Control Systems. University Questions

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1 University Questions UNIT-1 1. Distinguish between open loop and closed loop control system. Describe two examples for each. (10 Marks), Jan 2009, June 12, Dec 11,July 08, July 2009, Dec Write the differential equations for the mechanical system shown in fig. 1(b) and obtain F-V and F-I analogous electrical circuits. ( 10 Marks), Jan Mention merits and demerits of open loop and closed loop control systems and give an example for each. ( 6 Marks), July For the mechanical system shown in fig. 1(b) obtain the F-V analogous network. (8 Marks), July Obtain the transfer function of an armature controlled DC servomotor. (6 Marks), July 2009, Dec For the system shown in fig. Find the transfer function G(S) =. Consider J1= 1Kgm 2, K 1 = 1 Nm/rad, K 2 = 1 Nm/rad. B 1 = 1 Nm/rad/ Sec, B 2 = 1 Nm/ rad / sec. ( 6 Marks), Dec 2011 Dept. of ECE/SJBIT Page 1

2 7. Draw the mechanical network for the system shown in fig. write equations of performance and draw its analogous circuit based on F-V analogy. ( 10 Marks), Dec Write the differential equations of performance for the mechanical system shown in fig. Q1 (b). Draw its F-V analogous circuit. ( 08 Marks, June 2012) Dept. of ECE/SJBIT Page 2

3 UNIT-2 1. Obtain the C/R ratio for the block diagram shown using block diagram reduction technique ( 06 Marks, July 2009) 2. Find C(S)/ R(S) by Mason s gain formula ( 06 Marks, July 2009) 3. Explain briefly the following terms i) Forward path ii) path gain iii) loop gain iv) canonical form (08 Marks, July 2009) 4. Define the transfer function. Explain Mason s gain formula for determining the transfer function from signal flow graphs. ( 06 marks, Dec 2010) 5. For the block diagram shown in fig.q2 (b), determine the transfer function Q 2 (s)/q(s) using block diagram reduction algebra. (8 Marks, Dec 2010) Dept. of ECE/SJBIT Page 3

4 6. For the system described by the signal flow graph shown in fig. Q2(c), obtain the closed loop transfer function C(s) / R(s), using Mason s gain formula. ( 6 Marks, Dec 2010) 7. For the system represented by the following equation, find the transfer function X(s)/U(s) by signal flow graph. (8 Marks, Jan 2009) 8. Obtain the transfer function for the block diagram shown in fig. Q2(b) using block diagram reduction technique. ( 10 Marks, June 2012) 9. Obtain the closed loop transfer function C(s)/ R(s) for the signal flow graph of a system shown in fig. Q2(b) using Mason s gain formula. ( 10 Marks, June 2012) Dept. of ECE/SJBIT Page 4

5 10. Derive an expression for the closed loop transfer function of a negative feedback system. ( 4 Marks, Dec 2011) UNIT-3 1. Derive expressions for peak response time t p and maximum overshoot M p of an under damped second order control system subjected to step input. ( 6 Marks, June 2012) 2. A second order control system is represented by a transfer function given below. Where the proportional output and T is is is the input torque. A step unit of 10 N-m is applied to the system and test results are given below. i) Maximum overshoot is 6% ii) Peak time is 1 Sec iii) The steady state value of the output is 0.5 radian. Determine the value of J, F and K. ( 8 Marks, June 2012) 3. For a unity feedback control system with G(s) = 10(S+2) / S 2 (S+1). Find i) The static error coefficients ii) Steady state error when the input transform is ( 6 Marks, June 2012) 4. Define the following for an underdamped second order system i) Rise time ii) peak overshoot iii) settling time ( 6 Marks, Dec 2010,11) 5. Define the steady state error coefficients. Consider a unity feedback control system whose open loop transfer function is. Determine the steady state error when the input is r(t) = 1 + t + at 2 ; a 0. ( 6 Marks, Dec 2010) 6. The forward path transfer function of a certain unity negative feedback control system is G(s). The system is subjected to unit step input. From the transient response curves, it is observed that the system peak overshoot is 15% and the time at which it occurs is 1.8 secs. Determine the closed loop transfer function of the system. ( 8 Marks, Dec 2010) 7. For the negative feedback control system with G(s) = 50/ s(s+5) ; find i) Percentage overshoot for the unit step input ii) Settling time for a unit step input Dept. of ECE/SJBIT Page 5

