# Anna University Model Question Paper BE VI sem I&CE MODERN CONROL SYSTEM

ANNA UNIVERSITY :: CHENNAI – 600 025

MODEL QUESTION PAPER

VI – SEMESTER

B.E. INSTRUMENTATION AND CONTROL ENGINEERING

IL333 – MODERN CONROL SYSTEM

Time: 3hrs                                                                                                           Max. Marks: 100

PART – A (10 x 2 = 20 Marks)

1.         Define state of a system?

1. The transfer function of the system is given by

Y(s)/U(s)   =  10/4s2 + 2s + 1.

Determine the differential equation governing the system.

3.         What is meant by full order and reduced order observer?

4.         What are the differences between linear system and non-linear system?

5.        What is a singular point?

6.         What is meant by Jump resonance?

7.         State optimal control law.

8.         State Pontryagain’s minimum principle.

9.         What is the need for adaptive control?

10.       What is meant by tuning of controller? Give two examples.

PART – B (5 x 16 = 80 Marks)

11.       A single input system is described by the following sate equation

 .

 .

x1                    -1         0          0          x1                     10

 .

x2        =          1          -2         0          x2         +          1          u

x3                    2          1          -3         x3                     0

Design a state feed back controller which will give closed loop poles at –1 + 2i, -1 – 2i, -6                                                                                                                                                 (16)

 .
 .
 .

12.a)    A linear second order servo system is described by the equation

e+2δωne+ωn2 e = 0. Determine the singular points. Construct the phase trajectory, using the method of Isocline.                                                                                  (16)

## OR

12.b)    Consider a unity feed back system as shown in Fig.1 having a saturating amplifier with gain K. Determine the maximum value of K for the system to be stable. What would be the frequency and nature of limit cycle for a gain of K = 2.5                                         (16)

 G(s) = 1/s(1+0.5s) (1+4s)
 r(s)
 c(s)
 e(s)
 u(s)
 e = 1
 K
 +
 –
 Slope = K

Fig.1

13.a)i)  Explain any four non-linearity phenomena.                                                                       (8)

ii)  Derive the describing function for relay with dead zone.                                                 (8)

## OR

13.b)i)  Explain the second method of Liapunov’s stability theorem.                                           (8)

ii)  Explain Popov’s stability criteria.                                                                                     (8)

 .

14.a)    Test whether sufficient conditions for the existence of the asymptotically stable optimal control solution for the plant.

X         =          0          0          x          +          1          u

0          1                                  1

∞

with the performance index J = ∫0(x1+ u2 )dt. Determine the optimal state feedback control, the stability of the optimal closed-loop system and the minimum value of J for x1(0) = 1 and x2(0) = 2.                                                                                                    (16)

##### OR

∞

14.b)i)  Find the optimal control law which minimizes the performance index J = ∫0 (x2 + u2)dt       for the system

using Ricatti equation.                                                                                          (8)

 .

ii)    Consider the second order system as shown in Fig.2 where it is desirable to find optimum to minimize the integral square error J=  dt for initial condition c(0) = 1,c(0) = 0.

(8)

 1/s(s+2)
 r =0
 e
 c
 +
 –

Fig.2

15.a)i)  Explain in brief the different configurations and classifications of MRAC with a help of block diagrams.                                                                                                                           (16)

###### OR

15.b)i)  Explain the block diagram representation of self-tuning controller.                                 (8)

ii)  How can the parameter estimation and control law be implemented in self-tuning controller?                                                                                                                          (8)

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