No. of Printed Pages: 4 IBIEEE-009I B.Tech. -VIEP -ELECTRICAL ENGINEERING (BTELVI) Term-End Examination June, 2016 00036
BIEEE-009 DIGITAL CONTROL SYSTEM DESIGN
Time: 3 hours Maximum Marks: 70
Note: Attempt any seven questions. (iiJ All questions carry equal marks.
(iii) Use of scientific calculator is permitted. (ivJ Missing data, ifany; may be suitably assumed.

1. Determine pulse transfer function for the system shown in Figure 1. 5 <img src='./qimages/11249-1a.jpg'> <br>

Determine Z-transform of the function sin wt. 5

2. What is the trapezoidal rule of zero order hold Draw the block diagram of mathematical model for ZOH. 5

Explain multirate discrete data systems in detail. 5

3. State and explain Cayley-Hamilton theorem for computation of state transition matrix. 5

Explain the procedure for pole placement design, using state feedback for a SISO system. 5

4. Define critical gain. 5

For the open loop transfer function Ak

Write down the expression for critical gain. Assume all the poles and zeros be situated at real axis.

A system is represented by z^2 -0.25. Use bilinear transformation z r 1 1 to test the stability of where r is a complex variable. 5

5. A system has to be designed with maximum damping factor of o1. Use pictorial presentation to show mapping for s-plane to z-plane. 5

A lag compensator may be represented as
1 wT/1 BwT where B 1. Draw the approximate Bode plot on plain paper to show gain and phase over frequency.

6. Write one benefit of using PI controller. A PI controller may be represented as . 5

D(W)=Kp KI/W

On a plain paper draw the approximate sketch of Bode plot of PI controller by suitably converting the expression for

A system z 0.5 is cascaded with a digital controller

0.5)

For a step input show that the response is deadbeat. 5

7. Consider the matrix,

1 1 2
F 0 1 3
0 0 2

Determine eigenvalues and eigen vectors.

For a discrete data system, the state feedback control locus is given as u -KX .

Given, F 1 0 g 0
0 1.105 0.105

Desired closed loop system is given as
z2 -1.5894 z 0.6971 0
Verify whether the system is controllable. 5

8. A state space model is given as 5

X(k

where,

A 0 1 B 0
-1 -2 1

Using G [gl g2] test the controllability of AB.

Describe the causes and effects of loss of controllability and observability due to sampling. 5

9. Attempt any two of the following: 2x5=10 Pulse transfer function in z-domain Nyquist stability criterion Computer base simulation