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- FAQ: How does a pole at high frequency prevent PID amplification of high frequency noise? (03:31, 13 November 2005)
- FAQ: How does moving a pole at zero to a small value prevent integrator windup? (03:37, 13 November 2005)
- FAQ: What happens if a or L are negative in Zeigler-Nichols PID tuning? (03:39, 13 November 2005)
- FAQ: What are the conditions for stability or instability based on the number of zeroes in the RHP? (04:05, 13 November 2005)
- FAQ: Under what conditions is the Bode plot misleading versus the Nyquist plot for stability? (04:12, 13 November 2005)
- FAQ: Is the log in Bode integral formula log 10 or log e ? (17:47, 19 November 2005)
- FAQ: Isn't the sensitivity function the same as the function used for steady state error? How are they related? (17:49, 19 November 2005)
- FAQ: If I am controlling a second order delay-less plant, it will never give sustained oscillations with P control. Then how do I find the ultimate gain using the Ziegler Nichols method? (17:24, 31 December 2005)
- 10 Feb 06 Meeting Notes (19:28, 23 March 2006)
- 14 Mar 06 Meeting Notes (19:31, 23 March 2006)
- FAQ: How is 'open loop' a feedback mechanism? (06:39, 25 March 2006)
- FAQ: What is the definition of a system? (07:07, 25 March 2006)
- FAQ: How can we tell from the phase plots if the system is oscillating? (07:16, 25 March 2006)
- FAQ: How do we learn how to translate MATLAB equations into the Simulink diagrams? (07:27, 25 March 2006)
- FAQ: How do you know when your model is sufficiently complex? (07:34, 25 March 2006)
- FAQ: What is a state? How does one determine what is a state and what is not? (07:36, 25 March 2006)
- FAQ: What is the advantage of having a model? (07:36, 25 March 2006)
- FAQ: In the mass-spring system modelling the car, one of the springs is fixed to a wall. How does that model the car when that "spring" on the car is connected to the chassis? (07:36, 25 March 2006)
- 13 Jan 06 Meeting Notes (16:39, 16 April 2006)
- LaTeX Formatting Guidelines (16:47, 16 April 2006)
- AM05 Pending (17:02, 20 April 2006)
- FAQ: What is an example of a system with Re(λ)=0 that is not stable? What if Im(λ) is not zero? (15:08, 22 April 2006)
- FAQ: How do you show that exp(T S inv(T)) = T exp(S) inv(T)? (15:20, 22 April 2006)
- FAQ: How can I go from a continuous linear ODE to a discrete representation? (15:49, 22 April 2006)
- FAQ: What is a stochastic system? (17:48, 23 April 2006)
- FAQ: In a difference equation, how is the state continuous even though the time is discrete? (17:49, 23 April 2006)
- FAQ: Are the percentages in the definition of rise time, overshoot measured from the final value, or the size of the input change? (17:52, 23 April 2006)
- Implementation (21:32, 18 May 2006)
- FAQ: Can we get more information about state space formulation? (14:54, 28 May 2006)
- AM05 Changes (14:59, 28 May 2006)
- Action Items (23:34, 2 July 2006)
- Balance systems (02:31, 5 July 2006)
- Ball and beam system (04:35, 6 July 2006)
- Phase locked loop (04:36, 6 July 2006)
- Applications and Examples (15:55, 7 July 2006)
- 23 Apr 06 Meeting Notes (17:36, 8 July 2006)
- Appendices (20:51, 24 July 2006)
- Predator prey system (14:01, 5 September 2006)
- FAQ: In the predator prey example, where is the fox birth rate term? (14:11, 5 September 2006)
- FAQ: Why isn't there a term for the rabbit death rate besides being killed by the foxes? (14:12, 5 September 2006)
- FAQ: Why is the parameter "a" in the predator-prey problem used as both death of rabbit and birth of foxes? (16:10, 8 September 2006)
- Asymptotic stability of a nonlinear, damped, mass spring system (01:30, 12 September 2006)
- Exercise: Everyday examples of feedback systems* (16:44, 16 September 2006)
- Exercise: Vestibulo-occular reflex* (16:45, 16 September 2006)
- Exercise: Integral action produces zero steady state error* (17:06, 16 September 2006)
- Exercise: Human balance system* (17:50, 16 September 2006)
- Exercise: Exploring the dynamics of the ball and beam system (17:51, 16 September 2006)
- Exercise: Insect flight control modeling (17:52, 16 September 2006)
