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©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability1
Chapter 6
Stability
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability2
Figure 6.1Closed-loop polesand response:a. stable system;b. unstable system
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability3
Figure 6.2Common causeof problems in finding closed-loop poles:a. original system;b. equivalent system
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability4
Figure 6.3Equivalent closed-looptransfer function
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Chapter 6: Stability5
Table 6.1Initial layout forRouth table
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Chapter 6: Stability6
Table 6.2CompletedRouth table
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Chapter 6: Stability7
Figure 6.4a. Feedback system forExample 6.1;b. equivalentclosed-loop system
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Chapter 6: Stability8
Table 6.3Completed Routh table for Example 6.1
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Chapter 6: Stability9
Table 6.4CompletedRouth table for Example 6.2
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability10
Table 6.5Determining signs in first column of aRouth table with zero as first element in a row
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability11
Table 6.6Routh table for Example 6.3
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability12
Table 6.7Routh table for Example 6.4
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability13
Figure 6.5Root positionsto generate evenpolynomials:A , B, C,or any combination
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Chapter 6: Stability14
Table 6.8Routh table for Example 6.5
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability15
Table 6.9Summary of pole locations for Example 6.5
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability16
Figure 6.6Feedbackcontrol systemfor Example 6.6
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability17
Table 6.10Routh table for Example 6.6
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability18
Figure 6.7Feedback controlsystem forExample 6.7
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability19
Table 6.11Routh table for Example 6.7
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability20
Table 6.12AlternativeRouth table for Example 6.7
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Chapter 6: Stability21
Figure 6.8Feedbackcontrol systemfor Example 6.8
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Chapter 6: Stability22
Table 6.13Routh table for Example 6.8
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability23
Table 6.14Summary of pole locations for Example 6.8
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability24
Figure 6.9Jason is anunderwater, remote-controlled vehicle that has been used to explore the wreckage of the Lusitania. Themanipulator andcamera comprisesome of the vehicle’scontrol systems.
Courtesy of Woods Hole Oceanographic Institution.
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability25
Figure 6.10Feedback controlsystem for Example 6.9
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability26
Figure 6.11The FANUC Robot M- 400 can beconfigured for 4- or 5-axis of motion. It is seen here moving and stacking boxes.
Courtesy of Fanuc Robotics.
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability27
Table 6.15Routh table for Example 6.9
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability28
Table 6.16Routh table forExample 6.9 with K = 1386
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Chapter 6: Stability29
Table 6.17Routh table for Example 6.10
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Chapter 6: Stability30
Table 6.18Routh table for Example 6.11
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Chapter 6: Stability31
Table 6.19Routh table for antenna controlcase study
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Chapter 6: Stability32
Table 6.20Routh table for UFSS case study
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Chapter 6: Stability33
Figure P6.1
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability34
Figure P6.2
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability35
Figure P6.3
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Chapter 6: Stability36
Figure P6.4
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Chapter 6: Stability37
Figure P6.5
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Chapter 6: Stability38
Figure P6.6
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Chapter 6: Stability39
Figure P6.7
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Chapter 6: Stability40
Figure P6.8
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Chapter 6: Stability41
Figure P6.9
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Chapter 6: Stability42
Figure P6.10Closed-loop systemwith pole plot
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Chapter 6: Stability43
Figure P6.11Aircraft pitch loopmodel
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Chapter 6: Stability44
Figure P6.12Block diagram of achemical process-controlsystem
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Chapter 6: Stability45
Figure P6.13a. Soft Armused forfeeding;b. simplifiedblockdiagram
Courtesy of Kazuhiko Kawamura, Vanderbilt University.
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability46
Figure P6.14Towed vehicle roll control
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Chapter 6: Stability47
Figure P6.15Cutting force controlsystem
© 1997 ASME.
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Chapter 6: Stability48
Figure P6.16a. A magneticlevitationtransportation system;b. simplified blockdiagram (©1998 IEEE)
© Japan Air Lines/ Photo Researchers.
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability49
Table 6.1Initial layout forRouth table
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability50
Table 6.2CompletedRouth table
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Chapter 6: Stability51
Table 6.3Completed Routh table for Example 6.1
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability52
Table 6.4CompletedRouth table for Example 6.2
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability53
Table 6.5Determining signs in first column of aRouth table with zero as first element in a row
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability54
Table 6.6Routh table for Example 6.3
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability55
Table 6.7Routh table for Example 6.4
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability56
Table 6.8Routh table for Example 6.5
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Chapter 6: Stability57
Table 6.9Summary of pole locations for Example 6.5
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Chapter 6: Stability58
Table 6.10Routh table for Example 6.6
©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e
Chapter 6: Stability59
Table 6.11Routh table for Example 6.7
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Chapter 6: Stability60
Table 6.12AlternativeRouth table for Example 6.7
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Chapter 6: Stability61
Table 6.13Routh table for Example 6.8
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Chapter 6: Stability62
Table 6.14Summary of pole locations for Example 6.8
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Chapter 6: Stability63
Table 6.15Routh table for Example 6.9
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Chapter 6: Stability64
Table 6.16Routh table forExample 6.9 with K = 1386
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Chapter 6: Stability65
Table 6.17Routh table for Example 6.10
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Table 6.18Routh table for Example 6.11
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Chapter 6: Stability67
Table 6.19Routh table for antenna controlcase study
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Table 6.20Routh table for UFSS case study