Programme(s) Semester Course Code (S) Course Title BE 03 17MT305 Theory of Control Systems Course Outcomes

Regulation – 2017
Programme(s) Semester Course Code (s) Course Title

BE 03 17MT305 THEORY OF CONTROL SYSTEMS
COURSE OUTCOMES
C305.1 Impart the knowledge on basic components of control systems, various time domain,
frequency domain specifications, basic controllers and Characteristics equation of system
for stability
C305.2 Interpret various time domain and frequency domain tools for analysis and design of
linear control systems
C305.3 Apply the various techniques for determining transfer function of a system and to design
compensators
C305.4 Analyze the stability of systems from transfer function forms
C305.5 Evaluate the steady state error of various type and order of a system
PART A - 2 Marks BT CO
1. Distinguish the open loop and closed loop control systems. U C305.1
2. List the some of the applications for open loop and closed loop R C305.1
control system.
3. Define transfer function. R C305.1
4. Write the analogous electrical elements in force current analogy for A C305.1
the elements of mechanical translational system.
5. translational
Write system?
the torque balance equations for C305.1
a. Ideal rotational mass element A
b. Ideal rotational Dash-pot
c. Ideal rotational spring
6. Summarize the properties of signal flow graph. U C305.3
7. Write the mason’s gain formula. R C305.3
8. What is linear time invariant system? R C305.1
9. Why is negative feedback preferred in a closed loop system? R C305.1
10. Write the rule for moving the summing point ahead of a block. A C305.3
11. Define type and order of a system R C305.5
12. Give the response of first order system to a unit step input U C305.2
13. What is the effect of PID controller on the system performance? R C305.1
14. How the system is classified depending on the value of damping? R C305.2
15. Name the test signals used in time response analysis. R C305.1
16. What is the type of damping in the system C(s)/R(s) = 10/S2 +7S+10? A C305.1
17. Represent the time domain specifications with a neat sketch. U C305.1
18. What are static error constants? R C305.5
19. What is the effect on system performance when a proportional C305.1
AP
integral controller is introduced in a system?
20. What is steady state error? R C305.5
21. What is frequency response? R C305.1
22. List out the different frequency domain specifications. R C305.2
23. Define phase margin and gain Margin U C305.2
24. How do you calculate the gain margin from the polar plot? A C305.2
25. How do you find the stability of the system by using polar plot? A C305.4
26. Determine the Phase angle of the given transfer function A C305.3
G(S)=10/S(1+0.4S)(1+0.1S)
27. What is cut off frequency? R C305.2
28. What are the main advantages of Bode plot? R C305.3
29. Draw the polar plot of the function G(S) =1/S(S+T1)(1+ST2). A C305.4
30. The damping ratio and natural frequency of oscillation of a second E C305.2
order system is 0.5 and 8 rad/sec respectively. Calculate the resonant
peak and resonant frequency.
31. What is BIBO stability? R C305.4
32. Write down the characteristic equation for C(s)/R(s) = 9/(S2 +20S+9) A C305.4
33. Define Routh Hurwitz stability Criterion. R C305.4
34. What are the conditions required for a system to be stable? R C305.4
35. Define dominant poles and zeros. U C305.4
36. State Nyquist stability criteria. R C305.4
37. What are the applications and advantages of Routh – Hurwitz AP C305.4
criterion?
38. How will you find the root locus on real axis? A C305.4
39. What are the main significances of root locus? R C305.4
40. Define the terms asymptotes, centroid and Breakaway points in root R C305.4
locus.
41. What is the principle of compensation? What are the types of U C305.3
compensation?
42. What are all the advantages of the lag compensators? R C305.3
43. Sketch the diagram of the lead compensator. A C305.3
44. Under what circumstance is a lead compensators are preferred? Why? AP C305.3
45. Enumerate the design steps involved in the phase lead compensation. R C305.3
46. Compare the lead, lag, lag-lead compensation. U C305.3
47. What are the features of feedback compensation? R C305.3
48. What is the difference between controller and compensator? U C305.3
49. What are the applications of lead lag compensators? AP C305.3
50. What are the limitations of Lead compensators? A C305.3
PART B - 16 Marks BT CO Mark

Questions can be either one division with 16 Marks or (10+6) Marks or (8+8) s
Marks
1. (i) Write the Differential equations governing the mechanical

rotational system shown in fig. and find the transfer function.
A C305.1
10
(ii) Find out the transfer function of the circuit shown in fig. 6
R C305.1
2. (i) Write the differential equation governing the mechanical A 16

1 translational systems and find the transfer function. Draw the
force voltage and force current electrical analogies.
C305.1
3. (i) Describe the transfer function for the armature and field C305.1
1 controlled DC Motor. R 16
4. (i) Use Block diagram reduction technique finds the transfer

