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  1. Second Edition‏‎ (863,120 views)
  2. First Edition‏‎ (661,470 views)
  3. Errata‏‎ (433,974 views)
  4. Introduction‏‎ (216,945 views)
  5. System Modeling‏‎ (212,252 views)
  6. Dynamic Behavior‏‎ (194,059 views)
  7. PID Control‏‎ (171,002 views)
  8. Linear Systems‏‎ (164,107 views)
  9. State Feedback‏‎ (161,639 views)
  10. Frequency Domain Analysis‏‎ (153,537 views)
  11. Transfer Functions‏‎ (152,325 views)
  12. FAQ: What does it mean for a non-square matrix to be full rank?‏‎ (150,548 views)
  13. Frequency Domain Design‏‎ (149,987 views)
  14. Examples‏‎ (136,086 views)
  15. Output Feedback‏‎ (132,069 views)
  16. Josephson junction‏‎ (130,392 views)
  17. Robust Performance‏‎ (112,419 views)
  18. Cruise control‏‎ (106,892 views)
  19. Supplement: Optimization-Based Control‏‎ (96,251 views)
  20. Preface‏‎ (83,810 views)
  21. Version 2.11b‏‎ (77,513 views)
  22. FAQ: What is steady state error?‏‎ (69,510 views)
  23. Solutions‏‎ (67,691 views)
  24. Information for instructors‏‎ (67,117 views)
  25. Additional Examples‏‎ (56,363 views)
  26. Supplement: Biomolecular Feedback Systems‏‎ (56,211 views)
  27. Software‏‎ (50,928 views)
  28. Exercise: Exploring the performance of a cruise controller*‏‎ (47,070 views)
  29. Lecture: System Modeling‏‎ (46,607 views)
  30. Action Items‏‎ (46,184 views)
  31. Ball and beam system‏‎ (44,246 views)
  32. Bibliography‏‎ (42,261 views)
  33. Supplement: Networked Sensing, Estimation and Control Systems‏‎ (36,304 views)
  34. Lecture: Dynamic Behavior‏‎ (35,347 views)
  35. Lecture Index‏‎ (34,328 views)
  36. Frequently Asked Questions‏‎ (32,886 views)
  37. Phase locked loop‏‎ (32,290 views)
  38. Exercise: Exploring the dynamics of the ball and beam system‏‎ (31,434 views)
  39. Predator prey‏‎ (29,097 views)
  40. Vectored thrust aircraft‏‎ (27,385 views)
  41. Lecture: Introduction‏‎ (27,359 views)
  42. Version 2.4a‏‎ (25,100 views)
  43. Solutions Manual‏‎ (24,626 views)
  44. FAQ: What does the Nyquist plot look like for a system with poles at the origin?‏‎ (24,403 views)
  45. Course syllabus suggestions‏‎ (23,982 views)
  46. FAQ: What do the double vertical bars mean at the end of Section 4.1?‏‎ (22,924 views)
  47. Exercise: Vehicle powertrain modeling and cruise control‏‎ (22,760 views)
  48. Bicycle dynamics‏‎ (21,515 views)
  49. Second edition, version 3.0h posted‏‎ (21,417 views)
  50. Archived news‏‎ (21,094 views)
  51. Atomic force microscope‏‎ (20,038 views)
  52. Richard M. Murray‏‎ (19,984 views)
  53. Exercise: Popular articles about control*‏‎ (19,879 views)
  54. Information for authors‏‎ (19,274 views)
  55. Additional Exercises‏‎ (18,714 views)
  56. Index‏‎ (18,582 views)
  57. Exercise: Everyday examples of feedback systems*‏‎ (18,431 views)
  58. Version 2.9d‏‎ (17,516 views)
  59. Version 2.7c‏‎ (17,362 views)
  60. Exercise: Traffic light simulation‏‎ (15,398 views)
  61. Errata: In Examples 5.5 and 5.6, dynamics in modal form should use z, not x‏‎ (15,333 views)
  62. Karl J. Åström‏‎ (15,279 views)
  63. FAQ: Why is it better to use a lead controller than a PD controller?‏‎ (15,218 views)
  64. Root Locus Diagram‏‎ (15,164 views)
  65. Information for developers‏‎ (14,873 views)
  66. Version 2.10e‏‎ (14,279 views)
  67. E-book‏‎ (14,260 views)
  68. FAQ: What happens when the Nyquist plot goes exactly through -1?‏‎ (13,233 views)
  69. Version 2.10c‏‎ (13,072 views)
  70. Exercise: Insect flight control modeling‏‎ (13,034 views)
