Introduction to Linear Control Systems is designed as a standard introduction to linear control systems for all those who one way or another deal with control systems. It can be used as a comprehensive up-to-date textbook for a one-semester 3-credit undergraduate course on linear control systems as the first course on this topic at university. This includes the faculties of electrical engineering, mechanical engineering, aerospace engineering, chemical and petroleum engineering, industrial engineering, civil engineering, bio-engineering, economics, mathematics, physics, management and social sciences, etc.
The book covers foundations of linear control systems, their raison detre, different types, modelling, representations, computations, stability concepts, tools for time-domain and frequency-domain analysis and synthesis, and fundamental limitations, with an emphasis on frequency-domain methods. Every chapter includes a part on further readings where more advanced topics and pertinent references are introduced for further studies. The presentation is theoretically firm, contemporary, and self-contained. Appendices cover Laplace transform and differential equations, dynamics, MATLAB and SIMULINK, treatise on stability concepts and tools, treatise on Routh-Hurwitz method, random optimization techniques as well as convex and non-convex problems, and sample midterm and endterm exams.
The book is divided to the sequel 3 parts plus appendices.
PART I: In this part of the book, chapters 1-5, we present foundations of linear control systems. This includes: the introduction to control systems, their raison detre, their different types, modelling of control systems, different methods for their representation and fundamental computations, basic stability concepts and tools for both analysis and design, basic time domain analysis and design details, and the root locus as a stability analysis and synthesis tool.
PART II: In this part of the book, Chapters 6-9, we present what is generally referred to as the frequency domain methods. This refers to the experiment of applying a sinusoidal input to the system and studying its output. There are basically three different methods for representation and studying of the data of the aforementioned frequency response experiment: these are the Nyquist plot, the Bode diagram, and the Krohn-Manger-Nichols chart. We study these methods in details. We learn that the output is also a sinusoid with the same frequency but generally with different phase and magnitude. By dividing the output by the input we obtain the so-called sinusoidal or frequency transfer function of the system which is the same as the transfer function when the Laplace variable s is substituted with . Finally we use the Bode diagram for the design process.
PART III: In this part, Chapter 10, we introduce some miscellaneous advanced topics under the theme fundamental limitations which should be included in this undergraduate course at least in an introductory level. We make bridges between some seemingly disparate aspects of a control system and theoretically complement the previously studied subjects.
Appendices: The book contains seven appendices. Appendix A is on the Laplace transform and differential equations. Appendix B is an introduction to dynamics. Appendix C is an introduction to MATLAB, including SIMULINK. Appendix D is a survey on stability concepts and tools. A glossary and road map of the available stability concepts and tests is provided which is missing even in the research literature. Appendix E is a survey on the Routh-Hurwitz method, also missing in the literature. Appendix F is an introduction to random optimization techniques and convex and non-convex problems. Finally, appendix G presents sample midterm and endterm exams, which are class-tested several times.