1 function for the system shown in fig.
A
C305.3
16
5. (i) Draw a signal flow graph and find the closed loop transfer
1 function for the block diagram shown in fig.
AP
C305.3
16
6. (i) An Unity feedback system is characterized by an open loop

transfer function, G(S)=K/S(S+10).Determine the gain ‘K’, so A C305.2 16
that the system will have a damping ratio of 0.5 for this value of
K. Determine rise time, peak time, peak overshoot, settling time
and delay time subjected to a unit step input.
7. (i) An unity feedback system is characterized by the following A 8
C305.2
open loop transfer function G(s) = (0.4S+1)/S(S+0.6). Determine
the response C(t) for unit step input and sketch the response.
(ii) The open loop transfer function of a unity feedback system is E C305.5 8
G(S)=50/S(1+0.1S). Determine the error series of the system for
r(t)=1+2t+t2 and hence the steady state error.
8. (i) For a unity feedback control system the open loop transfer E C305.5
function G(S) =10(S+2)/S2(S+1). Find (i) position, velocity and 8
acceleration error constants.(ii) The steady state error when the
input is R(S) where R(S) =3/S –2/S2 +1/3S3
ii) Write short notes on PID mode of feedback control AP C305.1 8
9. (i) A positional control system with velocity feedback is shown
in fig. What is the response of the system for unit step input?
U C305.2
10
(ii) Write short notes on PD feedback controller. AP C305.1 6

The open loop transfer function of a unity feedback system
16
is given by G(S) =K/S (ST+1), where K and T are positive
10 i) U C305.2
constant. By what factor should the amplifier gain K be
reduced, so that the peak overshoot of unit step response
of the system is reduced from 75% to 25%.
Plot the Bode diagram for the following transfer function
and obtain the gain and phase cross over frequencies.
E C305.3 16
11 i) G(S) =K S / (1+0.2S) (1+0.02S).
2
Determine the value of K for a gain cross over

frequency of 20 rad/sec.
12 i) The open loop transfer function of a unity feedback system is C305.3 16
G(S) = 1/ S (1+S) (1+2S) Sketch the Polar plot and determine the A
Gain margin and Phase margin.
13 i) The open loop transfer function of a system is given by C305.3
16
G(S) =K/S(1+0.5S)(1+0.2S). Using bode plot find the value
E
of K so that i)The gain margin of the system is 6db and
ii)Phase margin of the system is 25⁰.
14 i) The open loop transfer function of a system is given by C305.3
A 16
G(S)=K/S(S2+S+4). Using polar plot, determine the value
of K, so that phase margin is 50⁰. What is the
corresponding value of gain margin?
15 i) Derive the correlation between time and frequency C305.3 8
AP
response analysis.
ii) Find out the resonant frequency and resonant peak value C305.3 8
U
for the system whose transfer function is given by
C(S)/R(S)= 5/S2+2S+5.
16 i) The characteristics equation of the system is given by S6+S5+2S4- AP C305.4 16
3S3-7S2-4S-4=0 Investigate the stability of the system using Routh
– Hurwitz criterion array and find the number or roots which lie
in the right half and the left half of the S-Plane
17 i) The open loop transfer function of a unity feedback control A 16
system is given by G(s)=K/(S+2)(S3+10S2+49S+100) C305.4
a) Examine the range of values of gain K, Using Routh –
Hurwitz criterion array for the system to be stable.
b) Also determine the value of K which causes sustained
oscillation in the system and then determine the
frequency of sustained oscillation
18 i) A unity feedback control system has an open loop transfer A C305.4 16
function G(S) = K (S+9) / S (S2+4S+11).Sketch the root locus.
19 i) Sketch the root locus of the system whose open loop transfer A 16
function is C305.4
G(S) = K / S (S+2) (S+4).
Find the value of K so that the damping ratio of the closed loop
system is 0.5.
20 i) Sketch the Nyquist plot for the system whose open loop transfer AP 16
function is C305.4
G(S) = K / S (S+2) (S+10).
Determine the range of k for which closed loop system is stable.
21 i) Consider a unity feedback uncompensated system with the AP 16
open loop transfer function as G(S)= 5/S(S+2). Design a lag C305.3
compensator for the system such that the compensated system
has static velocity error constant Kv=20 Sec-1, Phase margin
Pm=55⁰, and Gain margin gm=12db
22 i) Consider a unity feedback uncompensated system with the AP C305.3 16

open loop transfer function as G(S)= K/S(S+1). Design a lead
compensator for the system such that the compensated system
has static velocity error constant Kv=12 Sec-1, Phase margin
Pm=40⁰.
23 i) Consider a unity feedback uncompensated system with the AP 16
open loop transfer function as G(S)= K/S(S+1)(S+2). Design a C305.3
Lag- Lead compensator for the system such that the
compensated system has static velocity error constant Kv=10
Sec-1, Phase margin Pm=50⁰, and Gain margin gm>-10db
24 i) Explain the steps involve involved in the design of lag-Lead U C305.3 16
compensator using bode plot
25 i) A unity feedback system with forward path transfer function A 16
G(S)=K/S(1+0.3S)(1+0.5S)is to have C305.5
a) The velocity error constant Kv>-10 Sec^-1
b) Phase margin >-30deg. Design a suitable phase lag
compensator to meet the above specifications.
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Regulation – 2017

Programme(s) Semester Course Code (s) Course Title

PART B - 16 Marks BT CO Mark

1. (i) Write the Differential equations governing the mechanical

2. (i) Write the differential equation governing the mechanical A 16

4. (i) Use Block diagram reduction technique finds the transfer

6. (i) An Unity feedback system is characterized by an open loop

(ii) Write short notes on PD feedback controller. AP C305.1 6

Determine the value of K for a gain cross over

22 i) Consider a unity feedback uncompensated system with the AP C305.3 16

Faculty In-charge Course Coordinator Head of the Department

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