# Difference between revisions of "Errata"

This page contains information about errata for Feedback Systems. The errata listed here include known and corrected errors since the first printing of the book; clicking on the link will take you to a page with additional details. Typos and other relatively minor corrections are listed here but do not have separate pages with additional details (they also do not appear on individual chapter pages).

Conventions:

• Each line of text and each line of a displayed equation are counted as a line. Negative line numbers mean number of lines from the bottom of the page. First line on page = 1, last line on page = -1.
• Entries in boldface indicate errors which might change significantly the interpretation of the text.
• The version refers to the release number in which the error was found. Errors are corrected in all subsequent releases of the text.

### Third printing

Page Line Erratum Version
10   -1   In the "Instrumentation" subsection, "axon of the giant squid" should be "giant axon of the squid" 2.10c
37   4   In Example 2.1, the state space equations for the balance system are missing a divisor of J_t in one of the terms 2.10c
40   2   In Figure 2.7, the coefficients are for an update period of one day 2.10c
84   11   In the online version of the text, there is a formatting error in equation (3.23) 2.10c
86   -1   In equation (3.26), q_0 is not defined 2.10c
105   -3   On right hand side of displayed equation, x should be x_j 2.10c
121   10   In Example 4.13, inequality should be for x_1 instead of x_2 2.10c
132   1   Add a comma after "For other systems" for clarity 2.10c
141   -4, -8   In Example 5.4, there is a sign error in one of the terms 2.10c
148   2   In the caption for Figure 5.7, "drive" should be "driven" 2.10c
157   7   In equation (5.26), the u(k) term in the integral should be u(tau) 2.10c
158   -8   After equation (5.31), rolling friction term disappears if v = 0 2.10c
165   -4   In Exercise 5.8d, the left hand side of the first equation should be x(k+1) 2.10c
186   -3   In Examples 6.6, the output equation has 'x' for the state instead of 'c' 2.10c
191   -5   In Example 6.8, the state space dynamics have errors in the trigonometric terms 2.10c
192   -15   Diagonal entries for Q_v should be rho 2.10c
204   6   In Example 7.1, the output equation has 'x' for the state instead of 'c' 2.10c
213   8   Estimator dynamics in Theorem 7.3 are missing B k_r r term 2.10c
224   4   Output in Kalman decomposition for Example 7.7 is missing state error term 2.10c
225   -4   "phenomena knows" → "phenomena known" 2.10c
238   -9   In equation (8.15), second order partial derivative is written incorrectly 2.10c
238   -1   In Example 8.4, boundary condition and coefficients for psi(x) are incorrect 2.10c
247   11   Last equation in Example 8.6 has sign error in the second term 2.10c
263   -13   In Exercise 8.5, k in the denominator of G(s) should be (k+1) 2.10c
296   1   Caption for Figure 10.3b should be "Derivative action" 2.10c
297   11   After equation (10.5), low frequency limit bound be 1/T_d instead of T_d 2.10c
300   4   The b k_i term in the characteristic polynomial has an extra factor of s 2.10c
302   0   In Figure 10.7b,  should be  2.10c
310   -4   The PID integral time constant T_i for the op amp implementation should be equal to R_2 C_2 2.10c
318   -4 to -1   Reference input not included in Figure 11.2 and dimensions of blocks are listed incorrectly 2.10c
319   0   In Figure 11.3, the label 'y' at the input to P_2 should be removed 2.10c
328   -11   In Example 11.5, "" should be "" 2.10c
330   2   In the caption for Figure 11.11, Fz should be F1 2.10c
340   3-9   Contour integral in derivation of Bode's integral formula is analyzed incorrectly 2.10c
339   -9   In expression for I_1, limits have an extra factor of i 2.10c
357   -6, -8   For Youla parameterization, P = b(s)/a(s) = B(s)/A(s) and C0 = G0(s)/F0(s) 2.10c
361   13   Missing end parenthesis at end of sentence 2.10c
365   -13   The reference to the maximum complementary sensitivity should be to equation (12.7) 2.10c
369   -12   Replace "dashed" with "shaded" in the description of Figure 12.16a 2.10c
371   -4   Reference to Figure 12.17b should be to Figure 12.17 (right) 2.10c

