \over {{s^2}}}$$ is

A unity feedback system has the plant transfer function G p (s)=$${1 \over {\left( {s + 1} \right)\left( {2s + 1} \right)}}$$ (a) Determine the frequency at which the plant has a phase lah of 90 o . (b) An intergral cont...

The phase margin of a system with the open-loop transfer function G(s)H(s)=$${{(1 - s)} \over {(1 + s)(2 + s)}}$$ is?

The system with the open loop transfer function G(s)H(s)=$${1 \over {s\left( {{s^2} + s + 1} \right)}},$$ has a gain margin of

Consider a feedback system with the open loop transfer function given by $$G(s)H(s) = {K \over {s\left( {2s + 1} \right)}}.$$ Examine the stability of the closed-loop system using Nyquist stability.

The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)}}$$

The gain margin of a system having the loop transfer function G(s)H(s) =$${{\sqrt 2 } \over {s(s + 1)}}$$ is

The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. The gain margin of the system is

In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The phase margin of the system is

The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condition for the closed loop system to be st...

The open loop frequency response of a system at two particular frequencies are given by: 1.2 $$\angle - 180^\circ $$ and 1.0 $$\angle - 190^\circ $$. The closed loop unity feedback control system is then

A unity feedback system has open-loop transfer function $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}$$ Sketch Nyquist plot for the system and there from obtain the gain margin and the phase margin.

The open-loop transfer function of a feedback control system is G(s)=$${1 \over {{{\left( {s + 1} \right)}^3}}}$$ The gain margin of the system is

Nyquist plot consider a feed back system where the OLTF is: $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}.$$ Determine the asymptote which the nyquist plot approaches as $$\omega \to 0.$$ Find also...

From the Nicholas chart, one can determine the following quantities pertaining to a closed loop system:

The popular plot of G(s)=$${{10} \over {s{{\left( {s + 1} \right)}^2}}},$$ intercepts real axix at $$\omega = {\omega _0}$$ Then, the real part and $${\omega _0}$$ are respectively given by

A system has fourteen poles and two zeroes. Its high frequency asymptote, in its magnitude plot, has having a slope of