1. 1. Introduction - p. 3 2. Abstract - p. 3 3. 1.1 Introduction - p. 3 4. 1.2 Why control? - p. 4 5. 1.3 History of control - p. 5 6. 1.4 Why feedback? - p. 8 7. 1.5 Magic of feedback - p. 9 8. 1.6 Physical elements of a control system - p. 10 9. 1.7 Abstract elements of a control system - p. 11 10. 1.8 Design process - p. 12 11. 1.9 Types of control systems - p. 15 12. 1.10 Open-loop control - p. 16 13. 1.11 Closed-loop control - p. 20 14. 1.12 The 2-DOF control structure - p. 30 15. 1.13 The Smith predictor - p. 37 16. 1.14 Internal model control structure - p. 38 17. 1.15 Modern representation—Generalized model - p. 39 18. 1.16 Status quo - p. 41 19. 1.17 Summary - p. 72 20. 1.18 Notes and further readings - p. 72 21. 1.19 Worked-out problems - p. 81 22. 1.20 Exercises - p. 95 23. References - p. 107 24. Further Reading - p. 107 25. 2. System representation - p. 129 26. Abstract - p. 129 27. 2.1 Introduction - p. 129 28. 2.2 System modeling - p. 130 29. 2.3 Basic examples of modeling - p. 145 30. 2.4 Block diagram - p. 169 31. 2.5 Signal flow graph - p. 174 32. 2.6 Summary - p. 181 33. 2.7 Notes and further readings - p. 181 34. 2.8 Worked-out problems - p. 189 35. 2.9 Exercises - p. 221 36. References - p. 246 37. 3. Stability analysis - p. 265 38. Abstract - p. 265 39. 3.1 Introduction - p. 265 40. 3.2 Lyapunov and BIBO stability - p. 266 41. 3.3 Stability tests - p. 271 42. 3.4 Routh’s test - p. 273 43. 3.5 Hurwitz’ test - p. 279 44. 3.6 Lienard and Chipart test - p. 279 45. 3.7 Relative stability - p. 280 46. 3.8 D-stability - p. 282 47. 3.9 Particular relation with control systems design - p. 284 48. 3.10 The Kharitonov theory - p. 286 49. 3.11 Internal stability - p. 287 50. 3.12 Strong stabilization - p. 289 51. 3.13 Stability of LTV Systems - p. 290 52. 3.14 Summary - p. 295 53. 3.15 Notes and further readings - p. 295 54. 3.16 Worked-out problems - p. 299 55. 3.17 Exercises - p. 310 56. References - p. 325 57. 4. Time response - p. 333 58. Abstract - p. 333 59. 4.1 Introduction - p. 333 60. 4.2 System type and system inputs - p. 334 61. 4.3 Steady-state error - p. 335 62. 4.4 First-order systems - p. 339 63. 4.5 Second-order systems - p. 340 64. 4.6 Bandwidth of the system - p. 349 65. 4.7 Higher-order systems - p. 360 66. 4.8 Model reduction - p. 361 67. 4.9 Effect of addition of pole and zero - p. 365 68. 4.10 Performance region - p. 368 69. 4.11 Inverse response - p. 370 70. 4.12 Analysis of the actual system - p. 372 71. 4.13 Introduction to robust stabilization and performance - p. 384 72. 4.14 Summary - p. 393 73. 4.15 Notes and further readings - p. 393 74. 4.16 Worked-out problems - p. 396 75. 4.17 Exercises - p. 419 76. References - p. 431 77. 5. Root locus - p. 437 78. Abstract - p. 437 79. 5.1 Introduction - p. 437 80. 5.2 The root locus method - p. 440 81. 5.3 The root contour - p. 458 82. 5.4 Finding the value of gain from the root locus - p. 459 83. 5.5 Controller design implications - p. 462 84. 5.6 Summary - p. 485 85. 5.7 Notes and further readings - p. 486 86. 5.8 Worked-out problems - p. 487 87. 5.9 Exercises - p. 516 88. References - p. 527 89. Part II: Frequency domain analysis & synthesis - p. 527 90. 6. Nyquist plot - p. 533 91. Abstract - p. 533 92. 6.1 Introduction - p. 533 93. 6.2 Nyquist plot - p. 535 94. 6.3 Gain, phase, and delay margins - p. 560 95. 6.4 Summary - p. 601 96. 6.5 Notes and further readings - p. 602 97. 6.6 Worked-out problems - p. 605 98. 6.7 Exercises - p. 627 99. References - p. 638 100. 7. Bode diagram - p. 641 101. Abstract - p. 641 102. 7.1 Introduction - p. 641 103. 7.2 Bode diagram - p. 642 104. 7.3 Bode diagram and the steady-state error - p. 654 105. 7.4 Minimum phase and nonminimum phase systems - p. 657 106. 7.5 Gain, phase, and delay margins - p. 664 107. 7.6 Stability in the Bode diagram context - p. 669 108. 7.7 The high sensitivity region - p. 670 109. 7.8 Relation with Nyquist plot and root locus - p. 670 110. 7.9 Standard second-order systems - p. 671 111. 7.10 Bandwidth - p. 672 112. 7.11 Summary - p. 675 113. 7.12 Notes and further readings - p. 676 114. 7.13 Worked-out problems - p. 677 115. 7.14 Exercises - p. 691 116. References - p. 698 117. 8. Nichols-Krohn-Manger-Hall Chart - p. 701 118. 9. Frequency domain synthesis and design - p. 743 119. Abstract - p. 743 120. 9.1 Introduction - p. 743 121. 9.2 Basic controllers: proportional, lead, lag, and lead-lag - p. 745 122. 9.3 Controller simplifications: PI, PD, and PID - p. 763 123. 9.4 Controller structures in the Nyquist plot context - p. 766 124. 9.5 Effect of the controllers on the root locus - p. 769 125. 9.6 Design procedure - p. 772 126. 9.7 Specialized design and tuning rules of PID controllers - p. 774 127. 9.8 Internal model control - p. 784 128. 9.9 The Smith predictor - p. 785 129. 9.10 Implementation with operational amplifiers - p. 786 130. 9.11 Summary - p. 789 131. 9.12 Notes and further readings - p. 790 132. 9.13 Worked-out problems - p. 793 133. 