- Exercise: Traffic light simulation (17:52, 16 September 2006)
- Additional Exercises (17:53, 16 September 2006)
- Exercise: Exploring the dynamics of rolling mill (18:11, 16 September 2006)
- Exercise: Modeling and simulation of an exothermic reaction (03:32, 29 September 2006)
- Exercise: Vehicle powertrain modeling and cruise control (03:53, 29 September 2006)
- Exercise: Vehicle suspension system modeling and input response (04:09, 29 September 2006)
- Exercise: Properties of linear discrete time systems (04:13, 29 September 2006)
- 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? (00:57, 6 October 2006)
- Exercise: Congestion Control Stability Analysis (01:12, 6 October 2006)
- Exercise: Moving your finger through a flame without getting burned (06:40, 26 December 2006)
- FAQ: Who is Lyapunov? (15:10, 4 January 2007)
- FAQ: Does a stable system have a stable equilibrium point? a limit cycle? (15:16, 4 January 2007)
- FAQ: How do we choose epsilon in the definition of stability? (15:19, 4 January 2007)
- FAQ: What is closed form? (15:26, 4 January 2007)
- FAQ: How do you plot a 3D phase portrait? (15:34, 4 January 2007)
- Version 2.4a (01:43, 8 January 2007)
- Exercise: Supply chain simulation study (03:51, 25 February 2007)
- Traffic light controller (19:33, 6 March 2007)
- Delta-sigma converter (19:34, 6 March 2007)
- Writing Roadmap (04:39, 23 April 2007)
- Version 2.7a (15:30, 21 July 2007)
- Publication schedule (13:55, 26 September 2007)
- Version 2.9a (15:49, 8 January 2008)
- Errata location (01:31, 6 February 2008)
- FAQ: What types of students have taken courses using this text? (17:39, 9 February 2008)
- New Dynamic Behavior (16:04, 5 April 2008)
- Citation information (19:07, 5 April 2008)
- Information for developers (19:12, 5 April 2008)
- Errata: Solution for x 2j in block diagonal form discussion has sign errors (19:57, 5 April 2008)
- Information for authors (20:06, 5 April 2008)
- HOWTO: Add an errata entry (20:30, 5 April 2008)
- HOWTO: Add a FAQ entry (21:10, 5 April 2008)
- FAQ template (21:11, 5 April 2008)
- FAQ: In Example 5.3, why is the A matrix in the given form? (21:30, 5 April 2008)
- Frequently Asked Questions (21:37, 5 April 2008)
- Errata: In Example 12.6, n = -1 should be n = 1 (21:48, 5 April 2008)
- Exercise: Popular articles about control* (01:58, 6 April 2008)
- Exercise: Exploring the performance of a cruise controller* (02:30, 6 April 2008)
- FAQ: What does the Nyquist plot look like for a system with poles at the origin? (22:41, 6 April 2008)
- FAQ: What happens when the Nyquist plot goes exactly through -1? (16:21, 17 May 2008)
- FAQ: Are there rigorous ways of determining if it's impossible to meet certain/multiple performance specifications? (16:50, 17 May 2008)
- Errata: Explanation of the lack of zeros when B or C is full rank is confusing (17:14, 17 May 2008)
- Errata: Location of the process pole is missing a zero in figure caption for cruise control example (17:25, 17 May 2008)
- Errata: In Example 8.5, q should be replaced by theta (17:42, 17 May 2008)
- Errata: Maximum sensitivity occurs at frequency omega ms not omega sc (18:01, 17 May 2008)
- Errata: Arrow labeled u fd in Figure 11.3 is in the wrong direction (01:09, 18 May 2008)
- Errata: Numerator and denominator are switched in Exercise 11.11 (15:52, 19 May 2008)
- Errata: In Theorem 9.3, N should be Z (18:11, 19 May 2008)
- Errata: In Exercise 4.1, tau should be defined as t-t 0 (17:07, 26 May 2008)
- Errata: In Exercise 4.2, a e should be a (17:11, 26 May 2008)
- Errata: Parameter values are missing in Exercise 5.3 (21:58, 31 May 2008)
- Errata: Caption for Figure 8.15b is missing an s in the numerator (22:43, 31 May 2008)
- Errata: Toward end of Section 10.4, k i should be k t (22:48, 31 May 2008)
- Errata: In Exercise 5.7, the 5% settling time should be 3 tau instead of 2 tau (23:10, 31 May 2008)
- Errata: Exercise 11.4 should be Example 11.4 in Exercise 11.9 (23:11, 31 May 2008)
- Errata: T d should be T f in Exercise 11.9 (23:11, 31 May 2008)
- Root Locus Diagram (06:19, 15 June 2008)
