**DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING**

**QUESTION BANK**

**SUBJECT CODE : SEM / YEAR : 4 / III**

**SUBJECT NAME : CONTROL SYSTEMS**

__UNIT I__

CONTROL SYSTEM MODELLING

PART – A (2 Marks)CONTROL SYSTEM MODELLING

PART – A (2 Marks)

1. What is a system?

2. Define transfer function.

3. What do you mean by sensitivity of the control system?

4. Write Mason’s gain formula.

5. What is control system?

6. What are the two major types of control systems?

7. Define open loop and closed loop systems.

8. What is feedback? What type of feed back is employed in control system?

9. Why negative feedback is preferred in control systems?

10. Distinguish between open loop and closed loop systems.

11. State principle of superposition theorem.

12. What is time variant and Time invariant?

13. What is mathematical model of a system?

14. Write force balance equation of ideal spring, ideal mass.

15. Name the two types of electrical analogous for mechanical system.

16. What is signal flow graph?

17. Define non-touching loop.

__PART – B (16 Marks)__1. Write the differential equations governing the Mechanical system shown in fig .and

determine the transfer function.(16)

2. Determine the transfer function Y2(S)/F(S) of the system shown in fig.

(16)

3. Write the differential equations governing the Mechanical rotational system shown in

fig. Draw the Torque-voltage and Torque-current electrical analogous circuits.

(16)

4. Determine the overall transfer function C(S)/R(S) for the system shown in fig.(16)

5. Obtain the closed loop transfer function C(S)/R(S) of the system whose block

diagram is shown in fig.

(16)

6. For the system represented by the block diagram shown in fig. Determine C1/R1

and C2/R1.(16)

7. Obtain the closed loop transfer function C(S)/R(S_ of the system whose block

diagram is shown in fig.(16)

8. Find the overall gain of the system whose signal flow graph is shown in fig.

(16)

9. Draw a signal flow graph and evaluate the closed loop transfer function of a system

whose block is shown in fig.

(16)

10. Derive the transfer function for Armature controlled DC servo motor. (16)

11. Derive the transfer function for Field controlled DC servo motor. (16)

__UNIT II__

TIME RESPONSE ANALYSIS

PART – A (2 Marks)TIME RESPONSE ANALYSIS

PART – A (2 Marks)

1. What is time response?

2. What is transient and steady state response?

3. Name the test signals used in time response analysis.

4. Define step signal.

5. Define Ramp signal and parabolic signal.

6. What is an impulse signal?

7. How is system classified depending on the value of damping?

8. Sketch the response of a second order under damped system.

9. What is damped frequency of oscillation?

10. The closed-loop transfer function of second order system is

C(S)/R(S) =10/ S2 +6S +10. What is the type of damping?

11. List the time domain specifications.

12. Define rise time, delay time, peak time.

13. What is steady state error?

14. What are static error constants?

15. Define position, velocity error constants.

16. What are generalized error constants?

17. List the advantages of generalized error constants.

__PART B (16 Marks)__**1. (a)Derive the expressions and draw the response of first order system for unit step**

input. (8)

(b) Draw the response of second order system for critically damped case and when

input is unit step. (8)

2. Derive the expressions for Rise time, Peak time, Peak overshoot. (16)

3. A potential control system with velocity feedback is shown in fig. What is the

response of the system for unit step input?(16)

4. Measurements conducted on a Servomechanism show the system response to be

c(t)=1+0.2 ê 60t-1.2 ê –10 t. when subjected to a unit step. Obtain an expression for

closed loop transfer function. (16)

5. A positional control system with velocity feedback is shown in fig. What is the

response c(t) to the unit step input. Given that ς =0.5.and also calculate rise time, peak

time, Maximum overshoot and settling time.(16)

6. A unity feedback control system has an open loop transfer function G(S) = 10/S(S+2).

Find the rise time, percentage over shoot, peak time and settling time. (16)

7. A closed loop servo is represented by the differential equation, where c is the

displacement of the output shaft, r is the displacement of the input shaft and e= r-c.

