GATE-CH-1995-1-q-ctrl-1mark

Bode diagrams are generated from output response of the system subjected to which of the following input

• impulse

• step

• ramp

• sinusoidal

GATE-CH-1995-1-t-ctrl-1mark

According to Bode stability criterion, a system is unstable if the open loop frequency response exhibits an amplitude ratio exceeding unity at frequency for which phase lag is

• $0^{\circ }$

• ${45}^{\circ }$

• ${90}^{\circ }$

• ${180}^{\circ }$

GATE-CH-1998-1-24-ctrl-1mark

A first order system with a time constant of 1 min is subjected to frequency response analysis. At an input frequency of 1 radian/min, the phase shift is

• ${45}^{\circ }$

• $-{90}^{\circ }$

• $-{180}^{\circ }$

• $-{45}^{\circ }$

GATE-CH-1999-1-27-ctrl-1mark

A sinusoidal variation in the input passing through a linear first-order system

• becomes more oscillatory (frequency increases)

• becomes less oscillatory (frequency decreases)

• gets amplified (magnitude increases)

• gets attenuated (magnitude decrease)

GATE-CH-2000-1-27-ctrl-1mark

Select the correct statement from the following:

• The frequency response of a pure capacity process is unbounded
• The phase lag of a pure time delay system decreases with increasing frequency
• The amplitude ratio of a pure capacity process is inversely proportional to the frequency
• The amplitude ratio of a pure time delay system increases with frequency

GATE-CH-2000-1-28-ctrl-1mark

For a feedback control system to be stable, the

• roots of the characteristics equation should be real
• poles of the closed loop transfer function should lie in the left half of the complex plane
• Bode plots of the corresponding open loop transfer function should monotonically decrease
• poles of the closed loop transfer function should lie in the right half of the complex plane

GATE-CH-2002-1-15-ctrl-1mark

A first order system with unity gain and time constant $\tau$ is subjected to a sinusoidal input of frequency $\omega =1/\tau$. The amplitude ratio for this system is

• 1

• 0.5

• $1/\sqrt{2}$
• 0.25

GATE-CH-2002-2-16-ctrl-2mark

The frequency response of a first order system, has a phase shift with lower and upper bounds given by

• $[-\mathrm{\infty },\pi /2]$

• $[-\pi /2,\pi /2]$

• $[-\pi /2,0]$

• $[0,\pi /2]$

GATE-CH-2010-24-ctrl-1mark

The transfer function, $G(s)$, whose asymptotic Bode diagram is shown below, is

• $10s+1$

• $s-10$

• $s+10$

• $10s-1$

GATE-CH-2012-25-ctrl-1mark

The Bode stability criterion is applicable when

• Gain and phase curves decreases continuously with frequency
• Gain curve increases and phase curve decreases with frequency
• Gain curve and phase curve both increases with frequency
• Gain curve decreases and phase curve increases with frequency

GATE-CH-1992-19-b-ctrl-6mark

For the loop above, determine: 

(i) The maximum gain for stable operation.
{#1}

(ii) The corresponding frequency of oscillation (rad/min).
{#2}

GATE-CH-1997-26-ctrl-2mark

The open loop transfer function for a process is ${\displaystyle \frac{1}{4(3s+1{)}^4}}$, where the time constant is in minutes.
Determine: 

(i) the crossover frequency (rad/min)
{#1}

(ii) the ultimate gain.
{#2}

GATE-CH-2000-14-ctrl-5mark

A feedback control loop with a proportional controller has an open loop transfer function $G_L(s)={\displaystyle \frac{K_c}{s(5s+1{)}^2}}$ where time is in minutes.

(i) The crossover frequency in radians/min = _________

{#1}

(ii)The ultimate controller gain = _________

{#2}

GATE-CH-2006-84-85-ctrl-4mark

For the system shown below, $G_1(s)={\displaystyle \frac{1}{{\tau }_{1}s+1}}$, $G_2(s)={\displaystyle \frac{1}{{\tau }_{2}s+1}}$ and ${\tau }_2=2{\tau }_1$.

 
When the system is excited by the sinusoidal input $X(t)=\sin \omega t$, the intermediate response $Y$ is given by $Y=A\sin (\omega t+\varphi )$. 

(i) If the response $Y$ lags behind the input $X$ by 45${}^{\circ }$ and ${\tau }_1=1$, then the input frequency $\omega$ is
{#1}

(ii) For the same input, the amplitude of the output $Z$ will be
{#2}

GATE-CH-1998-2-21-ctrl-2mark

The frequency response of a dynamic element shows a constant magnitude ratio at all frequencies. The element exhibits a negative phase shift at all frequencies. The absolute value of the phase shift increases linearly with frequency. The element has the transfer function

• $e^{-\tau s}$

• ${\displaystyle \frac{{\tau }_{1}s+1}{{\tau }_{2}s+1}}$

• ${\displaystyle \frac{{\tau }_{1}s}{{\tau }_{2}s+1}}$

• ${\displaystyle \frac{{\tau }_{1}s+1}{{\tau }_{2}s}}$

GATE-CH-2000-2-23-ctrl-2mark

The time constant of a unity gain, first order plus time delay process is 5 min. If the phase lag at a frequency of 0.2 rad/min is 60^o, then the dead time (in minutes) is

• $5\pi /12$
• $\pi /6$
• $\pi /12$
• $\pi /3$

GATE-CH-2001-2-18-ctrl-2mark

An ideal PID controller has the transfer function $[1+{\displaystyle \frac{1}{0.5s}}+0.2s]$. The frequency at which the magnitude ratio of the controller is 1, is

