Question Paper Code: 11287
Electronics and Communication Engineering EC 2255 Control Systems Time: Three Hours
1. Dene open-loop a nd closed-loop control systems.
2. Write down t he transfer function o f the system whose block diagram is shown below.
3. How a control system is classied depending on t he value of damping? 4. Why derivative controller i s not used i n control system? 5. What i s meant by Corner frequency in frequency response analysis?
4 21Part A - (10 x 2 = 20 marks)
Answer ALL Questions
4Maximum: 100 marks
B.E./B.Tech.Degree Examinations, April/May 2011 Regulations 2008
6. Draw the circuit of lead compensator a nd draw its pole zero diagram. 7. State th e rule for obtaining t he breakaway point i n root locus. 8. Dene stability o f a system.
9. Name the methods of state space representation for phase variables. 10. What is meant by quantization?
Part B - (5 x 16 = 80 marks)
11. (a) (i) Consider t he mechanical system shown below. Identify th e variables a nd write t he dierential equation. (6)
(ii) Draw t he torque-voltage electrical analogous circuit for the following mechanical system shown . (4)
(iii) Obtain th e transfer function of t he following electrical network.
OR 11. (b) (i) A block diagram shown below.
Construct th e equivalent Signal Flow Graph a nd obtain
(8) (ii) For t he block diagram shown below, nd t he output C due to R and disturbance D. (8)
12. (a) (i) The unity feedback system is characterized by an open loop transfer function K . Determine t he gain K , so that th e system will have a damping G(s) = s(s + 10) ratio o f 0.5. For this value o f K , determine settling time, peak overshoot a nd time to peak overshoot for a unit step input. (8) K1 (2s + 1) (ii) A unity feedback system has the forward transfer function G(s) = . s(5s + 1)(1 + s)2 The input r(t) = (1 + 6t) is applied to the system. Determine th e minimum value o f K1 , if t he steady error i s to be less than 0.1. (8) 12. (b) With suitable block diagrams and equations, explain th e following types of controllers employed i n control systems: (1) Proportional controller (4) (2) Proportional-plus-integral controller (4) (3) PID controller (4) (4) Integral controller (4)
4 21OR 3
C using Masons formula. R
13. (a) Given G(s) =
13. (b) The open loop transfer function o f a unity feedback control system i s Gf (s) = k . s(s + 1)(s + 2)
Design a suitable lag-lead compensator so as to meet t he following specications: Static velocity error constant Kv = 10 sec1 , phase margin = 50 and Gain margin 10 dB. (16) 14. (a) (i) A unity feedback system is characterized by the open-loop transfer function, G(s) = (s + 2)(s3 k . + 10s2 + 49s + 100)
Using Routh-Stability criterion, calculate th e range o f values o f K for system to be stable. Determine t he value of K , which will cause sustained oscillations in t he closed loop system. Also determine the frequency of sustained oscillations. (10) (ii) State t he rules for construction o f t he Root-locus for a feedback system. (6) OR
14. (b) Draw the Nyquist plot for th e system whose open loop transfer function is G(s)H (s) = K . s(s + 2)(s + 10)
Determine t he range of K for which t he closed loop system i s stable. 15. (a) The state space representation o f a system is given below: 2 1 0 0 x 1 x1 x 2 = 0 3 1 x2 + 0 u x 3 x3 3 4 5 1 x1 x2 y= 0 1 0 x3
Obtain the transfer function. 11287
21(16) (16) (16)
Ke0.2s , nd K for th e following two cases: s(s + 2)(s + 8) (i) gain margin equal to 6 db (ii) Phase margin equal to 45 .
OR 15. (b) Write the state equations for th e system shown below i n which x1 , x2 a nd x3 constitute t he state vector.
Determine whether the system is completely controllable and observable.