Determine undamped natural frequency, damping ratio and percentage maximum

overshoot for unit step input. (16)

8. For a unity feedback control system the open loop transfer function

G(S) = 10(S+2)/ S2 (S+1).

Find (a) position, velocity and acceleration error constants.

(b) The steady state error when the input is R(S) where R(S) =3/S –2/S2 +1/3S3(16)

9. The open loop transfer function of a servo system with unity feed back system is

G(S) = 10/ S(0.1S+1).Evaluate the static error constants of the system. Obtain the

steady state error of the system when subjected to an input given by the polynomial

r(t) = a0 +a1t +a2 /2 t2 . (16)

__UNIT III__

FREQUENCY RESPONSE ANALAYSIS

PART – A ( 2 Marks)FREQUENCY RESPONSE ANALAYSIS

PART – A ( 2 Marks)

**1. What is frequency response analysis?**

2. What is Nichol’s chart?

3. What are the two contours of Nichols chart?

4. What are the advantages of Nichol’s chart?

5. Draw the polar plot of the function G(S) =1/S(S+T1)(1+ST2)

6. Determine the Phase angle of the given transfer function

G(S) = 10 / S (1+0.4S) (1+0.1S)

7. What is polar plot?

8. Define gain cross over frequency

9. Define Phase cross over frequency

10. Define Phase Margin

11. Define Gain Margin

12. How do you calculate the gain margin from the polar plot?

13. How do you find the stability of the system by using polar plot?

14. What are the advantages of Bode plot?

15. List the Frequency domain specifications

16. What is minimum phase system?

17. What is non-minimum transfer function?

18. What is cut off frequency?

19. Compare bode plot and Nyquist plot analysis.

20. What is Bandwidth?

21.What is lag-lead compensation?

22. What is lag-lead compensator?

23. Draw electrical lag-lead compensator network

24. Write transfer function of lag-lead compensator?

25. Compare series compensator and feed back compensator

__PART – B (16 Marks)__1. Plot the Bode diagram for the following transfer function and obtain the gain and

phase cross over frequencies.

G(S) = 10/ S(1+0.4S) (1+0.1S) (16)

2. The open loop transfer function of a unity feed back system is G(S) = 1/ S(1+S)

(1+2S) Sketch the Polar plot and determine the Gain margin and Phase margin. (16)

3. Sketch the Bode plot and hence find Gain cross over frequency ,Phase cross over

frequency, Gain margin and Phase margin.

G(S) = 0.75(1+0.2S)/ S(1+0.5S) (1+0.1S) (16)

4. Sketch the Bode plot and hence find Gain cross over frequency ,Phase cross over

frequency, Gain margin and Phase margin.

G(S) = 10(S+3)/ S(S+2) (S2+4S+100) (16)

5. Sketch the polar plot for the following transfer function .and find Gain cross over

frequency, Phase cross over frequency, Gain margin and Phase margin.

G(S) = 10(S+2)(S+4)/ S (S2 -3S+10) (16)

6. Construct the polar plot for the function GH(S) =2(S+1)/ S2. find Gain cross over

frequency ,Phase cross over frequency, Gain margin and Phase margin. (16)

7. Plot the Bode diagram for the following transfer function and obtain the gain and

phase cross over frequencies.

G(S) =KS2 / (1+0.2S) (1+0.02S). Determine the value of K for a gain cross over

frequency of 20 rad/sec. (16)

8. Sketch the polar plot for the following transfer function and find Gain cross over

frequency, Phase cross over frequency, Gain margin and Phase margin.

G(S) = 400/ S (S+2)(S+!0) (16)

9. A unity feed back system has open loop transfer function G(S) = 20/ S

(S+2)(S+5).Using Nichol’s chart determine the closed loop frequency response and

estimate all the frequency domain specifications. (16)

10. Sketch the Bode plot and hence find Gain cross over frequency ,Phase cross over

frequency, Gain margin and Phase margin.