- FAQ: Why is it better to use a lead controller than a PD controller? (16:55, 15 June 2008)
- Version 2.7c (04:03, 26 June 2008)
- Errata: In Exercise 4.6, Pm/J should be taken as 1 and factor of 1/2 is misplaced (13:16, 8 July 2008)
- Errata: Remove part (a) in Exercise 5.6 (15:58, 11 August 2008)
- Exercise: State feedback control of an AFM in contact mode (05:26, 12 August 2008)
- Errata: In Exercise 6.4, need to assume A is invertible and C A^-1 B is nonzero (00:55, 15 August 2008)
- Errata: In Exercise 9.9, 10/a should be 1/tau (23:53, 15 August 2008)
- Solutions (13:24, 19 August 2008)
- Errata: Sign error in second Lyapunov function in Exercise 4.4 (20:43, 5 October 2008)
- Errata: In Exercise 6.13, R should be removed and rho should be rho 1 (04:50, 20 October 2008)
- Other Time Domain Specifications (18:42, 15 November 2008)
- Errata: Closed loop dynamics matrix is incorrect in Example 4.6 (20:28, 15 November 2008)
- Errata: In Exercise 5.8, the initial condition is x 0 (20:57, 15 November 2008)
- FAQ: What are the parameters for the Whipple bicycle model? (21:32, 15 November 2008)
- FAQ: Why do the two terms for the rate of change of the congestion control window size in equation (3.16) have different units? (01:43, 16 November 2008)
- Errata: Formula for k r in equation (6.21) of Theorem 6.3 is incorrect (06:04, 16 November 2008)
- Errata: In equation (6.24), the sign of the sin(omega t) term is incorrect for zeta less than one (01:05, 23 November 2008)
- Errata: Extraneous 'LDH' and comment in the text (22:01, 25 November 2008)
- Errata: In Figure 10.13, the indices on the resistors and capacitors are incorrect (00:33, 28 November 2008)
- Errata: In Exercise 10.11, the dynamics for x 2 should test for e less than e 0, not e less than 1 (00:34, 28 November 2008)
- Errata: Numerical gains for Example 6.7 are incorrect (18:36, 28 November 2008)
- Errata: In Exercise 10.1, the second term in the denominator should be kp not kd (18:54, 28 November 2008)
- Errata: Values of zeta in the caption for Figure 6.8 don't match the figure (19:02, 28 November 2008)
- Errata: In equation (6.22), k omega^2 should be k omega 0^2 (19:06, 28 November 2008)
- Errata: Figure 10.11 is missing filter on derivative term (02:24, 29 November 2008)
- Errata: The signal u ff should be u fr in the caption for Figure 11.3 and associated text (01:17, 1 December 2008)
- Errata: Proportional gain in Example 11.4 transfer function should be kp (01:21, 1 December 2008)
- Errata: In Example 4.8, the linearized dynamics should contain 3 r e, not 2 r e (01:44, 1 December 2008)
- Errata: Denominator of vectored thrust process model should be Js^2 (01:45, 1 December 2008)
- Errata: Caption for Figure 12.4 doesn't quite match figure (04:37, 1 December 2008)
- Errata: "Assigning a closed loop zero" should be "assigning a closed loop pole" (21:59, 2 December 2008)
- Popular articles about control (22:04, 7 December 2008)
- Version N/A (17:59, 21 December 2008)
- Errata: In Example 4.9, V(x) should be V(z) (18:17, 21 December 2008)
- Errata: Typo in the caption for Figure 4.15 (18:18, 21 December 2008)
- Errata: In Exercise 4.1, x 0 should not be subtracted from time-shifted solution (18:20, 21 December 2008)
- Errata: In Exercise 4.14c, the transformation T and its inverse are swapped (18:21, 21 December 2008)
- Errata: Extraneous text "!linear" in Section 5.1 (18:23, 21 December 2008)
- Errata: Example 5.5 includes a damping term not shown in Figure 5.4 (18:24, 21 December 2008)
- Errata: In Examples 5.5 and 5.6, dynamics in modal form should use z, not x (18:26, 21 December 2008)
- Errata: In heuristic derivation of reachability test, α is missing subscript (18:27, 21 December 2008)
- Errata: Missing 's' in expression for characteristic polynomial in discussion of eigenvalue assignment (18:29, 21 December 2008)
- Errata: In computation of error dynamics, u ff argument is missing (18:33, 21 December 2008)
- Errata: References to first and second equations are switched in computer implementation discussion (18:34, 21 December 2008)
- Errata: Extraneous text "!design" in Chapter 12 (18:36, 21 December 2008)
