Download GTU BE/B.Tech 2018 Winter 7th Sem New 2172007 Modern Control Systems Question Paper

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Subject Code: 2172007

GUJARAT TECHNOLOGICAL UNIVERSITY

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BE - SEMESTER-VII (NEW) EXAMINATION - WINTER 2018
Subject Name: Modern Control Systems
Date: 03/12/2018
Time: 10:30 AM TO 01:00 PM
Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Using suitable block diagram, explain ON-OFF control systems. 03

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(b) Using suitable block diagrams, explain disturbance signals and their effects on the control systems? 04
(c) List various characteristics of feedback control systems and explain any two of them using block diagram and mathematical equations. 07

Q.2 (a) Define (i) centroid (ii) asymptotes (iii) dominant pole 03
(b) How locations of closed-loop pole decide the transient response of the system? Explain using suitable examples. 04
(c) What is lag compensator? What are the effects of lag compensator? Explain design steps for design of lag compensator using root locus technique. 07

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OR

Q.2 (a) For the control system represented by block diagram in Figure 1, design a lead compensator using root locus technique, such that wn=4 rad/sec and damping ratio= 0.5 for the compensated system. 07

Figure 1

Q.3 (a) List the advantages of frequency domain analysis of a control system. 03

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(b) With suitable diagrams define (i) Phase crossover frequency (ii) Gain crossover frequency (iii) Phase margin (iv) gain margin. 04
(c) A unit step input is applied to a unity feedback control system having open loop transfer function
K / s(1+sT)
Determine the value of K and T to have Mp=20% and resonant frequency wr= 6 rad/sec. Calculate the resonant peak (Mr). 07

OR

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Q.3 (a) List various effects of adding a pole in a given control system. 03
(b) Explain various effects of phase lead compensation. 04
(c) Explain design procedure to design phase lead compensation using bode plot technique. 07

Q.4 (a) List the advantages of state space approach of analyzing the control systems. 03
(b) Draw and explain block diagram of a linear system in state variable form. 04

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(c) A system is described by the following differential equation. Represent the system in state space. 07
d³y/dt³ + 3 d²y/dt² + 4 dy/dt + 8y = u₁(t) + u₂(t) + u₃(t)
And outputs are:
Y1= dy/dt + 3u1
Y2 = d²y/dt² +4u2+u3

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OR

Q.4 (a) Define (i) state variables (ii) state vector (iii) state space 03
(b) Compute state transition matrix for A = [[-1, 1], [0, -2]] 04
(c) Explain Taylor series expansion for computing the state transition matrix. 07

Q.5 (a) For sampled data control system, explain the effect of sampling period on steady state error. 03

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(b) Derive solution of state equation using Laplace transform method 04
(c) Using suitable block diagram, explain sampling process of a continuous time system. 07

OR

Q.5 (a) Explain observability for a state space system using suitable block diagram. 03
(b) Using suitable block diagram, explain pulse transfer function of systems in series. 04

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(c) Determine the stability of a sampled data control system having following characteristic polynomial 07
2z⁴+3z³+2z²-2z+1=0

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