ANNA UNIVERSITY :: CHENNAI - 600 025 MODEL QUESTION PAPER(V-SEMESTER) B.E. ELECTRONICS AND COMMUNICATION ENGINEERING EC334 - CONTROL SYSTEMS Time: 3hrs Max Marks: 100 Answer all Questions PART - A (10 x 2 = 20 Marks) 1. Derive the transfer function of the network shown in fig 1. 2. Write the differential equations of the mechanical system shown in fig 2. 3. Calculate the time response of the following system if the input r(t) is an unit impulse 4. Plot the time response of the first order system to a unit step and unit ramp input. 5. Write the transfer function of a PID controller. 6. Write the Hurwitz determinant for the system given by the characteristic equation 4s 3 + 2s 2 + 5s + 7 = 0 7. State the magnitude criterion with reference to a root locus plot.
8. Draw the frequency magnitude plot for an under damped and over damped second order system. 9. Mention any two functions of a compensator in a control system. 10. Draw the circuit of a lead compensator. PART - B (5 x 16 = 80 Marks) 11. The polarized solenoids shown in fig 3 produces a force proportional to the current in the coil. The coil has resistance R and inductance L. Write the differential equations of the system 12.a)i) Derive an expression for the peak over shoot of a second order system for an unit step input. ii) A mechanical vibratory system and its response when 2kg of force(step input) applied to the system is shown in fig 4. Determine the M, B and K of the system. (OR) 12.b) For the control system shown in fig 5, find the steady state error without the proportional and derivative (PD) controller for a unit ramp input. Show that with the PD controller this error can be made to zero for a specific
value of K. 13.a) For a feedback control system G(s) = K / (s+1) (s+3) (s+4) Calculate the value of K at which the system would become oscillatory in the closed loop [H(s) = 1], and obtain the frequency of such oscillations. Also, find the value of K so that the real parts of all the roots will be less than - 1. (OR) 13.b) Sketch the root locus plot of a unity feedback system with an open loop transfer function G(s) = K / s (s+2) (s+4) Determine the value of K so that the dominant pair of complex poles of the system has a damping ratio of 0.5. 14.a)i) Show that the constant M locus in G- plane is a circle for all values of M except M=1 ii) The open loop transfer function of a unity feedback control system is G(s) = K / s (1+0.1s) (1+s) Draw the Bode diagram and analyze the stability of the system for K =10. (OR) 14.b) The open loop transfer function of a feedback system is given by G(s) = K / s (T1s+1) (T2s+1) Draw the Nyquist plot. Derive an expression for gain K in terms of T1, T2 and specific gain margin G m. 15.a) A Unity feedback system has an open loop transfer function of G(s) = K / s (s+1) (s+5) Draw the root locus plot and determine the value of K to give a damping ratio of 0.3 A network having a transfer function of 10(1 +10s) /(1 +100s) is now introduced in tandem. Find the new value of K, which gives the same damping ratio for the closed -loop response. Compare the velocity error constant and settling time of the original and the compensated systems 15.b) A servomechanism has an open loop transfer function of G(s) = 10 / s (1+0.5s) (1+0.1s) Draw the Bode plot and determine the phase and gain margin. A networks having the transfer function (1+0.23s)/(1+0.023s) is now introduced in tandem. Determine the new gain and phase margins. Comment upon the improvement in system response caused by the network
EC 227 Control Systems Time: 3 Hours Max. Marks: 60 1. Answer Question No. 1 ( Part A) and any four of the remaining seven (Part B) 2. All parts of a Question must be answered in one place, otherwise they will not be valued. 3. Figures in the right hand margin indicate marks allotted. PART A 1. Answer the following. 10x2=20 a) What are the advantages of a closed-loop system? b) Compare the terms stability & sensitivity. c) The impulse response of a system is e-0.2t. Determine the transfer function of the system. d) How does the performance of an automatic control system is effected by a positive feedback signal. e) State Mason s gain formula. f) Define rise time and settling time. g) What are the effects of adding poles and zeros to the transfer function? h) State the advantages of frequency domain analysis. i) What will happen if a zero is added in the forward path of a second-order system? j) Define a series-parallel compensation. PART B Answer any four of the following. If you attempt more than four questions, only the first four in order will be valued. 2. Obtain the overall transfer function C/R from the signal flow graph shown: (10) 3. a) Determine the mathematical model for the system shown in the figure. (5) b) Derive the transfer function of field controlled dc servomotor. (5) 4. Measurements conducted on a servomechanism show the system response to be C(t)= 1 + 0.2 e-60t 1.2 e-10t when subjected to a unit-step input. a) Obtain the expression for the closed-loop transfer function.
b) Determine the undamped natural frequency and damping ratio of the system. (10) 5. Sketch the root locus diagram for the feedback control system having the following open-loop transfer function. Assume that K will take all positive values from 0 to. G(s) = (10) 6. Draw the Bode plot of a closed-loop system which has the open-loop transfer function. G(s)H(s) = Determine the maximum value of T for system to be stable. (10) 7. Write short notes on the following: a) Effect of derivative control on transient and steady state performance of f.b.control system. (5) b) Discuss lead compensator. Sketch the Bode plot of a lead compensator and give the design steps of a lead compensator. (5) 8. a) Explain Routh-Hurwitz criterion. (4) b) Investigate the stability of the system with characteristic equation. s5+2s4+24s3+48s2 25s 50 = 0 Also find all the roots of this equation. (6)
DEGREE EXAMINATION, 2007. Fifth Semester Electronics and Communication Engineering EC 1304- CONTROL SYSTEMS (Regulation 2004) Time: Three hours (Provide Polar graph, Answer ALL questions. PART A- (10 x2=20 marks) Maximum: 100 marks 1. Differentiate between positional servomechanism and rate servomechanism. 2. What is an error detector in a control system? 3. Write the force equation for the system shown: 4. Find the output for the block diagram given below:
How the transient response of a system with feedback differ to that without. feedback? 6. Why are differentiators generally not used in systems? 7. State the effect of addition of poles in a Root Locus. 8. Nichols chart can be used to determine response. 9. Draw the polar plot of a lag lead compensator. 10. A tachometer has a gain of 0.05 Determine the output voltage when the shaft speed is 20 PART B-(5x 16= 80 marks) 11. (a) Obtain the analogous electrical network for the system given below:
Explain the rules for block diagram reduction and hence find the transfer function for the following block diagram. 12. (a) Determine the time response specifications and expression for output for, unit step input to a system having the system equation as A dt 2 Assume zero initial conditions. Sketch the root locus for the system and comment on stability. 13. (a) Explain mapping theorem and principle of argument and hence draw the Nyquist plot for the system whose open loop transfer function is Or A unity feedback control system has = K Bode plot and find the value of K when gain is 10 db. \ 14. (a) Draw the circuit of a lag lead compensator and derive its transfer function. What are the effects? and circuit to demonstrate the action of the transfer function.
15. (a) Derive the steady state error for a rate servomechanism. Draw and explain the block diagram of the servo. Or Explain the application of control system in system based on feedback. of antenna