- Errata: Missing ydot after equation (10.16) (18:37, 21 December 2008)
- Errata: The Wright brothers made their first successful flight in 1903, not 1905 (18:42, 21 December 2008)
- Errata: In discussion on disturbance signals, "can" should be "cannot" (18:42, 21 December 2008)
- Errata: In Exercise 2.7, reference to inverted pendulum may be confusing (18:43, 21 December 2008)
- Errata: In Equation (3.19), the second term in the window dynamics should contain \rho c (18:43, 21 December 2008)
- Errata: In Exercise 3.2: use observable form, delta is the steering angle and "title" should be "tilt" (18:43, 21 December 2008)
- Errata: State space dynamics in Exercise 3.5 are not correct (18:43, 21 December 2008)
- Atomic force microscope (03:05, 22 December 2008)
- Bicycle dynamics (05:16, 22 December 2008)
- Errata: Equation (5.15) is linear in the initial conditions and *input* (05:25, 22 December 2008)
- Errata: Missing factor of A in second term of equation (5.26) (05:32, 22 December 2008)
- Errata: In Example 5.8, the third nodal equation should be deleted (05:59, 22 December 2008)
- Errata: The labels for v2 and v3 are misplaced in Figure 5.12 (06:04, 22 December 2008)
- Congestion control (17:15, 22 December 2008)
- Errata: In the last paragraph of Section 7.1, "reachable" should be replaced by "observable" (15:53, 23 December 2008)
- Errata: Minus sign is missing in gain scheduled feedback (17:13, 24 December 2008)
- Errata: In section on pole/zero cancellations, pole and zero are at s = -a (16:14, 28 December 2008)
- Errata: Before Example 9.3, range of theta should be -pi/2 to pi/2 (18:56, 30 December 2008)
- Errata: In Example 8.9, the expression for sigma is not correct (19:02, 30 December 2008)
- Errata: Missing parenthesis in exponential for output signal (19:12, 30 December 2008)
- Errata: In Example 8.8, explanation of effects of poles and zeros is incorrect and confusing (19:33, 30 December 2008)
- Errata: In description of Bode plot for second order transfer function, 'a' should be omega 0 (19:39, 30 December 2008)
- Errata: Bennett's books on the history of control were published in 1979 and 1993 (23:28, 31 December 2008)
- Errata: Missing factor of 2 pi in residue formula for proof of Theorem 9.3 (18:45, 1 January 2009)
- Version 2.9d (17:46, 17 January 2009)
- Version 2.10a (17:46, 17 January 2009)
- How do I create a new FAQ page? (17:50, 17 January 2009)
- Errata: In Example 5.5 and 5.6, m1 and m2 should be m (17:51, 26 January 2009)
- Errata: In Example 7.2, the observer gain is given by equation (7.11) (22:32, 21 February 2009)
- Errata: In Example 7.4, hats are missing in displayed equation for u (22:36, 21 February 2009)
- Richard M. Murray (07:03, 22 February 2009)
- Karl J. Åström (07:04, 22 February 2009)
- Errata: After equation (12.23), generalized error is z, not w (18:09, 1 March 2009)
- Errata: F R v F^T term dropped in proof of Theorem 7.4 (05:37, 9 March 2009)
- Errata: Global Lyapunov stability requires additional conditions (16:28, 5 April 2009)
- Errata: In Exercise 8.8, second transfer function should be G yn instead of G yd (16:40, 5 April 2009)
- FAQ: Should the sum in Bode's integral formula be over the real part of the unstable poles? (16:48, 5 April 2009)
- Errata: In Example 6.3, z 2 should be x 1/omega instead of x 2/omega (15:44, 15 April 2009)
- Errata: Riemann sphere has radius (not diameter) 1 (15:58, 12 May 2009)
- Errata: In Example 12.8, process zero is at s = -2 (15:59, 12 May 2009)
- Errata: In Example 12.9, poles are at -a, -p1, -p2 (16:07, 12 May 2009)
- Errata: Reference to equation (6.17) should be to equation (6.15) (18:01, 2 June 2009)
- FAQ: In Section 6.4 (integral action), doesn't the value of z e depend on K? (10:31, 4 June 2009)
- Errata: In Exercise 7.11, output to check is the feedforward signal (17:34, 10 June 2009)
- Errata: In Exercise 7.13, missing equals sign in covariance specification (17:39, 10 June 2009)
- Errata: In Example 8.3, a = 10 rad/s (15:05, 12 June 2009)
- Errata: In Figure 8.3, the gain falls off at omega = a R1 k / R2 (15:12, 12 June 2009)
- Errata: d(P 1, P 2) is the longest chordal distance, not shortest (15:35, 25 June 2009)
