Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 3141708 Control Theory Previous Question Paper

Seat No.: ________

Enrolment No.___________

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE - SEMESTER? IV EXAMINATION ? SUMMER 2020**

**Subject Code: 3141708**

**Date:27/10/2020**

**Subject Name: Control Theory**

**Time: 10:30 AM TO 01:00 PM**

**Total Marks: 70**

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**MARKS**

**Q.1 (a)**Differentiate between open loop and close loop system

**03**

**(b)**For mechanical translational system. Write the analogous

**04**

electrical elements in force voltage and force-current analogy.

**(c)**Explain standard Test signals & derive equation of steady state

**07**

e

rror.

**Q.2 (a)**Define transfer function and Explain importance of Laplace

**03**

transform in control system.

**(b)**Explain following terms with necessary diagrams. (1) Delay Time

**04**

(2) Rise Time (3) Peak Time (4) Steady state error

**(c)**For the given mechanical system Write down differential

**07**

equations, mechanical circuit diagram and obtain force-current

analogy.

**OR**

**(c)**What is force voltage analogous system? Which are the analogues

**07**

quantities according to this method?

**Q.3 (a)**State the limitation of Routh criterion and how these limitations

**03**

are overcome by Root Locus.

**(b)**Explain the mathematical model of thermal system.

**04**

**(c)**A linear feedback control system has the block diagram shown in

**07**

Figure. Using block diagram reduction rules, obtain overall

transfer function C(S)/R (S).

1

**OR**

**Q.3 (a)**Derive unit step response of a first order system.

**03**

**(b)**By means of Routh criterion, determine the stability of the system

**04**

described by characteristic equations.

S4+8S3+18S2+16S+5=0

Comment on location of the roots.

**(c)**For the signal flow graph shown in Figure, using Masson's gain

**07**

formula determine the overall transfer function C/ R.

**Q.4 (a)**Define pole, zero and order of a system.

**03**

**(b)**Explain Performance Indices.

**04**

**(c)**List all the rules to construct a root locus and explain.

**07**

**OR**

**Q.4 (a)**Derive expression of KP, KV, KA for Type `0' control system

**03**

**(b)**Define and explain following terms with respect to frequency

**04**

response (i) Gain Margin (ii) Phase Margin

**(c)**Explain Sensitivity of Control Systems to Parameter Variations.

**07**

**Q.5 (a)**Define : 1) state variable, 2) state vector, 3) state space

**03**

**(b)**With example explain the location of the roots of characteristics

**04**

equation for the stable control system.

**(c)**Sketch the root locus for the given open loop transfer function

**07**

()()= K /s (s + 2)(s + 3)

**OR**

**Q.5 (a)**Explain the Nyquist stability criterion.

**03**

**(b)**Sketch polar plot for the system with open loop transfer function

**04**

is ()(

)= 1/(s + 4)(s + 2)

**(c)**Sketch the Bode plot and determine the gain margin and phase

**07**

margin for the given unity feedback control system.

()()= k / s (1+0.02s)(1 + 0.04s).

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This post was last modified on 04 March 2021