6 UNIT-4 iii) Steady state error for the input defined by the polynomial r(t) = 2 + 4t + 6t 2, t 0 ( 10 Marks, Dec 2011) 1. Explain Routh-Hurwitz s criterion for determining the stability of a system and mention any three limitations of R-H criterion. ( 10 Marks, June 2012) 2. A unity feedback control system is characterized by the open loop transfer function 3. Define: i) Marginally stable systems; ii) absolutely stable system; iii) conditionally stable systems. ( 06 Marks, June 2012) 4. Define the term stability applied to control system sand what is the difference between absolute stability and relative stability. ( 4 Marks, Dec 2012) 5. Using Routh s stability criterion determine the stability of the following systems: i) Its open loop transfer function has poles at s = 0, s= -1, s = -3 and s = -5. Gain K = 10. ii) It s a type 1 system with an error constant of 10/sec and poles at s = -3 and s = -6 ( 8 Marks, Dec 2012) 6. Using R-H Criterion determine the stability of the system having the characteristic equation, S S S S + 75 = 0 has roots more negative than S = -2. ( 8 Marks, Dec 2012) Dept. of ECE/SJBIT Page 6

7 UNIT 5 1. Sketch the root locus for a unity feedback control system with open loop transfer function: ( 12 Marks, june 2012) 2. Show that root locus for a unity feedback control system with are the arcs of circle of radius and centered at the origin. ( 8 Marks, June 2012) 3. The open loop transfer function of a feedback control system in Check whether the following points are on the root locus. If so, find the value of K at these points, i) S = -1.5 ii) S = j2 ( 6 Marks, Dec 2012) 4. Sketch the root locus plot for a negative feedback control system characterized by an open loop transfer function, Comment on stability. (14 Marks, Dec 2012) 5. Sketch the root locus diagram for a unit feedback control system with G(s) = k / S( S+8S+17) using the rules of construction and by determining the break away/ break in points and the angle of departure. Find the value of K for which the system just oscillates. From the root locus, determine the value of K for a damping ratio of 0.5. ( 20 Marks, June 2010) 6. Define and explain the significance of angle and magnitude condition, as applied to the root locus method of stability analysis of linear system. ( 6 Marks, Dec 2010) 7. Define brake away / in point on a root locus. Explain any one method of determining the same. (6 Marks, Dec 2010) 8. For the following characteristic polynomial s + 2s +2 + K ( S+1) = 0, draw the root locus for 0 K. (8 Marks, Dec 2010) Dept. of ECE/SJBIT Page 7

8 UNIT 6 1. State the advantages and limitations of frequency domain approach. ( 6 Marks, Dec 2012) 2. Determine the transfer function, of a system whose asyptotic gain plot is shown in fig. ( 10 Marks, Dec 2012) 3. Explain Nyquist s stability criterion. ( 4 Marks, Dec 2010, June 2010) 4. The open loop transfer function of a unity negative feedback is given by: Using the Nyquist criteria, find the values of K for which the closed loop system is just stable. ( 8 Marks, Dec 2010) 5. Derive an expression for the resonant frequency and resonant peak for a closed loop system having a second order transfer function. ( 8 Marks, Dec 2010) 6. Discuss the stability of the unity feedback control system with G (s) = 1/ S 2 ( S+1) by using Nyquist criteria. If H(s) = 1+ 2s, test the stability of the system. ( 14 Marks, June 2010) 7. Dept. of ECE/SJBIT Page 8

9 UNIT June Dec June 2010 Dept. of ECE/SJBIT Page 9

10 Dec 2010 UNIT Dec May 2010 Dept. of ECE/SJBIT Page 10

11 4. June 2012 Dec 2012 Dept. of ECE/SJBIT Page 11

12 Dept. of ECE/SJBIT Page 12

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