  71. Lecture: PID Control‏‎ (12,859 views)
  72. Implementation‏‎ (12,560 views)
  73. Exercise: Vehicle suspension system modeling and input response‏‎ (12,219 views)
  74. Lecture: PID Tools‏‎ (11,404 views)
  75. Lecture: Loop Analysis‏‎ (11,315 views)
  76. Lecture: Transfer Functions‏‎ (11,137 views)
  77. FAQ: In the predator prey example, where is the fox birth rate term?‏‎ (10,834 views)
  78. Traffic light controller‏‎ (10,764 views)
  79. Exercise: Congestion Control Stability Analysis‏‎ (10,648 views)
  80. Applications and Examples‏‎ (10,630 views)
  81. FAQ: How is 'open loop' a feedback mechanism?‏‎ (10,579 views)
  82. FAQ: Can we get more information about state space formulation?‏‎ (10,429 views)
  83. FAQ: Can a control system include a human operator as a component?‏‎ (10,313 views)
  84. Lecture: State Feedback‏‎ (10,018 views)
  85. FAQ: What is the definition of a system?‏‎ (9,996 views)
  86. Lecture: Linear Systems‏‎ (9,419 views)
  87. Balance systems‏‎ (9,291 views)
  88. Lecture: Output Feedback‏‎ (9,249 views)
  89. Version 2.10b‏‎ (9,129 views)
  90. FAQ: What is a stochastic system?‏‎ (8,861 views)
  91. Delta-sigma converter‏‎ (8,833 views)
  92. Caltech CDS 101/110‏‎ (8,746 views)
  93. FAQ: How can I go from a continuous linear ODE to a discrete representation?‏‎ (8,700 views)
  94. FAQ: How do we learn how to translate MATLAB equations into the Simulink diagrams?‏‎ (8,618 views)
  95. Lecture: Loop Shaping‏‎ (8,570 views)
  96. FAQ: Why isn't there a term for the rabbit death rate besides being killed by the foxes?‏‎ (8,541 views)
  97. Lecture: Introduction to Control‏‎ (8,518 views)
  98. Second edition, version 3.0j posted‏‎ (8,448 views)
  99. Lecture: ODEs‏‎ (8,432 views)
  100. Exercise: Exploring the dynamics of rolling mill‏‎ (8,317 views)
  101. HOWTO: Add an errata entry‏‎ (8,315 views)
  102. Predator prey system‏‎ (8,309 views)
  103. Exercise: Human balance system*‏‎ (8,290 views)
  104. FAQ: How do you know when your model is sufficiently complex?‏‎ (8,232 views)
  105. Second edition, version 3.0i posted‏‎ (8,196 views)
  106. Errata: In Exercise 3.2: use observable form, delta is the steering angle and "title" should be "tilt"‏‎ (8,072 views)
  107. Exercise: Supply chain simulation study‏‎ (7,857 views)
  108. FAQ: What is the advantage of having a model?‏‎ (7,777 views)
  109. Exercise: Modeling and simulation of an exothermic reaction‏‎ (7,725 views)
  110. FAQ: What is a state? How does one determine what is a state and what is not?‏‎ (7,674 views)
  111. Exercise: Vestibulo-occular reflex*‏‎ (7,658 views)
  112. FAQ: Why is the parameter "a" in the predator-prey problem used as both death of rabbit and birth of foxes?‏‎ (7,470 views)
  113. Exercise: Moving your finger through a flame without getting burned‏‎ (7,404 views)
  114. No errata reported in most recent version of this chapter‏‎ (7,308 views)
  115. Compartment model‏‎ (7,215 views)
  116. FAQ: What does closed loop mean?‏‎ (7,204 views)
  117. FAQ: If every equilibrium point can be transformed to the origin and then analyzed using a Lyapunov function, how can a system have both stable and unstable equilibrium points?‏‎ (6,962 views)
  118. Exercise: Integral action produces zero steady state error*‏‎ (6,794 views)
  119. Lecture: Limits of Performance‏‎ (6,396 views)
  120. Appendices‏‎ (6,314 views)
  121. Exercise: Properties of linear discrete time systems‏‎ (6,274 views)
  122. FAQ: What is an example of a system with Re(λ)=0 that is not stable? What if Im(λ) is not zero?‏‎ (6,129 views)
