Chapter 6 · Nise/Control Systems Engineering, 3/e 24 Chapter 6: Stability Figure 6.9 Jasonis an...

©2000, John Wiley & Sons, Inc.Nise/Control Systems Engineering, 3/e

Chapter 6: Stability1

Chapter 6

Stability



Figure 6.1Closed-loop polesand response:a. stable system;b. unstable system



Figure 6.2Common causeof problems in finding closed-loop poles:a. original system;b. equivalent system



Figure 6.3Equivalent closed-looptransfer function



Table 6.1Initial layout forRouth table



Table 6.2CompletedRouth table



Figure 6.4a. Feedback system forExample 6.1;b. equivalentclosed-loop system



Table 6.3Completed Routh table for Example 6.1



Table 6.4CompletedRouth table for Example 6.2



Table 6.5Determining signs in first column of aRouth table with zero as first element in a row



Table 6.6Routh table for Example 6.3



Figure 6.5Root positionsto generate evenpolynomials:A , B, C,or any combination



Table 6.9Summary of pole locations for Example 6.5



Figure 6.6Feedbackcontrol systemfor Example 6.6



Figure 6.7Feedback controlsystem forExample 6.7



Table 6.12AlternativeRouth table for Example 6.7



Figure 6.8Feedbackcontrol systemfor Example 6.8



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.



Figure 6.10Feedback controlsystem for Example 6.9



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.



Table 6.16Routh table forExample 6.9 with K = 1386



Table 6.19Routh table for antenna controlcase study



Table 6.20Routh table for UFSS case study



Figure P6.1



Figure P6.2



Figure P6.3



Figure P6.4



Figure P6.5



Figure P6.6



Figure P6.7



Figure P6.8



Figure P6.9



Figure P6.10Closed-loop systemwith pole plot



Figure P6.11Aircraft pitch loopmodel



Figure P6.12Block diagram of achemical process-controlsystem



Figure P6.13a. Soft Armused forfeeding;b. simplifiedblockdiagram

Courtesy of Kazuhiko Kawamura, Vanderbilt University.



Figure P6.14Towed vehicle roll control