### Second printing

Page Line Erratum Version
21   7   Stanford one the competition should be Stanford won the competition 2.10c
29   -12   Missing space after sentence ending with "controlled differential equation" 2.10b
52   0   In Figure 2.16, theta should be O 2.10b
85   -7   Equation (3.24) should have c in the numerator instead of c0 2.10b
87   3   In equation (3.27), the state used for the output should be c, not x 2.10b
97   -11, -4   Equation (4.4) is labeled incorrectly 2.10b
107   12-15   In Example 4.6, u_d is not computed correctly 2.10b
115   -5   In Example 4.11, Taylor series term is missing factor of 1/2 2.10b
118   17   After equation (4.18), solution trajectory should be x(t; a) instead of x(t: a) 2.10b
121   5 to 6   Global Lyapunov stability requires additional conditions 2.10b
152   -5   In the complex input u = exp(s t), s should be i omega, not i omega t 2.10b
157   -15   Missing factor of B in displayed equation after equation (5.28) 2.10b
171   8   In equation (6.5), the 4, 3 entry of W_r should be g m^2 l^2 M_t/mu 2.10b
174   -3   In Example 6.3, z_2 should be x_1/omega instead of x_2/omega 2.10b
179   -3   Reference to equation (6.17) should be to equation (6.15) 2.10b
216   -7 to -3   F R_v F^T term dropped in proof of Theorem 7.4 2.10b
221   -12, -6   In Example 7.6, the coefficient in front of thetadot should be v/b 2.10b
222   4, 5   In equation (7.25), the last two endpoint equations are not correct 2.10b
228   13   In Exercise 7.11, output to check is the feedforward signal 2.10b
228   -12   In Exercise 7.13, missing equals sign in covariance specification 2.10b
234   -12   In displayed equation above equation (8.7), U should be u in the expression for the output 2.10b
237   4   In Figure 8.3, the gain falls off at omega = a R1 k / R2 2.10b
237   5   In Example 8.3, a = 10 rad/s 2.10b
238   8   In Example 8.3, a = 10 rad/s 2.10b
240   -12   After equation (8.17), "looses" should be "loses" 2.10b
248   2   Formula for Ger should have the ' on dp, not dc 2.10b
248   7   Formula for Ged should not have the ' on dc and is missing a minus sign 2.10b
254   -7   Replace  with  2.10b
255   8   Replace  with  2.10b
256   0, 5, 6   In Figure 8.15 and accompanying text a should be omega0 2.10b
264   16   In Exercise 8.8, second transfer function should be G_yn instead of G_yd 2.10b
276   -6, -2   In Example 9.6, the critical gain is k = 0.5 instead of k = 1 2.10b
277   4   In Figure 9.8, the gain of the system is k = 1 2.10b
278   2   In proof of Theorem 9.3, "residues of the poles of is" should be "residue for the poles is" 2.10b
284   -10   In Example 9.10, there is an extra factor of a in the second term of the step response 2.10b
335   11, 13   In Example 11.9, the bound on the gain crossover frequency should be 6.48 rad/sec 2.10b
351   8   Riemann sphere has radius (not diameter) 1 2.10b
351   10   d(P_1, P_2) is the longest chordal distance, not shortest 2.10b
357   0   In Figure 12.8, the signs of A and B are reversed 2.10b
363   -18   In Example 12.8, process zero is at s = -2 2.10b
363   -17   In Example 12.8, controller zero is at s = 3.5 2.10b
364   -10 to -4   In Example 12.9, poles are at -a, -p1, -p2 2.10b
367   -1   Remove extra word "in" 2.10b
371   -11   After equation (12.23), generalized error is z, not w 2.10b
379   23   Desborough is misspelt (p 380, line 1 in online version) 2.10b