  123. Exercise: State feedback control of an AFM in contact mode‏‎ (6,104 views)
  124. Errata: In Example 4.9, V(x) should be V(z)‏‎ (5,905 views)
  125. FAQ: How do you plot a 3D phase portrait?‏‎ (5,823 views)
  126. FAQ: How are stability, performance and robustness different?‏‎ (5,778 views)
  127. Version 3.0j‏‎ (5,746 views)
  128. Lecture: Robust Performance‏‎ (5,707 views)
  129. Errata: In Exercise 4.1, x 0 should not be subtracted from time-shifted solution‏‎ (5,684 views)
  130. Publication schedule‏‎ (5,636 views)
  131. AM05 Changes‏‎ (5,599 views)
  132. Other Time Domain Specifications‏‎ (5,478 views)
  133. Errata: In Exercise 2.7, reference to inverted pendulum may be confusing‏‎ (5,476 views)
  134. FAQ: What is closed form?‏‎ (5,468 views)
  135. Errata: Extraneous text "!design" in Chapter 12‏‎ (5,408 views)
  136. FAQ: What are the parameters for the Whipple bicycle model?‏‎ (5,379 views)
  137. FAQ: In a difference equation, how is the state continuous even though the time is discrete?‏‎ (5,312 views)
  138. FAQ: Are the percentages in the definition of rise time, overshoot measured from the final value, or the size of the input change?‏‎ (5,272 views)
  139. Congestion control‏‎ (5,268 views)
  140. FAQ: Does a stable system have a stable equilibrium point? a limit cycle?‏‎ (5,123 views)
  141. Sandbox‏‎ (5,046 views)
  142. Queuing systems‏‎ (4,858 views)
  143. Errata: Missing ydot after equation (10.16)‏‎ (4,853 views)
  144. Version 2.10a‏‎ (4,760 views)
  145. Version 3.0h‏‎ (4,714 views)
  146. FAQ: How do you show that exp(T S inv(T)) = T exp(S) inv(T)?‏‎ (4,674 views)
  147. Errata: In Example 9.6, the critical gain is k = 0.5 instead of k = 1‏‎ (4,632 views)
  148. FAQ: How do we choose epsilon in the definition of stability?‏‎ (4,610 views)
  149. FAQ: Who is Lyapunov?‏‎ (4,589 views)
  150. OBC Errata‏‎ (4,524 views)
  151. Errata: In Exercise 4.6, Pm/J should be taken as 1 and factor of 1/2 is misplaced‏‎ (4,493 views)
  152. Citation information‏‎ (4,464 views)
  153. Errata: Exponential signal is incorrect on the left-hand side of harmonic expansion equation‏‎ (4,422 views)
  154. Errata: In Example 8.8, explanation of effects of poles and zeros is incorrect and confusing‏‎ (4,415 views)
  155. FAQ: In Example 5.3, why is the A matrix in the given form?‏‎ (4,403 views)
  156. FAQ: Are there rigorous ways of determining if it's impossible to meet certain/multiple performance specifications?‏‎ (4,335 views)
  157. FAQ: What types of students have taken courses using this text?‏‎ (4,335 views)
  158. Errata: Arrow labeled u fd in Figure 11.3 is in the wrong direction‏‎ (4,317 views)
  159. Errata: In Exercise 5.7, the 5% settling time should be 3 tau instead of 2 tau‏‎ (4,316 views)
  160. Errata: Example 5.5 includes a damping term not shown in Figure 5.4‏‎ (4,277 views)
  161. Errata: In equation (6.24), the sign of the sin(omega t) term is incorrect for zeta less than one‏‎ (4,220 views)
  162. FAQ: How can we tell from the phase plots if the system is oscillating?‏‎ (4,172 views)
  163. FAQ: Why does the effective service rate f(x) go to zero when x = 0 in Example 2.10 on queuing systems?‏‎ (4,171 views)
  164. Errata: Numerator and denominator are switched in Exercise 11.11‏‎ (4,167 views)
  165. Version 2.9a‏‎ (4,162 views)
  166. BFS:Archived news‏‎ (4,162 views)
  167. Errata: Dynamics matrix in Example 6.7 has errors in (3,4) and (4,4) entries‏‎ (4,132 views)
  168. Errata: Missing γ in equation (4.9)‏‎ (4,132 views)
