GATE-CH-0800-1-ctrl-1mark

The characteristic equation of a process is: \[ C = \frac{G_1G_2}{1+G_1G_2H}R + \frac{G_2}{1+G_1G_2H}U\] The open-loop transfer function is:

• \(G_1G_2H\)

• \(1+G_1G_2H\)

• \(\dfrac{G_2}{1+G_1G_2H}\)

• \(\dfrac{G_1G_2}{1+G_1G_2H}\)

GATE-CH-1995-1-r-ctrl-1mark

The root locus method, a pole of a transfer function \(G(s)\) is the value of \(s\) for which \(G(s)\) approaches:

• \(-1\)

• 0

• 1

• \(\infty \)

GATE-CH-1997-1-25-ctrl-1mark

The open-loop transfer function of a process is \(K\dfrac {(s+1)(s+4)}{(s+2)(s+3)}\). In the root locus diagram, the poles will be at

• \(-1,-4\)

• \(1,4\)

• \(-2,-3\)

• \(2,3\)

GATE-CH-1998-1-23-ctrl-1mark

The Root locus plot of the roots of the characteristic equation of a closed loop system having the open loop transfer function \[ \frac {K(s+1)}{s(2s+1)(3s+1)} \] will have a definite number of loci for variation of \(K\) from 0 to \(\infty \). The number of loci is

• 1

• 3

• 4

• 2

GATE-CH-2010-5-ctrl-1mark

Match the location of the poles/zeros in the \(s\)-plane, listed in GROUP I, with the system response characteristics in GROUP II.

GROUP I	GROUP II
P. Pole in the right half plane	I. Stable response
Q. Pole at origin	II. Integrating response
R. Zero in the right half plane	III. Unstable response
	IV. Inverse response

• P-I, Q-II, R-III
• P-III, Q-IV, R-I
• P-III, Q-II, R-IV
• P-I, Q-IV, R-III

GATE-CH-2014-9-ctrl-1mark

Integral of the time-weighted absolute error (ITAE) is expressed as

• \(\displaystyle \int_0^\infty \frac{|\epsilon(t)|}{t^2}dt\)
• \(\displaystyle \int_0^\infty \frac{|\epsilon(t)|}{t}dt\)
• \(\displaystyle \int_0^\infty t|\epsilon(t)|dt\)
• \(\displaystyle \int_0^\infty t^2|\epsilon(t)|dt\)

GATE-CH-1993-26-b-ctrl-5mark

A closed loop feedback control system consists of a second order process \[ G_p(s) = \frac {K_p}{(\tau _1s + 1) (\tau _2s + 1)} \] and a proportional controller \(G_c(s) = K_c\). The roots of characteristic equation of the closed loop system are \(-2\) and \(-1\) in absence of controller and roots are \(-1.5 \pm 0.5i\) when \(K_c = 4\).

(A) Determine (i) \(K_p\), (ii) \(\tau _1\), (iii) \(\tau _2\). 

(i) \(K_p\)
{#1}

(ii) \(\tau _1\)
{#2}

(ii) \(\tau _1\)
{#3}

(B) Determine the maximum value of \(K_c\) so that the response of the system to a step input is non-oscillatory.
{#4}

GATE-CH-1994-28-ctrl-5mark

The characteristic equation of a closed loop control system is \[s^4 + 4 s^3 + 6 s^2 + 2 s + 3 = 0 \] The system is

• stable

• unstable

GATE-CH-1999-2-17-ctrl-2mark

Which of the systems having the following transfer functions is stable?

• \(1/(s^{2} + 2)\)

• \(1/(s^{2} -2s + 3)\)

• \(1/(s^{2} + 2s + 2)\)

• \(e^{-20s}/(s^{2} + 2s - 1)\)

GATE-CH-2005-47-ctrl-2mark

Given the characteristic equation below, select the number of roots which will be located to the right of the imaginary axis \[ s^4+5s^3-s^2-17s+12=0\]

• One
• Two
• Three
• Zero

GATE-CH-2009-42-ctrl-2mark

The characteristic equation of a closed loop system using a proportional controller with gain \(K_c\) is \[ 12 s^3+19 s^2 + 8s + 1 + K_c = 0\] At the onset of instability, the value of \(K_c\) is

• 35/3
• 10
• 25/3
• 20/3

GATE-CH-1997-27-ctrl-5mark

A control system is shown below.

Using the Routh test, determine the value of \(K_c\), at which the system just becomes unstable.

• Answer

GATE-CH-1998-24-ctrl-5mark

The characteristic equation of a closed loop control system is \[0.25 s^3 + 0.8 s^2 + 5.6 s + 1 + 0.35 K = 0 \] Find the limiting value of \(K\), above which the closed loop system will be unstable.

• Answer

GATE-IN-2014-50-ctrl-2mark

Consider a transport lag process with a transfer function \(G_p(s)=e^{-s}\). The process is controlled by a purely integral controller with transfer function \(G_c(s)=K_i/s\) in a unity feedback configuration. The value of \(K_i\) for which the closed loop plant has a pole at \(s=-1\), is _________

• Answer

GATE-CH-1995-29-ctrl-5mark

The transfer function of a process, measuring device, controller and control valve, respectively is given by \[ G_p = \frac {K_p}{(s+1)(s+4)}; \quad \quad G_m=1; \quad \quad G_c=K_c; \quad \quad G_v=1 \] The root locus diagram of the system is given in figure.

• [(a)] Identify locations of point \(A\) and \(B\).
• [(b)] At \(K_c=1\), the roots of the system are located at point \(C\). Identify the location of point \(C\).
• [(c)] Determine the value of \(K_p\).

• Answer