CONTENTS
CHAPTER-1 MATHEMATICAL MODELS OF CONTROL SYSTEM 1. 1
1.1 Control system...... 1.1
1. 2Examples of control systems...... 1. 3
1. 3 Mathematical models of control systems...... 1. 6
1. 4 Mechanical translational systems...... 1. 7
1. 5Mechanical rotational systems...... 1. 17
1. 6Electrical systems...... 1. 22
1. 7Transfer function of armature controlled DC motor...... 1. 25
1. 8 Transfer function of field controlled DC motor...... 1. 27
1. 9 Electrical analogous of mechanical translational systems...... 1. 29
1. 10Electrical analogous of mechanical rotational systems...... 1. 46 1. 11 Block diagrams...... 1. 55
1. 12Signal flow graph...... 1. 81
1. 13Thermal system...... 1.101
1. 14Hydraulic system...... 1.104
1. 15Pneumatic system...... 1.109
1.16 Short questions and answers...... 1.113
1.17Exercises...... 1.119
CHAPTER-2 COMPONENTS OF CONTROL SYSTEM2. 1
2. 1Components of automatic control system...... 2. 1
2. 2Potentiometers...... 2. 2
2. 3Synchros...... 2. 5
2. 4Controllers...... 2. 10
2. 5Servomotors...... 2. 22
2. 6DC Servomotors...... 2. 23
2. 7AC Servomotors...... 2. 25
2. 8Stepper motors...... 2. 30
2. 9Tachogenerator...... 2. 36
2. 10Modulator and Demodulator...... 2. 38
2. 11Gear trains...... 2. 42
2. 12Gyroscope...... 2. 45
2. 13Solved problems...... 2. 47
2. 14Short questions and answers...... 2. 54
2. 15Exercises...... 2. 60
CHAPTER-3 TIME RESPONSE ANALYSIS 3. 1
3. 1Time response...... 3. 1
3. 2 Test signals...... 3. 2
3. 3 Order of a system...... 3. 4
3. 4Review of partial fraction expansion...... 3. 5
3. 5Response of first order system for unit step input...... 3. 8
3. 6Second order system...... 3. 9
3. 7Time domain specifications...... 3. 16
3. 8Response with P, PI, PD and PID controllers...... 3. 21
3. 9Type number of control systems...... 3. 37
3. 10Steady state error...... 3. 37
3.11Static error constants...... 3. 38
3. 12Steady state error when the input is unit step signal...... 3. 38
3. 13Steady state error when the input is unit ramp signal...... 3. 39
3. 14Steady state error when the input is unit parabolic signal...... 3. 40
3. 15Generalized error coefficient...... 3. 41
3. 16Evaluation of Generalized error coefficients...... 3. 43
3. 17Correlation between static and dynamicerror coefficients...... 3. 44
3. 18Alternate method for generalized error coefficients...... 3. 44
3. 19Short questions and answers...... 3. 54
3. 20Exercises...... 3. 60
CHAPTER-4 FREQUENCY RESPONSE ANALYSIS4. 1
4. 1Sinusoidal transfer function and frequency response...... 4. 1
4. 2 Frequency domain specifications...... 4. 3
4. 3 Frequency domain specifications of second order system...... 4. 4
4. 4Correlation between time and Frequency Response...... 4. 7
4. 5Frequency Response plots...... 4. 9
4. 6Bode plot...... 4. 9
4. 7Polar plot...... 4. 39
4. 8Nichols plot...... 4. 64
4. 9Closed loop response from open loop response...... 4. 67
4. 10M and N circles...... 4. 67
4. 11Nichols chart...... 4. 73
4. 12Short questions and answers...... 4. 86
4. 13Exercises...... 4. 90
CHAPTER-5 CONCEPTS OF STABILITY AND ROOT LOCUS 5. 1
5. 1Impulse response and stability...... 5. 1
5. 2 Location of poles on s-plane for stability...... 5. 3
5. 3 Routh Hurwitz criterion...... 5. 9
5. 4Mathematical preliminaries for Nyquist stability criterion...... 5. 27
5. 5Nyquist stability criterion...... 5. 30
5. 6Relative stability...... 5. 57
5. 7Gain margin and phase margin...... 5. 58
5. 8Root locus...... 5. 63
5. 9Short questions and answers...... 5. 99
5. 10Exercises...... 5.103
CHAPTER-6 LINEAR SYSTEM DESIGN 6. 1
6. 1Introduction to design using compensators...... 6. 1
6. 2 Lag compensator...... 6. 4
6. 3 Lead compensator...... 6. 28
6. 4Lag-lead compensator...... 6. 53
6. 5PI, PD and PID controllers...... 6. 69
6. 6Feedback compensation...... 6. 88
6. 7Short questions and answers...... 6.102
6. 8Exercises...... 6.109
APPENDIX A. 1
Appendix-ILaplace transform pairs and properties ...... A. 1
Appendix-IIRoots of algebraic equation by Lin’s method...... A. 3
INDEX I. 1