### First printing

Page Line Erratum Version
15   6   In Figure 1.11, caption refers to "numbers in circles" that are not present in figure 2.9d
19   -11   The Wright brothers made their first successful flight in 1903, not 1905 2.9d
25   -1   In Exercise 1.1, "loosing" should be "losing" 2.9d
32   12   In discussion on disturbance signals, "can" should be "cannot" 2.9d
62   -6   In Exercises 2.4 and 5.9, the (2,1) entry of the dynamics matrix should be ab-b 2.9d
63   -8   In Exercise 2.7, reference to inverted pendulum may be confusing 2.9d
80   5   In Equation (3.19), the second term in the window dynamics should contain \rho c 2.9d
91   -6   In Exercise 3.2: use observable form, delta is the steering angle and "title" should be "tilt" 2.9d
92   -9   State space dynamics in Exercise 3.5 are not correct 2.9d
106   7   Solution for x_2j in block diagonal form discussion has sign errors 2.9d
107   12-23   Closed loop dynamics matrix is incorrect in Example 4.6 2.9d
108   8   Missing γ in equation (4.9) 2.9d
110   11, 13   In Example 4.8, the linearized dynamics should contain 3 r_e, not 2 r_e 2.9d
112   -1   In Example 4.9, V(x) should be V(z) 2.9d
117   3   Typo in the caption for Figure 4.15 2.9d
126   -5   In Exercise 4.1, x_0 should not be subtracted from time-shifted solution 2.9d
126   -5   In Exercise 4.1, tau should be defined as t-t_0 2.9d
127   5   In Exercise 4.2, a_e should be a 2.9d
127   15   Sign error in second Lyapunov function in Exercise 4.4 2.9d
128   3   In Exercise 4.6, Pm/J should be taken as 1 and factor of 1/2 is misplaced 2.9d
129   -2   In Exercise 4.14c, the transformation T and its inverse are swapped 2.9d
131   -15   Extraneous text "!linear" in Section 5.1 2.9d
135   12   In equation (5.5), the upper limit of the integral should be t 2.9d
144   -7   Example 5.5 includes a damping term not shown in Figure 5.4 2.9d
144   -4   In Example 5.5 and 5.6, m1 and m2 should be m 2.10a
145   5   In Examples 5.5 and 5.6, dynamics in modal form should use z, not x 2.9d
146   -15   Equation (5.15) is linear in the initial conditions and *input* 2.10a
148   -1   In Example 5.5 and 5.6, m1 and m2 should be m 2.10a
149   8   In Examples 5.5 and 5.6, dynamics in modal form should use z, not x 2.9d
154   -10   In Example 5.8, the third nodal equation should be deleted 2.10a
155   0   The labels for v2 and v3 are misplaced in Figure 5.12 2.10a
156   -10   In AFM dynamics, c and k are missing subscript 2 2.9d
157   7   Missing factor of A in second term of equation (5.26) 2.10a
164   -11   Parameter values are missing in Exercise 5.3 2.9d
164   -3   Remove part (a) in Exercise 5.6 2.9d
165   11   In Exercise 5.7, the 5% settling time should be 3 tau instead of 2 tau 2.9d
165   16   In Exercise 5.8, the initial condition is x_0 2.9d
166   3   In Exercises 2.4 and 5.9, the (2,1) entry of the dynamics matrix should be ab-b 2.9d
168   12   The control matrix in the equilibrium set should be 'B' instead of 'b' 2.10a
169   -12   In heuristic derivation of reachability test, α is missing subscript 2.9d
180   -2   Formula for k_r in equation (6.21) of Theorem 6.3 is incorrect 2.9d
181   9   Missing 's' in expression for characteristic polynomial in discussion of eigenvalue assignment 2.9d
183   -7   In equation (6.22), k omega^2 should be k omega_0^2 2.9d
184   -10   In equation (6.24), the sign of the sin(omega t) term is incorrect for zeta less than one 2.9d
185   4   Values of zeta in the caption for Figure 6.8 don't match the figure 2.9d
188   -2   Dynamics matrix in Example 6.7 has errors in (3,4) and (4,4) entries 2.9d
189   22   Numerical gains for Example 6.7 are incorrect 2.9d
197   3   In Figure 6.15, reference velocity is v_r = 20 m/s 2.10a