9.14 Exercises - p. 831 134. References - p. 838 135. Part III: Advanced Issues - p. 838 136. 10. Fundamental limitations - p. 847 137. Abstract - p. 847 138. 10.1 Introduction - p. 847 139. 10.2 Relation between time and frequency domain specifications - p. 849 140. 10.3 The ideal transfer function - p. 851 141. 10.4 Controller design via the TS method - p. 858 142. 10.5 Interpolation conditions - p. 859 143. 10.6 Integral and Poisson integral constraints - p. 862 144. 10.7 Constraints implied by poles and zeros - p. 869 145. 10.8 Actuator and sensor limitations - p. 877 146. 10.9 Delay - p. 881 147. 10.10 Eigenstructure assignment by output feedback - p. 883 148. 10.11 Noninteractive performance - p. 891 149. 10.12 Minimal closed-loop pole sensitivity - p. 894 150. 10.13 Robust stabilization - p. 898 151. 10.14 Special results for positive systems - p. 901 152. 10.15 Generic design procedure - p. 902 153. 10.16 Summary - p. 906 154. 10.17 Notes and further readings - p. 907 155. 10.18 Worked-out problems - p. 913 156. 10.19 Exercises - p. 927 157. References - p. 953 158. Appendices A–G - p. 953 159. Appendix A. Laplace transform and differential equations - p. 977 160. Appendix B. Introduction to dynamics - p. 993 161. Appendix C. Introduction to MATLAB® - p. 1009 162. Appendix D. Treatise on stability concepts and tests - p. 1037 163. Appendix E. Treatise on the Routh’s stability test - p. 1053 164. Appendix F. Genetic algorithm: A global optimization technique - p. 1061 165. Appendix G. Sample exams - p. 1079 166. Colour Plate - p. cp1 167. Index - p. 1093
Introduction to Linear Control Systems is designed as a standard introduction to linear control systems for all those who one way or another deal with control systems. It can be used as a comprehensive up-to-date textbook for a one-semester 3-credit undergraduate course on linear control systems as the first course on this topic at university. This includes the faculties of electrical engineering, mechanical engineering, aerospace engineering, chemical and petroleum engineering, industrial engineering, civil engineering, bio-engineering, economics, mathematics, physics, management and social sciences, etc.
The book covers foundations of linear control systems, their raison detre, different types, modelling, representations, computations, stability concepts, tools for time-domain and frequency-domain analysis and synthesis, and fundamental limitations, with an emphasis on frequency-domain methods. Every chapter includes a part on further readings where more advanced topics and pertinent references are introduced for further studies. The presentation is theoretically firm, contemporary, and self-contained. Appendices cover Laplace transform and differential equations, dynamics, MATLAB and SIMULINK, treatise on stability concepts and tools, treatise on Routh-Hurwitz method, random optimization techniques as well as convex and non-convex problems, and sample midterm and endterm exams.
The book is divided to the sequel 3 parts plus appendices.
PART I: In this part of the book, chapters 1-5, we present foundations of linear control systems. This includes: the introduction to control systems, their raison detre, their different types, modelling of control systems, different methods for their representation and fundamental computations, basic stability concepts and tools for both analysis and design, basic time domain analysis and design details, and the root locus as a stability analysis and synthesis tool.
PART II: In this part of the book, Chapters 6-9, we present what is generally referred to as the frequency domain methods. This refers to the experiment of applying a sinusoidal input to the system and studying its output. There are basically three different methods for representation and studying of the data of the aforementioned frequency response experiment: these are the Nyquist plot, the Bode diagram, and the Krohn-Manger-Nichols chart. We study these methods in details. We learn that the output is also a sinusoid with the same frequency but generally with different phase and magnitude. By dividing the output by the input we obtain the so-called sinusoidal or frequency transfer function of the system which is the same as the transfer function when the Laplace variable s is substituted with . Finally we use the Bode diagram for the design process.