- FAQ: In the congestion control model, what does it mean to evaluate r i at time t - tau i? (15:21, 2 July 2009)
- Josephson junction (16:43, 23 August 2009)
- ASCC 2009 Workshop (06:34, 26 August 2009)
- Errata: In equation (3.27), the state used for the output should be c, not x (00:05, 21 September 2009)
- Errata: In the complex input u = exp(s t), s should be i omega, not i omega t (00:10, 21 September 2009)
- Errata: In Figure 2.16, theta should be O (07:36, 7 October 2009)
- Errata: In Figure 1.11, caption refers to "numbers in circles" that are not present in figure (07:51, 7 October 2009)
- OBC: Trajectory Generation and Tracking (04:16, 8 October 2009)
- OBC: Optimal Control (04:22, 8 October 2009)
- OBC: Sensor Fusion (04:29, 8 October 2009)
- OBC: Receding Horizon Control (04:36, 8 October 2009)
- OBC: Stochastic Systems (04:37, 8 October 2009)
- OBC: Kalman Filtering (04:37, 8 October 2009)
- Errata: Equation (3.24) should have c in the numerator instead of c0 (22:39, 10 October 2009)
- Queuing systems (23:11, 10 October 2009)
- FAQ: Why does the effective service rate f(x) go to zero when x = 0 in Example 2.10 on queuing systems? (23:21, 10 October 2009)
- Errata: In Example 4.6, u d is not computed correctly (18:54, 18 October 2009)
- Errata: In Example 4.11, Taylor series term is missing factor of 1/2 (18:58, 18 October 2009)
- OBC:Archived news (01:36, 23 December 2009)
- NCS:Archived news (18:10, 24 December 2009)
- Errata: In Example 9.6, the critical gain is k = 0.5 instead of k = 1 (17:47, 25 December 2009)
- Errata: In Example 7.6, the coefficient in front of thetadot should be v/b (00:33, 5 January 2010)
- Errata: In equation (7.25), the last two endpoint equations are not correct (00:38, 5 January 2010)
- Errata: In Example 9.10, there is an extra factor of a in the second term of the step response (00:42, 5 January 2010)
- Errata: In Figure 12.8, the signs of A and B are reversed (16:37, 5 January 2010)
- Errata: In Example 11.9, the bound on the gain crossover frequency should be 6.48 rad/sec (17:09, 5 January 2010)
- OBC Errata (18:25, 10 January 2010)
- Errata: Missing factor of B in displayed equation after equation (5.28) (07:35, 13 January 2010)
- Supplement: Networked Sensing, Estimation and Control Systems (00:37, 23 January 2010)
- Errata: Equation (4.4) is labeled incorrectly (11:19, 4 February 2010)
- Errata: Formula for Ger should have the ' on dp, not dc (21:59, 20 February 2010)
- Errata: Formula for Ged should not have the ' on dc and is missing a minus sign (22:03, 20 February 2010)
- Errata: In Figure 8.15 and accompanying text a should be omega0 (22:21, 20 February 2010)
- Errata: In equation (6.5), the 4, 3 entry of W r should be g m^2 l^2 M t/mu (05:07, 23 February 2010)
- Errata: In Example 12.8, controller zero is at s = 3.5 (05:48, 23 February 2010)
- Version 2.10b (15:43, 4 March 2010)
- Errata: In Figure 2.7, the coefficients are for an update period of one day (17:27, 4 March 2010)
- Errata: In Example 5.4, there is a sign error in one of the terms (20:52, 17 April 2010)
- Version 2.10c (20:02, 18 April 2010)
- Information for instructors (17:55, 30 April 2010)
- Errata: Estimator dynamics in Theorem 7.3 are missing B k r r term (20:32, 18 May 2010)
- Errata: In Exercise 8.5, k in the denominator of G(s) should be (k+1) (20:38, 21 May 2010)
- Errata: In Example 6.8, the state space dynamics have errors in the trigonometric terms (00:38, 10 June 2010)
- Caltech CDS 101/110 (17:56, 17 June 2010)
- FAQ: Can a control system include a human operator as a component? (18:35, 17 June 2010)
- FAQ: How are stability, performance and robustness different? (18:35, 17 June 2010)
- Lecture: Introduction to Control (18:37, 17 June 2010)
- FAQ: What does closed loop mean? (18:38, 17 June 2010)
- Lecture Index (19:36, 17 June 2010)
- Errata: In equation (3.26), q 0 is not defined (18:44, 28 August 2010)
- FAQ: What do the double vertical bars mean at the end of Section 4.1? (19:03, 28 August 2010)
- Errata: In equation (5.26), the u(k) term in the integral should be u(tau) (19:11, 28 August 2010)