Figure 8.1 a. Closed- loop system; b. equivalent transfer function

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Figure 8.1 a. Closed- loop system; b. equivalent transfer function Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 2 Vector representation of complex numbers: a. s =  + j; b Figure 8.2 Vector representation of complex numbers: a. s =  + j; b. (s + a); c. alternate representation of (s + a); d. (s + 7)|s5 + j2 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.3 Vector representation of Eq. (8.7) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.4 a. CameraMan® Presenter Camera System automatically follows a subject who wears infrared sensors on their front and back (the front sensor is also a microphone); tracking commands and audio are relayed to CameraMan via a radio frequency link from a unit worn by the subject. b. block diagram. c. closed-loop transfer function. Courtesy of ParkerVision. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 8.1 Pole location as a function of gain for the system of Figure 8.4 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.5 a. Pole plot from Table 8.1; b. root locus Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.6 a. Example system; b. pole-zero plot of G (s) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.7 Vector representation of G(s) from Figure 8.6(a) at -2+ j 3 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.8 Poles and zeros of a general open-loop system with test points, Pi, on the real axis Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.9 Real-axis segments of the root locus for the system of Figure 8.6 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.10 Complete root locus for the system of Figure 8.6 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.11 System for Example 8.2 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.12 Root locus and asymptotes for the system of Figure 8.11 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.13 Root locus example showing real- axis breakaway (-1) and break-in points (2) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.14 Variation of gain along the real axis for the root locus of Figure 8.13 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 8.2 Data for breakaway and break-in points for the root locus of Figure 8.13 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 8.3 Routh table for Eq. (8.40) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 15 Open-loop poles and zeros and calculation of: a Figure 8.15 Open-loop poles and zeros and calculation of: a. angle of departure; b. angle of arrival Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.16 Unity feedback system with complex poles Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 17 Root locus for system of Figure 8 Figure 8.17 Root locus for system of Figure 8.16 showing angle of departure Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.18 Finding and calibrating exact points on the root locus of Figure 8.12 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.19 a. System for Example 8.7; b. root locus sketch Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.20 Making second-order approximations Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.21 System for Example 8.8 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.22 Root locus for Example 8.8 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 8.4 Characteristics of the system of Example 8.8 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 23 Second- and third-order responses for Example 8. 8: a Figure 8.23 Second- and third-order responses for Example 8.8: a. Case 2; b. Case 3 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.24 System requiring a root locus calibrated with p1 as a parameter Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 25 Root locus for the system of Figure 8 Figure 8.25 Root locus for the system of Figure 8.24, with p1 as a parameter Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.26 Positive-feedback system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8. 27 a. Equivalent positive- feedback system for Example 8 Figure 8.27 a. Equivalent positive- feedback system for Example 8.9; b. root locus Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.28 Portion of the root locus for the antenna control system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.29 Step response of the gain-adjusted antenna control system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.30 Root locus of pitch control loop without rate feedback, UFSS vehicle Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.31 Computer simulation of step response of pitch control loop without rate feedback, UFSS vehicle Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.32 Root locus of pitch control loop with rate feedback, UFSS vehicle Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 8.33 Computer simulation of step response of pitch control loop with rate feedback, UFSS vehicle Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8-1 (p. 474) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.2 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.3 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8-4 (p. 476) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8-5 (p. 477) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.6 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8-7 (p. 479) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.8 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.9 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.10 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.11 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.12 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.13 a. Robot equipped to perform arc welding; (figure continues) Courtesy of FANUC Robotics. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.13 (continued) b. block diagram for swing motion system © 1967 H.L. Hardy. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.14 Block diagram of smoother © 1985 Rockwell International. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8. 15 a. Active vibration absorber ((c)1992 AIAA); b Figure P8.15 a. Active vibration absorber ((c)1992 AIAA); b. control system block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8. 16 Floppy disk drive: a. physical representation; b Figure P8.16 Floppy disk drive: a. physical representation; b. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.17 Simplified block diagram of pupil servomechanism Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.18 Active suspension system © 1985 ASME. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.19 F4-E pitch stabilization loop Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.20 Pitch axis attitude control system utilizing momentum wheel Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.21 a. Combustor with microphone and loud speaker ((c)1995 IEEE); b. block diagram ((c)1995 IEEE) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.22 a. Wind turbines generating electricity near Palm Springs, California; (figure continues) © Jim Corwin/ Photo Researchers Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure P8.22 (continued) b. Control loop for a constant-speed pitch-controlled wind turbine ((c)1998 IEEE); c. Drivetrain ((c)1998 IEEE) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.