Instrumentation and Process Control GATE-2015

Q 1. Match the output signals as obtained from four measuring devices in response to a unit step change in the input signal.

A) P-IV, Q-III, R-II, S-I
B) P-III, Q-I, R-II, S-IV
C) P-IV, Q-I, R-II, S-III
D) P-II, Q-IV, R-III, S-I

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Q 2. The transfer function for the disturbance response in an open-loop process is given by G_d^{open}\left(s\right) . The corresponding transfer function for the disturbance response in a closed-loop feedback control system with proportional controlled is given by G_d^{closed}\left(s\right) . Select the option that is ALWAYS correct {O[G(s)] represents order of transfer function G(s)}:

A) O\left\lfloor G_d^{open}\left(s\right)\right\rfloor=O\left\lfloor G_d^{closed}\left(s\right)\right\rfloor
B) O\left\lfloor G_d^{open}\left(s\right)\right\rfloor\neq O\left\lfloor G_d^{closed}\left(s\right)\right\rfloor
C) O\left\lfloor G_d^{open}\left(s\right)\right\rfloor\geq O\left\lfloor G_d^{closed}\left(s\right)\right\rfloor
D) O\left\lfloor G_d^{open}\left(s\right)\right\rfloor\leq O\left\lfloor G_d^{closed}\left(s\right)\right\rfloor

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Q 3. Which one of the following transfer functions, upon a unit step change in the disturbance at t = 0, will show a stable time domain response with a negative initial slope (i.e., slope t = 0):

A) G\left(s\right)=\frac1{s+1}-\frac2{s+4}
B) G\left(s\right)=\frac1{s+1}+\frac2{s+4}
C) G\left(s\right)=\frac1{s+1}+\frac2{s-4}
D) G\left(s\right)=\frac1{s-1}+\frac2{s-4}

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Q 4. The block diagram for a process with feedback control for output deviation variable h is shown in the figure below. All transfer functions are given with pre-factor of s in minutes. A unit step change is made in the set-point at t = 0. The time required for h to reach 50% of its ultimate value, in minutes (up to two decimal places), is: __________________

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Q 5. Consider a control system with the open loop transfer function given by:

G_{OL}\left(s\right)=\frac{K_ce^{-0.3s}}{1.5s+1}

In the above function, pre-factor of s is in minutes and K_c­is the gain of proportional controller. The frequency for phase margin of 30^o is 4.04 rad/min. The value of K_c for a gain margin of 1.7 (up to one decimal place) is _______________.

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