GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-V (NEW) EXAMINATION - WINTER 2020
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Subject Code: 2150909 Date: 22/01/2021Subject Name: Control System Engineering
Time: 10:30 AM TO 12:30 PM Total Marks: 56
Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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| MARKS | |
| Q.1 | |
| (a) Describe the components and variables of biological control system involved in walking in a prescribed direction. | 03 |
| (b) Write the difference between open loop and closed loop control system. | 04 |
| (c) Explain transfer function and write its advantages and disadvantages. | 07 |
| Q.2 | |
| (a) Name the analogous electrical elements in force-voltage analogy for the elements of mechanical translational system. | 03 |
| (b) Can a signal flow graph be drawn for nonlinear system? State Mason’s gain formula. | 04 |
| (c) Reduce the block diagram shown in Figure 1 to a single transfer function C(s)/R(s) using block diagram reduction technique. | 07 |
R(s) + 1 + 50 + C(s)
— > —
- 52 = s+1 A
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2 |e5 2
Figure 1
| Q.3 | |
| (a) Define the following terms | 03 |
| 1) Delay time 2) Rise time 3) Peak time | |
| (b) Distinguish between type and order of a control system. | 04 |
| (c) Find the steady-state errors for inputs of 5u(t), 5tu(t), and 5t2u(t) to the system shown in Figure 3. The function u(t) is the unit step. | 07 |
R(s) + E(s) o 120(s + 2) C(s)»
(s+3)(s+4)
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Figure 3| Q.4 | |
| (a) Define the following terms. | 03 |
| (b) Explain standard test signals used in control system. | 04 |
| (c) The closed loop transfer function of unity feedback control system is given by | 07 |
c(s) _ 100
R(s) ~ s2+8s+100
Determine
- Damping ratio
- Natural undamped resonance frequency
- Percentage peak overshoot
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| Q.5 | |
| (a) What are the conditions to be satisfied for the Root locus to exist at any point in the s-plane? | 03 |
| (b) Write a short note on the correlation between time and frequency responses. | 04 |
| (c) For the closed loop transfer function | 07 |
T(s) = 10 / (s8 + 1.25s7 + 12.5s6 + 22.5s5 + 39s4 + 59s3 + 48s2 + 38s + 20)
Check stability of the system. Find how many poles are in the right-half plane? Using Routh-Hurwitz stability criterion
| Q.6 | |
| (a) What is a Root locus? How can you tell from the Root locus if a system is unstable? | 03 |
| (b) Explain how do you determine the gain crossover frequency and phase crossover frequency from the Bode plot? | 04 |
| (c) The unity feedback system has | 07 |
G(s)H(s) = k / (s(s+5)(s+10))
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Draw the rough sketch of the Root locus.
| Q.7 | |
| (a) Define the Bode plot. What do you mean by an-approximate Bode plot? | 03 |
| (b) Briefly explain about Polar plots. | 04 |
| (c) Sketch the Bode plots for the transfer function given below: | 07 |
G(S)H(S) = 200 / ((S+2)(S+5)(S+10))
| Q.8 | |
| (a) By applying the final-value theorem, find the final value of f(t) whose Laplace transform is given by | 03 |
F(s) = 5 / (s(s+1))
| (b) State Nyquist .stability criterion. Why the Nyquist criterion is called a frequency response method? | 04 |
| (c) Derive Overall transfer function of Field controlled DC motor. | 07 |
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