Ec2255 Cs Qb

UNIT 1 CONTROL SYSTEM MODELING

PART A 1. What is system and control system? 2. What are the types of control system and explain it? 3. Write the application for open loop and closed loop control system. 4. Distinguish the open loop and closed loop control systems. 5. What are the components of control system? 6. Define transfer function. 7. What is differential equation? 8. What are the basic elements used for modeling mechanical translational

system?

9. Write the force balance equation for a. Ideal mass element b. Ideal Dash-pot c. Ideal spring

10. What are the basic elements used for modeling mechanical rotational system? 11. Write the torque balance equations for

a. Ideal rotational mass element b. Ideal rotational Dash-pot c. Ideal rotational spring

12. What are all the two types of electrical analogous of mechanical system? 13. What is Block diagram? 14. What are all the components of Block diagram? 15. What is a signal flow graph? 16. What is transmittance? 17. Define non-touching loops. 18. Write the properties of signal flow graph. 19. Write the masons gain formula. 20. Compare the block diagram representation and signal flow graph.

PART B 1. Write the Differential equations governing the mechanical translational

system shown in fig. and find the transfer function.

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2. Find the transfer function Y2(S) / F(S)

3. Write the Differential equations governing the mechanical rotational system

shown in fig. and find the transfer function.

4. Write the differential equation governing the mechanical translational systems

and find the transfer function. Draw the force voltage and force current electrical

analogies.



5. Derive the transfer function for the armature and field controlled DC Motor.

6. Find the transfer function C(S)/R(S) for the system shown in fig.

7. Using Block diagram reduction technique finds the transfer function for the

system shown in fig.

8. For the Block diagram shown in fig. Find C1 / R1 and C2 / R1.



9. Find the overall gain C(S) / R(S) for the signal flow graph shown in fig.

10. Obtain the overall gain C(S) / R(S) for the signal flow graph shown in fig.



11. Draw a signal flow graph and find the closed loop transfer function for the

block diagram shown in fig.

UNIT 2 TIME RESPONSE ANALYSIS

PART A

1. What is time response? 2. What is transient and steady state response? 3. Define pole and zero. 4. What is first order and second order systems? 5. What is the order of a system? 6. Distinguish between type and order of a system. 7. How the system is classified depending on the value of damping? 8. What are all the time domain specifications? 9. Define delay time and rise time. 10. Define peak overshoot and settling time. 11. With a neat sketch explain all the time domain specifications. 12. What will be the nature of response of a second order system with different types

of damping?

13. What is damped frequency of oscillation? 14. What is steady state error? 15. What are static error constants? 16. What is the effect on system performance when a proportional controller is

introduced in a system?

17. What is the effect of PI controller on the system performance?



18. What is the effect of PID controller on the system performance?

PART B 1. Derive the expressions and draw the response of first order system for unit Step input.

2. Draw the response of second order system for critically damped case and when

input is unit step.

3. Derive the expressions for second order system for under damped case and

when the input is unit step.

4. Derive the expressions for Rise time, Peak time, Peak overshoot, delay time.

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

response of the system for unit step input?

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.

7. The unity feedback system is characterized by an open loop transfer function is

G(S)= K / S(S+10). Determine the gain K ,so that the system will have a damping ratio of 0.5.For this

value of K, determine settling time, Peak overshoot and time to Peak overshoot

for a unit-step input.

8. A system has open loop transfer function as:

G(S) H(S) = 10/ S(S+5) Find the undamped natural frequency, the damping ratio, the damped natural

frequency, rise time, peak time, peak overshoot and the settling time with 2 %

criterion.

9. Find the static error coefficients for a system whose T/F is,

G(S) H(S) =10/ S (1+S) (1+2S)

And also find the steady state error for r (t) =1+ t + t2/2.

10. 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 Polynomial r(t) = a0 +a1t +a2 /2

t2

11. For a system G(S) H(S) = K/S2

(S+2) (S+3). Find the value of K to limit

steady state error to 10 when input to system is 1+10t+40/2 t2

12. Explain P, PI, PID, PD controllers

UNIT 3

FREQUENCY RESPONSE ANALYSIS

PART A 1. What is frequency response?

2. List out the different frequency domain specifications?

3. Define resonant Peak (r)? 4. Define Resonant frequency (f)? 5. What is bandwidth?

6. Define Cut-off rate?

7. Define Gain Margin? 8. Define Phase cross over?

9. What is phase margin?

10. What is Bode plot?

11. What are the main advantages of Bode plot?

12. Define Corner frequency?

13. What is polar plot?

14. Define gain cross over frequency?

15. Define Phase cross over frequency?

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

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

18. State Nyquist stability Criterion.

19. What are the two segments of Nyquist contour.

20. Compare bode plot and Nyquist plot analysis.

21. What are M circles?

22. What are N circles?

24. What is Nichols chart?

25. What are two contours of Nichols chart?

26. How is the Resonant Peak (Mr), resonant frequency (Wr ) ,and bandWidth

determined from Nichols chart?

