# Anna University Model Question Paper BE VI sem I&CE CONTROL SYSTEMS

MODEL PAPER

B.E. DEGREE EXAMINATION.

Fourth Semester

Instrumentation and Control Engineering

IL 231 — CONTROL SYSTEMS

Time : Three hours                                                                        Maximum : 100 marks

Graph sheet, Semi log sheet, Polar sheet may be provided.

PART A — (10 ´ 2 = 20 marks)

1. Give the governing equation for the system shown in Figure 1.
 M
 x
 O
 Spring Constant = K
 Mass = M
 F = Force
 Displacement x

Figure 1

1. Derive the overall transfer function of a closed loop system.
2. What is PI and PID controller?
3. Define different types of error coefficient.
4. Define gain margin and phase margin.
5. What is the significance of –1 + j0 point?
6. State and explain Nyquist stability criteria.
7. When does a particular row becomes zeroes in Routh array table?
8. What is the need for compensation?
9. What are the time specifications to meet in a system design?

PART B — (5 ´ 16 = 80 marks)

1. (i)      Find the stability of the system whose characteristics equation is given by .                                                                                (4)

(ii)     Find the transfer function  for the signal flow graph shown in Figure 11 (ii) using Mason’s gain formula.              (12)

 G3(s)
 G6(s)
 G5(s)
 G10(s)
 G8(s)
 G4(s)
 G9(s)
 G7(s)
 G2(s)
 G1(s)
 R(s)
 C(s)
 1
 1

Figure 11(ii)

1. (a)     (i)      What is the response of the second order system for step input? From this derive the expression for rise time and peak overshoot time.                                                               (8)

(ii)    With an example, explain how an addition of pole/zero will change the performance of a system.                                (8)

Or

(b)     Draw the root–locus curve for the open loop transfer function  and obtain the following :

(i)      Centroid

(ii)    Angle of asymptotes

(iii)   Breakaway point

(iv)    Intersection of root locus with imaginary axis

(v)     The range of k for which the system is stable.

1. (a)     Draw the bode plot for the transfer function  and find the phase margin and gain margin from the plot.

Or

(b)     (i)      What is M and N circle? How do they relate with Nichols Chart? What is the use of this chart?                                 (6)

(ii)    How do you find the frequency response of a closed non unity feedback system using Nichols Chart?                 (8)

(iii)   What is non–minimum phase system? Explain.                              (2)

1. (a)     (i)      State and prove the stability criteria for BIBO system.                (4)

(ii)    Test the stability using Nyquist Criteria for the closed loop system given the open loop transfer function .                 (12)

Or

(b)     (i)      Find the number of positive roots of the given polynomial using Routh criteria .                                      (8)

(ii)    How is the relative stability of two systems are compared using bode plot?                                                    (8)

1. (a)     Derive the transfer function of an armature controlled DC motor.

Or

(b)     How can a compensation technique improve the performance of a system? Explain with an example.

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