• 0.5/0.2

• 0.2/0.5

• 0.2$\times$0.5

• $1/\sqrt{0.2\times 0.5}$

GATE-CH-2003-77-ctrl-2mark

Find the ultimate gain and frequency for a proportional controller in the case of a process having the following transfer function

$$G_p(s)=\frac{1}{(4s+1)(2s+1)(s+1)}$$

• ${\displaystyle \omega =\frac{1}{\sqrt{14}};K_c=\frac{45}{7\sqrt{14}}}$

• ${\displaystyle \omega =\sqrt{\frac{7}{6}};K_c=\frac{46}{3}}$

• $\omega =1;K_c=13$

• ${\displaystyle \omega =\sqrt{\frac{7}{8}};K_c=\frac{45}{4}}$

GATE-CH-2004-80-ctrl-2mark

Consider a system with open-loop transfer function

$$G(s)=\frac{1}{(s+1)(2s+1)(5s+1)}$$

Match the range of $\omega$ (frequency) in Group I with the slope of the asymptote of the $\log \text{AR}$ (amplitude ratio) versus $\log \omega$ plot in Group II.

Group I	Group II
(P) $0<\omega <0.2$	(1) $-5$
(Q) $\omega >1$	(2) $-3$
	(3) $-2$
	(4) $-1$
	(5) $$zero

• P-5, Q-2

• P-4, Q-2

• P-5, Q-3

• P-4, Q-1

GATE-CH-2005-50-ctrl-2mak

The value of ultimate period of oscillation $P_u$ is 3 minutes, and that of the ultimate controller gain $K_{cu}$ is 2. Select the correct set of tuning parameters (controller gain $K_c$, derivative time constant ${\tau }_D$ in minutes, and the integral time constant ${\tau }_I$ in minutes) for a PID controller using Ziegler-Nichols controller settings.

• $K_c=1.1;{\tau }_I=2.1;{\tau }_D=1.31$

• $K_c=1.5;{\tau }_I=1.8;{\tau }_D=0.51$

• $K_c=1.5;{\tau }_I=1.8;{\tau }_D=0.51$

• $K_c=1.2;{\tau }_I=1.5;{\tau }_D=0.38$

GATE-CH-2006-58-ctrl-2mark

A process is perturbed by a sinusoidal input, $u_t=A\sin \omega t$. The resulting process output is $Y(s)={\displaystyle \frac{KA\omega }{(\tau s+1)(s^2+{\omega }^2)}}$. If $y(0)=0$, the differential equation representing the process is

• ${\displaystyle \frac{dy(t)}{dt}}+\tau y(t)=Ku(t)$

• $\tau {\displaystyle \frac{dy(t)}{dt}}+y(t)=KAu(t)$

• $\tau {\displaystyle \frac{dy(t)}{dt}}+y(t)=Ku(t)$

• ${\displaystyle \tau [{\displaystyle \frac{dy(t)}{dt}}+y(t)]=KAu(t)}$

GATE-EE-2013-A-15-ctrl-1mark

The Bode plot of a transfer function $G(s)$ is shown in the figure below.

The gain $(20\log |G(s)|)$ is 32 dB and -8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all $\omega$. Then $G(s)$ is

• ${\displaystyle \frac{39.8}{s}}$

• ${\displaystyle \frac{39.8}{s^2}}$

• ${\displaystyle \frac{32}{s}}$

• ${\displaystyle \frac{32}{s^2}}$

GATE-IN-2014-23-ctrl-1mark

A plant has an open-loop transfer function, $$G_p(s)=\frac{20}{(s+0.1)(s+2)(s+100)}$$ The approximate model obtained by retaining only one of the above poles, which is closest to the frequency response of the original transfer function at low frequency is

• ${\displaystyle \frac{0.1}{s+0.1}}$
• ${\displaystyle \frac{2}{s+2}}$
• ${\displaystyle \frac{100}{s+100}}$
• ${\displaystyle \frac{20}{s+0.1}}$

GATE-CH-2017-51-ctrl-2mark

The open loop transfer function of a process with a proportional controller (gain $K_c$) is $$G_{OL}=K_c\frac{e^{-2s}}{s}$$ Based on Bode criterion for closed-loop stability, the ultimate gain of the controller, rounded to 2 decimal places, is ______

• Answer

GATE-CH-2018-44-ctrl-2mark

Consider the following transfer function: $$G(s)=\frac{3}{(5s+1{)}^2}$$ where, the natural period of oscillation is in min. The amplitude ratio at a frequency of 0.5 rad/min is ________ (rounded off to second decimal place).

• Answer

GATE-CH-2019-49-ctrl-2mark

For the closed loop system shown in figure, the phase margin (in degrees) is ___________

• Answer

GATE-IN-2014-46-ctrl-2mark

The transfer function of a system is given by ${\displaystyle G(s)=\frac{e^{-s/500}}{s+500}}$. The input to the system is $x(t)=\sin 100\pi t$. In periodic steady state the output of the system is found to be $y(t)=A\sin (100\pi t-\varphi )$. The phase angle ($\varphi$) in degree is _______

• Answer

GATE-CH-1999-2-18-ctrl-2mark

Each item given in the left-hand column is closely associated with a specific characteristic listed in the right-hand column. Match each of the items with the corresponding characteristic.

• I. Transportation lag

Answer 1D. Unstable responseC. HyperbolicF. Phase angle is $-{90}^{\circ }$E. Increase in phase marginB. Phase lag is proportional to frequencyA. Increase in gain margin

• II. Control valve

Answer 2D. Unstable responseC. HyperbolicF. Phase angle is $-{90}^{\circ }$E. Increase in phase marginB. Phase lag is proportional to frequencyA. Increase in gain margin