  169. Errata: Explanation of the lack of zeros when B or C is full rank is confusing‏‎ (4,093 views)
  170. Errata: In Equation (3.19), the second term in the window dynamics should contain \rho c‏‎ (4,085 views)
  171. FAQ: In Section 6.4 (integral action), doesn't the value of z e depend on K?‏‎ (4,024 views)
  172. FAQ: Should the sum in Bode's integral formula be over the real part of the unstable poles?‏‎ (4,022 views)
  173. Errata: In Exercises 2.4 and 5.9, the (2,1) entry of the dynamics matrix should be ab-b‏‎ (4,007 views)
  174. ASCC 2009 Workshop‏‎ (4,000 views)
  175. Errata: The formula given for the rise time of a second order system in Table 6.1 is only approximate‏‎ (3,990 views)
  176. Errata: State space dynamics in Exercise 3.5 are not correct‏‎ (3,962 views)
  177. Errata: In Theorem 9.3, N should be Z‏‎ (3,946 views)
  178. Errata: Extraneous text "!linear" in Section 5.1‏‎ (3,912 views)
  179. Errata: Sign error in second Lyapunov function in Exercise 4.4‏‎ (3,904 views)
  180. Errata: Location of the process pole is missing a zero in figure caption for cruise control example‏‎ (3,902 views)
  181. Errata: In heuristic derivation of reachability test, α is missing subscript‏‎ (3,887 views)
  182. Errata: In equation (5.5), the upper limit of the integral should be t‏‎ (3,886 views)
  183. Errata: Sign error in equation (8.17) - (sI - A) should be (A - sI)‏‎ (3,869 views)
  184. Errata: Formula for k r in equation (6.21) of Theorem 6.3 is incorrect‏‎ (3,866 views)
  185. Errata: In Exercise 4.14c, the transformation T and its inverse are swapped‏‎ (3,818 views)
  186. Errata: In Example 6.7, the open loop eigenvalues are incorrect‏‎ (3,815 views)
  187. Errata: Parameter values are missing in Exercise 5.3‏‎ (3,808 views)
  188. Errata: In Example 8.5, q should be replaced by theta‏‎ (3,785 views)
  189. Errata: Solution for x 2j in block diagonal form discussion has sign errors‏‎ (3,742 views)
  190. Errata: Maximum sensitivity occurs at frequency omega ms not omega sc‏‎ (3,737 views)
  191. Errata: In Example 2.1, the state space equations for the balance system are missing a divisor of J t in one of the terms‏‎ (3,701 views)
  192. Errata: F R v F^T term dropped in proof of Theorem 7.4‏‎ (3,696 views)
  193. Errata: In Example 4.8, the linearized dynamics should contain 3 r e, not 2 r e‏‎ (3,692 views)
  194. Errata: Typo in the caption for Figure 4.15‏‎ (3,684 views)
  195. Errata: In Exercise 10.11, the dynamics for x 2 should test for e less than e 0, not e less than 1‏‎ (3,662 views)
  196. Version 2.11a‏‎ (3,654 views)
  197. Errata location‏‎ (3,653 views)
  198. Errata: Toward end of Section 10.4, k i should be k t‏‎ (3,645 views)
  199. Errata: In Exercise 4.2, a e should be a‏‎ (3,629 views)
  200. Version 2.7a‏‎ (3,625 views)
  201. Errata: In Example 7.2, the observer gain is given by equation (7.11)‏‎ (3,617 views)
  202. Errata: References to first and second equations are switched in computer implementation discussion‏‎ (3,614 views)
  203. Errata: In Example 6.6 and 7.1, the output equation has 'x' for the state instead of 'c'‏‎ (3,568 views)
  204. Errata: Closed loop dynamics matrix is incorrect in Example 4.6‏‎ (3,552 views)
  205. OBC:Archived news‏‎ (3,552 views)
  206. Errata: In Exercise 4.1, tau should be defined as t-t 0‏‎ (3,547 views)
  207. Errata: In AFM dynamics, c and k are missing subscript 2‏‎ (3,510 views)
  208. Errata: In computation of error dynamics, u ff argument is missing‏‎ (3,505 views)
  209. How do I create a new FAQ page?‏‎ (3,478 views)
