Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-1 (p. 354) Gain-phase characteristics of an ideal low-pass filter.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-2 (p. 355) Typical gain-phase characteristics of a feedback control system.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-3 (p. 357) Magnification versus normalized frequency of the prototype second-order control system.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-4 (p. 358) M r versus damping ratio for the prototype second-order system.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-5 (p. 358) Normalized resonant frequency versus damping ratio for the prototype second-order system. u r =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-6 (p. 359) Bandwidth/ω n versus damping ratio for the prototype second-order system.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-7 (p. 360) Correlation among pole locations, unit-step response, and the magnitude of frequency response of the prototype second-order system.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-8 (p. 361) Bandwidth of a second-order system with open-loop transfer function G(s) = (1 + Ts)/[s(s )]

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-9 (p. 362) Magnification curves for the second-order system with the forward-path transfer function G(s) in Eq. (9-32). (a) ω n = 1, ζ = (b) (a) ω n = 1, ζ = 0.2.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-10 (p. 363) Unit-step responses of a second-order system with a forward-path transfer function G(s).

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-11 (p. 363) Unit-step responses of a second-order system with a forward-path transfer function G(s).

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-12 (p. 364) Magnification curves for a third-order system with a forward-path transfer function G(s).

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-13 (p. 365) Unit-step responses of a third-order system with a forward-path transfer function G(s).

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-14 (p. 367) Definition of encirclement.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-15 (p. 367) Definition of enclosed points and regions. (a) Point A is enclosed by Γ. (b) Point A is not enclosed, but B is enclosed by the locus Γ.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-16 (p. 368) Definition of the number of encirclements and enclosures.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-17 (p. 368) (a) Arbitrarily chosen closed path in the s-plane. (b) Corresponding locus Γs in the Δ(s)-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-18 (p. 370) Examples of the determina- tion of N in the Δ(s)-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-19 (p. 371) (a) Pole-zero configuration of Δ(s) in Eq. (9-44) and the s-plane trajectory Γs. (b) Δ(s)-plane locus Γ Δ, which corresponds to the Γ s locus of (a) through the mapping of Eq. (9-44)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-20 (p. 373) Nyquist path.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-21 (p. 376) Polar plot of G(s)H(s) = K/[s(s + a)(s + b)] interpreted as a mapping of the jω-axis of the s-plane onto the G(s)H(s)-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-22 (p. 377) Root-locus diagram of G(s)H(s) = K/[s(s + a)(s + b)] interpreted as a mapping of the real axis of the G(s)H(s)-plane onto the s-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-23 (p. 377) G(s)H(s) plots that correspond to constant-damping-ratio lines in the s-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-24 (p. 378) Root loci that correspond to different phase-angle loci in the G(s)H(s)-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-25 (p. 379) Nyquist plot of L(s)/K = for ω =  to ω = 0.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-26 (p. 380) L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-27 (p. 381) Nyquist plot of for ω =  to ω = 0.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-28 (p. 381) Nyquist plot of K/L eq (jω) for for ω =  to ω = 0.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-29 (p. 382) RL of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-30 (p. 382) Nyquist plot of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-31 (p. 383) Nyquist plot of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-32 (p. 383) Nyquist plot of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-33 (p. 384) Nyquist plot of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-34 (p. 385) Nyquist plots. Curve (1): Curve (2):

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-35 (p. 386) Nyquist plots. Curve (1): Curve (2):

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-36 (p. 387) Correlation among Nyquist plots, step responses, and frequency responses.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-37 (p. 388) Definition of the gain margin in the polar coordinates.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-39 (p. 390) Nyquist plots showing systems with the same gain margin but different degrees of relative stability.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-39 (p. 391) Phase margin defined in the L(jω)-plane.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-40 (p. 391) Nyquist plot of L(s) of

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-41 (p. 393) Determination of gain margin and phase margin on the Bode plot.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-42 (p. 394) Bode plot of L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-43 (p. 395) Bode plot of L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-44 (p. 397) Bode plot of L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-45 (p. 398) Nyquist plot of L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-46 (p. 398) Root loci of G(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-47 (p. 399) Gainphase plot of L(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-48 (p. 401) Constant-M circles in polar coordinates.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-49 (p. 402) (a) Polar plots of G(s) and constant-M loci. (b) Corresponding magnification curves.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-50 (p. 403) Nichols chart.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-51 (p. 404) Bode diagrams of the system in Example 9-9.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-52 (p. 405) Gain-phase plots and Nichols chart of the system in Example 9-9.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-53 (p. 406) Closed-loop frequency response of the system in Example 9-9.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-54 (p. 407)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-55 (p. 408) Magnitude-phase plots of G(jω) and 1/G(jω) for G(s) =

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-56 (p. 410) Frequency Response Tool main window.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-57 (p. 410) Transfer Function Input module.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-58 (p. 411) Entering G(s) using the Transfer Function Input module.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-59 (p. 412) Frequency Response Tool main window, after clicking the “Calculate” button.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-61 (p. 413) Closed-loop system magnitude and phase plots for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-62 (p. 414) Loop transfer function phase and gain margin plots for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-63 (p. 414) The SISO Design tool for Example 9-1, K = 1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-64 (p. 415) The SISO Design tool for Example 9-1, K = 10,000.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-65 (p. 415) Activation of plot option within the SISO Design tool for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-66 (p. 416) Closed-loop unit step, closed-loop Bode response, and the open-loop Nyquist diagrams for Example 9-1, K = 1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-67 (p. 417) Closed-loop unit step, closed-loop Bode response, and the open-loop Nyquist diagrams for Example 9-1, K = 240.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-68 (p. 418) Selecting the Root Locus option in the SISO Design tool for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-69 (p. 418) The Root Locus and Open-Loop Bode diagrams in the SISO Design tool for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-70 (p. 419) Addition of a real zero to the root-locus and Bode diagrams in the SISO Design tool for Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-71 (p. 420) Adding a real zero and a gain to the system in Example 9-1.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-72 (p. 420) The root-locus and Bode diagrams in the SISO Design tool for Example 9-1 with an added real zero at z = -5 and a gain K = 240.

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9-73 (p. 421) Closed-loop unit-step response, Bode diagram of the closed- loop frequency response, and open-loop Nyquist diagram for Example 9-1, when C = G_c(s) = 240 ( s)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-6 (p. 424)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-14 (p. 425)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-16 (p. 426)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-20 (p. 427)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-28 (p. 429)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-33 (p. 430)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-34 (p. 431)

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9P-39 (p. 432)