G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S). (16)

11. Write the short notes on correlation between the time and frequency response? (16)

12. What is compensation? Why it is needed for control system? Explain the types of

compensation? (16)

13. Realize the basic compensators using electrical network and obtain the transfer

function. (16)

14. Design a suitable lead compensators for a system with unity feedback and having

open loop transfer function G(S)= K/ S(S+1) (S+4) to meet the

specifications.(i)Damping ratio=0.5 (ii) Undamped natural frequency Wn =2 rad/sec.

(16)

15. A unity feed back system has an open loop transfer function G(S)= K/ S(S+1)

(0.2S+1).Design a suitable phase lag compensators to achieve following

specifications Kv= 8 and Phase margin 40 deg with usual notation. (16)

16. Explain the procedure for lead compensation and lag compensation? (16)

17. Explain the design procedure for lag- lead compensation. (16)

18. Consider a type 1 unity feed back system with an OLTF Gf(S) =K/S (S+1) (S+4).

The system is to be compensated to meet the following specifications Kv > 5sec and

PM>43 deg. Design suitable lag compensators

__UNIT IV__

STABILITY ANALYSIS

PART – A (2 Marks)STABILITY ANALYSIS

PART – A (2 Marks)

1. What are the two methods of designing a control system?

2. What is the time domain specification needed to design a control system?

3. What is the frequency domain specification needed to design a control system?

4. State Nyquist stability Criterion.

5. What is root locus?

6. What is the necessary condition for stability?

7. What is characteristic equation?

8. How the roots of characteristic are related to stability?

9. Define stability.

10. What do you mean by dominant pole?

11. What are break away points?

12. How will you find the root locus on real axis?

__PART – B (16 Marks)__**1. Using Routh criterion determine the stability of the system whose characteristics**

equation is S4+8S3+18S2+16S+5 =0 . (16)

2. F(S)=S6 +S5-2S4-3S3-7S2-4S1-4 =0.Find the number of roots falling in the RHS plane

and LHS plane. (16)

3. Draw the Nyquist plot for the system whose open loop transfer function is

G(S)H(S) =K/S (S+2) (S+10).Determine the range of K for which closed loop

system is stable.(16)

4. Construct Nyquist plot for a feedback control system whose open loop transfer

function is given by G(S)H(S) =5/ S(1-S).comment on the stability of open loop

and closed loop transfer function.(16)

5. Sketch the Nyquist plot for a system with the open loop transfer function G(S)H(S)

=K(1+0.5S) (1+S) / (1+10S) (S-1).determine the range of values of K for which the

system is stable. (16)

__UNIT V__

STATE VARIABLE ANALYSIS & DIGITAL CONTROL SYSTEMS

PART – A (2 Marks)STATE VARIABLE ANALYSIS & DIGITAL CONTROL SYSTEMS

PART – A (2 Marks)

1. What is sampled data control system?

2. Write the advantages and disadvantages of sampled data control system.

3. State sampling theorem.

4. What is periodic sampling?

5. What are hold circuits & explain it.

6. What are the problems encountered in a practical hold circuits?

7. What are the methods available for the stability analysis of sampled data control

system?

8. What are the advantages of state face analysis?

9. What are state variables?

10. What are phase variables?

__PART B (16 Marks)__**1. Write notes on controllability and absorbability. (16)**

2. Explain sampling theorem briefly and sample & hold operation. (16)

3. Explain stability analysis of sampled control system and Jury’s stability. (16)

4. Explain state space representation for descries time system. (8)

5. Explain state space representation for continues time system. (8)

6. Explain the solution for state equation for discrete time system. (8)

7. Explain the solution for state equation for continues time system (8)

8. Explain jury’s stability test. (16)