  210. Errata: Proportional gain in Example 11.4 transfer function should be kp‏‎ (3,430 views)
  211. Errata: Figure 10.11 is missing filter on derivative term‏‎ (3,407 views)
  212. Second Edition:Archived news‏‎ (3,365 views)
  213. Errata: Equation (4.4) is labeled incorrectly‏‎ (3,361 views)
  214. Errata: The Wright brothers made their first successful flight in 1903, not 1905‏‎ (3,357 views)
  215. OBC: Stochastic Systems‏‎ (3,327 views)
  216. Errata: In Example 12.6, n = -1 should be n = 1‏‎ (3,324 views)
  217. OBC: Kalman Filtering‏‎ (3,314 views)
  218. Errata: Missing 's' in expression for characteristic polynomial in discussion of eigenvalue assignment‏‎ (3,268 views)
  219. Errata: In discussion on disturbance signals, "can" should be "cannot"‏‎ (3,257 views)
  220. Errata: T d should be T f in Exercise 11.9‏‎ (3,246 views)
  221. Errata: In description of Bode plot for second order transfer function, 'a' should be omega 0‏‎ (3,242 views)
  222. Errata: In Example 5.5 and 5.6, m1 and m2 should be m‏‎ (3,241 views)
  223. Errata: Extraneous 'LDH' and comment in the text‏‎ (3,227 views)
  224. Errata: Global Lyapunov stability requires additional conditions‏‎ (3,211 views)
  225. Errata: Remove part (a) in Exercise 5.6‏‎ (3,198 views)
  226. Writing Roadmap‏‎ (3,190 views)
  227. Errata: Missing parenthesis in exponential for output signal‏‎ (3,184 views)
  228. Errata: Exercise 11.4 should be Example 11.4 in Exercise 11.9‏‎ (3,182 views)
  229. Errata: In Exercise 5.8, the initial condition is x 0‏‎ (3,174 views)
  230. Errata: In Example 5.8, the third nodal equation should be deleted‏‎ (3,167 views)
  231. FAQ: Why do the two terms for the rate of change of the congestion control window size in equation (3.16) have different units?‏‎ (3,165 views)
  232. Errata: In equation (6.22), k omega^2 should be k omega 0^2‏‎ (3,147 views)
  233. Errata: Denominator of vectored thrust process model should be Js^2‏‎ (3,136 views)
  234. Errata: In Example 8.9, the expression for sigma is not correct‏‎ (3,122 views)
  235. Errata: In Figure 10.13, the indices on the resistors and capacitors are incorrect‏‎ (3,102 views)
  236. Errata: In Exercise 9.9, 10/a should be 1/tau‏‎ (3,079 views)
  237. Errata: Before Example 9.3, range of theta should be -pi/2 to pi/2‏‎ (3,068 views)
  238. Errata: Riemann sphere has radius (not diameter) 1‏‎ (3,065 views)
  239. Errata: In Exercise 6.4, need to assume A is invertible and C A^-1 B is nonzero‏‎ (3,054 views)
  240. Errata: Caption for Figure 8.15b is missing an s in the numerator‏‎ (3,049 views)
  241. Errata: In Exercise 10.1, the second term in the denominator should be kp not kd‏‎ (3,034 views)
  242. Errata: In the complex input u = exp(s t), s should be i omega, not i omega t‏‎ (3,026 views)
  243. Errata: In Exercise 6.13, R should be removed and rho should be rho 1‏‎ (3,025 views)
  244. Errata: Values of zeta in the caption for Figure 6.8 don't match the figure‏‎ (2,968 views)
  245. Errata: Numerical gains for Example 6.7 are incorrect‏‎ (2,948 views)
  246. Errata: Equation (5.15) is linear in the initial conditions and *input*‏‎ (2,919 views)
  247. Errata: "Assigning a closed loop zero" should be "assigning a closed loop pole"‏‎ (2,919 views)
  248. Errata: Bennett's books on the history of control were published in 1979 and 1993‏‎ (2,912 views)
  249. MATLAB subdirectory help‏‎ (2,908 views)
  250. Errata: Caption for Figure 12.4 doesn't quite match figure‏‎ (2,894 views)

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