27. What are the advantages of Nichols chart?

28 What is compensation? And compensator?

29. What are the different types of compensator available?



30. What are the two types of compensation schemes?

31. What is series compensation?

32. What is feedback compensation?

33. When lag/lead/lag-lead compensation is employed?

34. What are the uses of lead compensator?

35. What is lag compensation?

36. Draw the electrical lag network?

37. Draw the pole-zero plot of lag compensator?

38. What are the characteristics of lag compensation?

39. Draw the bode plot of lag compensator?

40. What is lead compensation?

41. Draw the electrical lead compensator network?

42. Draw the bode plot of lead compensator?

43. What is lag-lead compensation?

44. What is lag-lead compensator?

45. Draw electrical lag-lead compensator network?

46. Write transfer function of lag-lead compensator?

47. Compare series compensator and feed back compensator?

PART B 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)

2. 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)


over Frequency, Gain margin and Phase margin.

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

4. 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.


over Frequency, Gain margin and Phase margin.

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

6. 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.

7. 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)

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+10)

9. 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.

10. 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.

11. 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.

12. Using Nichols chart determine the gain margin, phase margin and bandwidth

of the system described by

GH(S) = 2/S (1+S) (1+S/3).

13. For a certain system,

G(S) = K / S (S+1) ( S+2). Design a suitable lag - lead compensator to give, velocity error constant = 10

sec-1

, phase margin = 50, gain margin 10 dB.

14. For a certain system,

G(S) = 0.025/S (1+0.5 S) (1+0.05 S). Design a suitable lag compensator to give, velocity error constant = 20 sec

-1,

phase margin = 40

15. A unity feedback system has an OLTF

G(s) = K / s(s+2)(s+60).

Design a Lead-Lag compensator is to meet the following specifications.

(i) P.M is atleast 40, (ii) Steady state error for ramp input 0.04 rad.



UNIT 4 STABILITY ANALYSIS

PART A 1. Define stability.

2. What is the necessary condition for stability?

3. Define Relative stability.

4. Define Routh Hurwitz stability criterion.

5. What is root locus? Explain with suitable example.

6. Write a note on angle and magnitude condition of root locus.

7. What is direct root locus, inverse root locus and root contours?

8. What are root loci.

9. What are the effects adding open loop poles and zero on the nature of the root

locus and on system?

10. Explain the terms: i.Asymptodes ii.Centroid iii.Breakaway point

11. Explain the method of calculating breakaway point.

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

13. What are the main significances of root locus.

14. What is a dominant pole?

PART B 1. Apply Routh criterion to check the stability of

S6 + 9S

5 + 20S

4 + 12S

3 + 8S

2 + 16S+16 = 0

2. For K = 2, determine whether the following unity feedback system is stable.

Use Routh criterion.

G(S) = K (1+2S) (1+4S) /S2 (S

2 + 2S + 10)

3. Find the range of K for stability of s4 +2s

3 + 2s

2 + (3+K)s + K = 0 ,for k>0


G(S) = K / S (S2+4S+13).Sketch the root locus

5. Sketch the root locus of the system whose open loop transfer function is

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.


G(S) = K (S+9) / S (S2+4S+11).Sketch the root locus.

7. Sketch the root locus of the system whose open loop transfer function is



G(S) = K / S (S+4) (S2+4S+20).

8. Determine the stability of closed loop system by Nyquist stability criterion,

whose open loop transfer function is given by,

G(S) H(S) = (s+2)/(s+1)(s-1).

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

G(S) = K / S (S+2) (S+10). Determine the range of k for which closed loop system is stable.

10. 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 k for which closed loop system is stable.

UNIT 5

STATE VARIABLE ANALYSIS AND DIGITAL CONTROL SYSTEMS

PART A

1. Explain the concept of state.

2. Define state variables and state vectors.

3. What is state trajectory?

4. Define state space.

5. Explain the advantages of state variable method over conventional method.

6. Derive the transfer function from state model.

7. What are the different methods of state variable representations?

8. Elaborate upon the basis of selecting suitable state variables for a system.

9. What is characteristics equation of a system matrix A?

10. What is homogeneous and nonhomogeneous state equation?

11. Define state transition matrix using classical method.

12. What is zero input response and zero state response?

13. What is Jordans canonical form? 14. Obtain the complete solution of nonhomogeneous state equation using time

domain method and Laplace transform method.

15. State the properties of state transition matrix.

16. Define the various methods of obtaining state transition matrix from state model.



PART B

1. Obtain the state model for the block diagram shown.

U(S) Y(S)

2. Obtain the state model in standard Bush form of a system shown in fig.

U(S)

Y(S)

-

3. Obtain the transfer function of the system having state model.

X (t) = -5 -1 2

3 -1 X (t) + 5 u(t)

Y (t) = 1 2X (t)

1/S

1/S +1

1/S +2

S+3 / S(S+10)

4/(S+1)

24/ (S+8)



4. Obtain the solution of nonhomogeneous state equation using laplace transform

method.and explain laplace transform method of obtaining eAt.

5. Obtain the complete solution of nonhomogeneous state equation using time

domain method.

6. Explain the concepts of controllability and observability



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Ec2255 Cs Qb