PART III: In this part, Chapter 10, we introduce some miscellaneous advanced topics under the theme fundamental limitations which should be included in this undergraduate course at least in an introductory level. We make bridges between some seemingly disparate aspects of a control system and theoretically complement the previously studied subjects.
Appendices: The book contains seven appendices. Appendix A is on the Laplace transform and differential equations. Appendix B is an introduction to dynamics. Appendix C is an introduction to MATLAB, including SIMULINK. Appendix D is a survey on stability concepts and tools. A glossary and road map of the available stability concepts and tests is provided which is missing even in the research literature. Appendix E is a survey on the Routh-Hurwitz method, also missing in the literature. Appendix F is an introduction to random optimization techniques and convex and non-convex problems. Finally, appendix G presents sample midterm and endterm exams, which are class-tested several times.
1. 1. Introduction - p. 3 2. Abstract - p. 3 3. 1.1 Introduction - p. 3 4. 1.2 Why control? - p. 4 5. 1.3 History of control - p. 5 6. 1.4 Why feedback? - p. 8 7. 1.5 Magic of feedback - p. 9 8. 1.6 Physical elements of a control system - p. 10 9. 1.7 Abstract elements of a control system - p. 11 10. 1.8 Design process - p. 12 11. 1.9 Types of control systems - p. 15 12. 1.10 Open-loop control - p. 16 13. 1.11 Closed-loop control - p. 20 14. 1.12 The 2-DOF control structure - p. 30 15. 1.13 The Smith predictor - p. 37 16. 1.14 Internal model control structure - p. 38 17. 1.15 Modern representation—Generalized model - p. 39 18. 1.16 Status quo - p. 41 19. 1.17 Summary - p. 72 20. 1.18 Notes and further readings - p. 72 21. 1.19 Worked-out problems - p. 81 22. 1.20 Exercises - p. 95 23. References - p. 107 24. Further Reading - p. 107 25. 2. System representation - p. 129 26. Abstract - p. 129 27. 2.1 Introduction - p. 129 28. 2.2 System modeling - p. 130 29. 2.3 Basic examples of modeling - p. 145 30. 2.4 Block diagram - p. 169 31. 2.5 Signal flow graph - p. 174 32. 2.6 Summary - p. 181 33. 2.7 Notes and further readings - p. 181 34. 2.8 Worked-out problems - p. 189 35. 2.9 Exercises - p. 221 36. References - p. 246 37. 3. Stability analysis - p. 265 38. Abstract - p. 265 39. 3.1 Introduction - p. 265 40. 3.2 Lyapunov and BIBO stability - p. 266 41. 3.3 Stability tests - p. 271 42. 3.4 Routh’s test - p. 273 43. 3.5 Hurwitz’ test - p. 279 44. 3.6 Lienard and Chipart test - p. 279 45. 3.7 Relative stability - p. 280 46. 3.8 D-stability - p. 282 47. 3.9 Particular relation with control systems design - p. 284 48. 3.10 The Kharitonov theory - p. 286 49. 3.11 Internal stability - p. 287 50. 3.12 Strong stabilization - p. 289 51. 3.13 Stability of LTV Systems - p. 290 52. 3.14 Summary - p. 295 53. 3.15 Notes and further readings - p. 295 54. 3.16 Worked-out problems - p. 299 55. 3.17 Exercises - p. 310 56. References - p. 325 57. 4. Time response - p. 333 58. Abstract - p. 333 59. 4.1 Introduction - p. 333 60. 4.2 System type and system inputs - p. 334 61. 4.3 Steady-state error - p. 335 62. 4.4 First-order systems - p. 339 63. 4.5 Second-order systems - p. 340 64. 4.6 Bandwidth of the system - p. 349 65. 4.7 Higher-order systems - p. 360 66. 4.8 Model reduction - p. 361 67. 4.9 Effect of addition of pole and zero - p. 365 68. 4.10 Performance region - p. 368 69. 4.11 Inverse response - p. 370 70. 4.12 Analysis of the actual system - p. 372 71. 4.13 Introduction to robust stabilization and performance - p. 384 72. 4.14 Summary - p. 393 73. 4.15 Notes and further readings - p. 393 74. 4.16 Worked-out problems - p. 396 75. 4.17 Exercises - p. 419 76. References - p. 431 77. 5. Root locus - p. 437 78. Abstract - p. 437 79. 