Posted Date: 18 Aug 2012      Posted By:: S.Jaya Abirami    Member Level: Bronze  Points: 5 (Rs. 4)

# 2012 Anna University of Technology Tiruchirappalli B.E Electrical and Electronics Engineering EE 1354 – Modern control systems (As per Trichy Anna University syllabus) for B.E(EEE) of May/June 2012 Question paper

 Course: B.E Electrical and Electronics Engineering University/board: Anna University of Technology Tiruchirappalli

18th Aug 2012...This question paper is for those who are preparing for EE 1354 - Modern control systems examination for EEE students in sixth semester under Trichy Anna University syllabus. This will help you to get an idea for attending the examination.

# EE 1354 – Modern control systems (As per Trichy Anna University syllabus)

## May/June 2012 Question paper :< /H2>

### Part-A: 1. Define state and state variable.2. Define controllability.3. Explain sampling theorem.4. What is Zero order hold?5. What is Observability?6. Define sampling time of a discrete time systems?7. Compare linear and Non-Linear systems.8. Define dead zone Non-Linearity.9. Draw the functional block of MIMO systems.10. Define decoupling.

#### Part-B:

11.a) (i) Develop the state model of a linear system and draw the block diagram of state model. (8)
(ii) Obtain the Eigen values, Eigen vectors, modal matrix and Jordan form of matrix. (8)
A = -4 1 0
0 -3 1
0 0 -2

(or)
b) (i) Explain the pole placement design of continuous time system with a suitable example. (8)
(ii) Consider the system described by the state equation. (8)
.
x(t) = A(t)X(t) + b(t)U(t)

Where A(t) = 1 e^-t b = 0
0 -1 1
Is this system is controllable at t=0? If yes, find the minimum energy control to drive it from x(0) = 0 to x^1 = 1 at t=1.
1

12.a) (i) Explain the signal reconstruction and sampling theorem. (8)
(ii) Explain any four Z-Transforms theorem in detail. (8)
(Or)
b) (i) Explain the response of sampled data system to step and ramp inputs. (8)
(ii) Explain the Jurys test for a discrete time system and comment your conclusions. (8)

13. a) (i) What is the effect of Pole placement by state feedback? (8)
(ii) Consider the system defined by

X(K+1) = FX(K)
Y(K) = CX(K)

Where F = -1 1
1 -2

C = 1 0
Design a full order state observer. The designed Eigen values for the observer matrix are (mu)1 = 0.8 and (mu)2 = 0.6 (8)
(or)
b) (i) Explain the effect of state feedback on controllability. (8)
(ii) What are the effect of sampling time on controllability? Explain. (8)

14.a) (i) State and explain Liapunov stability theorem.
(ii) Consider the second order system described by
.
x1 = 0 1 x1
. *
x2 -1 -1 x2
The equilibrium state is origin. Determine stability of the system using Liapunov method.
(or)
b) Draw the phase trajectory of the system described by the equation
.. . 2
x + x + x = 0. Comment on stability of the system. (16)

15. a) (i) What is MIMO system? What are the different models of MIMO system? Explain. (8)
(ii) Explain the transfer function representation of MIMO system. (8)
(or)
b) Explain the following:
(i) Multivariable Nyquist plot. (8)
(ii) Model predictive control. (8)

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