198   14   In Exercise 6.4, need to assume A is invertible and C A^-1 B is nonzero 2.9d
199   -1, -2   In AFM dynamics, c and k are missing subscript 2 2.9d
200   9   In Exercise 6.13, R should be removed and rho should be rho_1 2.9d
206   10,11   In the last paragraph of Section 7.1, "reachable" should be replaced by "observable" 2.9d
209   2   In Example 7.2, the observer gain is given by equation (7.11) 2.9d
214   -13   In Example 7.4, hats are missing in displayed equation for u 2.10a
220   12   In computation of error dynamics, u_ff argument is missing 2.9d
220   -13   Minus sign is missing in gain scheduled feedback 2.9d
224   -7   References to first and second equations are switched in computer implementation discussion 2.9d
240   -16, -13   Sign error in equation (8.17) - (sI - A) should be (A - sI) 2.9d
240   -11   Explanation of the lack of zeros when B or C is full rank is confusing 2.9d
241   -4, -6   In Example 8.5, q should be replaced by theta 2.9d
247   -1   In section on pole/zero cancellations, pole and zero are at s = -a 2.10a
248   1   In section on pole/zero cancellations, pole and zero are at s = -a 2.10a
249   3   Location of the process pole is missing a zero in figure caption for cruise control example 2.9d
250   -16   Missing parenthesis in exponential for output signal 2.10a
253   -1   In description of Bode plot for second order transfer function, 'a' should be omega_0 2.10a
254   12   In description of Bode plot for second order transfer function, 'a' should be omega_0 2.10a
254-5   -10 to 9   In Example 8.8, explanation of effects of poles and zeros is incorrect and confusing 2.10a
256   1   Caption for Figure 8.15b is missing an s in the numerator 2.9d
257   5   In Example 8.9, the expression for sigma is not correct 2.10a
272   8   Before Example 9.3, range of theta should be -pi/2 to pi/2 2.10a
277   13   In Theorem 9.3, N should be Z 2.9d
278   3   Missing factor of 2 pi in residue formula for proof of Theorem 9.3 2.10a
288   -4, -3   Exponential signal is incorrect on the left-hand side of harmonic expansion equation 2.9d
292   18   In Exercise 9.9, 10/a should be 1/tau 2.9d
307   -9   Toward end of Section 10.4, k_i should be k_t 2.9d
308   0   Figure 10.11 is missing filter on derivative term 2.9d
310   -4   In Figure 10.13, the indices on the resistors and capacitors are incorrect 2.9d
311   -3   Missing ydot after equation (10.16) 2.9d
313   8,9   In Exercise 10.1, the second term in the denominator should be kp not kd 2.9d
314   -5   In Exercise 10.11, the dynamics for x_2 should test for e less than e_0, not e less than 1 2.9d
315   -8   Extraneous 'LDH' and comment in the text 2.9d
319   0   Arrow labeled u_fd in Figure 11.3 is in the wrong direction 2.9d
319   4, -2   The signal u_ff should be u_fr in the caption for Figure 11.3 and associated text 2.9d
319   -7   Extraneous text "!design" in Chapter 12 2.9d
323   -9   Maximum sensitivity occurs at frequency omega_ms not omega_sc 2.9d
325   -9   Proportional gain in Example 11.4 transfer function should be kp 2.9d
330   5   Denominator of vectored thrust process model should be Js^2 2.9d
336   -8   Extraneous text "!design" in Chapter 12 2.9d
345   12   Exercise 11.4 should be Example 11.4 in Exercise 11.9 2.9d
345   14   T_d should be T_f in Exercise 11.9 2.9d
345   -5   Numerator and denominator are switched in Exercise 11.11 2.9d
351   2,3   Caption for Figure 12.4 doesn't quite match figure 2.9d
356   6, 12   In Example 12.6, n = -1 should be n = 1 2.9d
363   -11   "Assigning a closed loop zero" should be "assigning a closed loop pole" 2.9d
369   -1   Extraneous text "!design" in Chapter 12 2.9d
378   15,16   Bennett's books on the history of control were published in 1979 and 1993 2.10a