5.1 Introduction - p. 437 80. 5.2 The root locus method - p. 440 81. 5.3 The root contour - p. 458 82. 5.4 Finding the value of gain from the root locus - p. 459 83. 5.5 Controller design implications - p. 462 84. 5.6 Summary - p. 485 85. 5.7 Notes and further readings - p. 486 86. 5.8 Worked-out problems - p. 487 87. 5.9 Exercises - p. 516 88. References - p. 527 89. Part II: Frequency domain analysis & synthesis - p. 527 90. 6. Nyquist plot - p. 533 91. Abstract - p. 533 92. 6.1 Introduction - p. 533 93. 6.2 Nyquist plot - p. 535 94. 6.3 Gain, phase, and delay margins - p. 560 95. 6.4 Summary - p. 601 96. 6.5 Notes and further readings - p. 602 97. 6.6 Worked-out problems - p. 605 98. 6.7 Exercises - p. 627 99. References - p. 638 100. 7. Bode diagram - p. 641 101. Abstract - p. 641 102. 7.1 Introduction - p. 641 103. 7.2 Bode diagram - p. 642 104. 7.3 Bode diagram and the steady-state error - p. 654 105. 7.4 Minimum phase and nonminimum phase systems - p. 657 106. 7.5 Gain, phase, and delay margins - p. 664 107. 7.6 Stability in the Bode diagram context - p. 669 108. 7.7 The high sensitivity region - p. 670 109. 7.8 Relation with Nyquist plot and root locus - p. 670 110. 7.9 Standard second-order systems - p. 671 111. 7.10 Bandwidth - p. 672 112. 7.11 Summary - p. 675 113. 7.12 Notes and further readings - p. 676 114. 7.13 Worked-out problems - p. 677 115. 7.14 Exercises - p. 691 116. References - p. 698 117. 8. Nichols-Krohn-Manger-Hall Chart - p. 701 118. 9. Frequency domain synthesis and design - p. 743 119. Abstract - p. 743 120. 9.1 Introduction - p. 743 121. 9.2 Basic controllers: proportional, lead, lag, and lead-lag - p. 745 122. 9.3 Controller simplifications: PI, PD, and PID - p. 763 123. 9.4 Controller structures in the Nyquist plot context - p. 766 124. 9.5 Effect of the controllers on the root locus - p. 769 125. 9.6 Design procedure - p. 772 126. 9.7 Specialized design and tuning rules of PID controllers - p. 774 127. 9.8 Internal model control - p. 784 128. 9.9 The Smith predictor - p. 785 129. 9.10 Implementation with operational amplifiers - p. 786 130. 9.11 Summary - p. 789 131. 9.12 Notes and further readings - p. 790 132. 9.13 Worked-out problems - p. 793 133. 9.14 Exercises - p. 831 134. References - p. 838 135. Part III: Advanced Issues - p. 838 136. 10. Fundamental limitations - p. 847 137. Abstract - p. 847 138. 10.1 Introduction - p. 847 139. 10.2 Relation between time and frequency domain specifications - p. 849 140. 10.3 The ideal transfer function - p. 851 141. 10.4 Controller design via the TS method - p. 858 142. 10.5 Interpolation conditions - p. 859 143. 10.6 Integral and Poisson integral constraints - p. 862 144. 10.7 Constraints implied by poles and zeros - p. 869 145. 10.8 Actuator and sensor limitations - p. 877 146. 10.9 Delay - p. 881 147. 10.10 Eigenstructure assignment by output feedback - p. 883 148. 10.11 Noninteractive performance - p. 891 149. 10.12 Minimal closed-loop pole sensitivity - p. 894 150. 10.13 Robust stabilization - p. 898 151. 10.14 Special results for positive systems - p. 901 152. 10.15 Generic design procedure - p. 902 153. 10.16 Summary - p. 906 154. 10.17 Notes and further readings - p. 907 155. 10.18 Worked-out problems - p. 913 156. 10.19 Exercises - p. 927 157. References - p. 953 158. Appendices A–G - p. 953 159. Appendix A. Laplace transform and differential equations - p. 977 160. Appendix B. Introduction to dynamics - p. 993 161. Appendix C. Introduction to MATLAB® - p. 1009 162. Appendix D. Treatise on stability concepts and tests - p. 1037 163. Appendix E. Treatise on the Routh’s stability test - p. 1053 164. Appendix F. Genetic algorithm: A global optimization technique - p. 1061 165. Appendix G. Sample exams - p. 1079 166. Colour Plate - p. cp1 167. Index - p. 1093
