Errata

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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.

Second printing

Page	Line	Erratum	Version
52	0	In Figure 2.16, theta should be O	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
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
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
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
264	16	In Exercise 8.8, second transfer function should be G_yn instead of G_yd	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
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
363	-18	In Example 12.8, process zero is at s = -2	2.10b
363	-17	In Example 12.8, controller zeros 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

First printing

Page	Line	Erratum	Version
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 2.5 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
147	0	The labels for v2 and v3 are misplaced in Figure 5.12	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
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 2.5 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	-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