Figure 9 - DINUSdinus.ac.id/repository/docs/ajar/kd-slide-10_file_2013-03-20... · 33 Chapter 9: Design via Root Locus Figure 9.27 s-plane picture used to calculate the location of

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

Chapter 9: Design via Root Locus1

Figure 9.1a. Sample root locus,showing possibledesign point viagain adjustment (A)and desired designpoint that cannot bemet via simple gainadjustment (B);b. responses frompoles at A and B



Figure 9.2Compensationtechniques:a. cascade;b. feedback



Figure 9.3Pole at A is:a. on the rootlocus without compensator;b. not on theroot locus withcompensatorpole added;(figure continues)



Figure 9.3(continued)c. approximately on the root locus withcompensatorpole and zero added



Figure 9.4Closed-loopsystem forExample 9.1:a. beforecompensation;b. after ideal integralcompensation



Figure 9.5Root locus foruncompensatedsystem ofFigure 9.4(a)



Figure 9.6Root locus forcompensatedsystem of Figure 9.4(b)



Figure 9.7Ideal integral compensated system response and theuncompensated systemresponse of Example 9.1



Figure 9.8PI controller



Figure 9.9a. Type 1 uncompensated system;b. Type 1 compensatedsystem;c. compensatorpole-zero plot



Figure 9.10Root locus:a. before lag compensation;b. after lag compensation



Figure 9.11Compensated systemfor Example 9.2



Figure 9.12Root locus forcompensated system of Figure 9.11



Table 9.1Predicted characteristics of uncompensated and lag-compensated systems for Example 9.2



Figure 9.13Step responses ofuncompensated andlag-compensatedsystems forExample 9.2



Figure 9.14Step responses of the system for Example 9.2 using different lagcompensators



Figure 9.15Using ideal derivativecompensation:a. uncompensated;b. compensatorzero at –2;(figure continues)



Figure 9.15(continued)c. compensatorzero at –3;d. compensatorzero at – 4



Figure 9.16Uncompensated system and ideal derivativecompensation solutions from Table 9.2



Table 9.2Predicted characteristics for the systems of Figure 9.15



Figure 9.17Feedbackcontrol systemfor Example 9.3



Figure 9.18Root locus for uncompensatedsystem shown in Figure 9.17



Table 9.3Uncompensated and compensated system characteristics for Example 9.3



Figure 9.19Compensateddominant polesuperimposed over the uncompensatedroot locus forExample 9.3



Figure 9.20Evaluating the location of the compensatingzero for Example 9.3



Figure 9.21Root locus for thecompensated system of Example 9.3



Figure 9.22Uncompensated andcompensated system step responses ofExample 9.3



Figure 9.23PD controller



Figure 9.24Geometry of leadcompensation



Figure 9.25Three of the infinitepossible leadcompensator solutions



Figure 9.26Lead compensatordesign, showingevaluation ofuncompensatedand compensateddominant poles forExample 9.4



Table 9.4Comparison of lead compensation designs for Example 9.4



Figure 9.27s-plane pictureused to calculatethe location ofthe compensatorpole for Example 9.4



Figure 9.28Compensated systemroot locus



Figure 9.29Uncompensatedsystem and leadcompensationresponses forExample 9.4



Figure 9.30PID controller



Figure 9.31Uncompensated feedback control system for Example 9.5



Figure 9.32Root locus for theuncompensatedsystem ofExample 9.5



Table 9.5Predicted characteristics of uncompensated, PD- , and PID- compensated systems of Example 9.5



Figure 9.33Calculating thePD compensatorzero for Example 9.5



Figure 9.34Root locus forPD-compensatedsystem ofExample 9.5



Figure 9.35Step responses foruncompensated,PD-compensated, andPID-compensatedsystems ofExample 9.5



Figure 9.36Root locus for PID-compensatedsystemof Example 9.5



Figure 9.37Uncompensatedsystem forExample 9.6



Figure 9.38Root locus for uncompensatedsystem of Example 9.6



Table 9.6Predicted characteristics of uncompensated, lead-compensated, and lag-lead-compensated systems of Example 9.6



Figure 9.39Evaluating thecompensator pole forExample 9.6



Figure 9.40Root locus for lead-compensated system of Example 9.6



Figure 9.41Root locus for lag-lead-compensated systemof Example 9.6



Figure 9.42Improvement in stepresponse forlag-lead-compensatedsystem ofExample 9.6



Figure 9.43Improvement inramp response error for the system ofExample 9.6:a. lead-compensated;b. lag-lead-compensated



Figure 9.44a. Root locusbefore cascading notch filter;b. typical closed-loopstep response before cascading notch filter;(figure continues)



Figure 9.44(continued)c. pole-zero plot of a notch filter;d. root locus aftercascading notch filter;e. closed-loop step response after cascading notch filter.



Table 9.7Types of cascade compensators (slide 1 of 2)

(continued next slide)



Table 9.7Types of cascade compensators (slide 2 of 2)



Figure 9.45Generic controlsystem with feedbackcompensation



Figure 9.46A position control system that uses a tachometer as adifferentiator in the feedback path. Can you see the similarity between this system and the schematic onthe front end papers?

Photo by Mark E. Van Dusen.



Figure 9.47a. Transfer function of a tachometer;b. tachometer feedback compensation



Figure 9.48Equivalentblock diagramof Figure 9.45



Figure 9.49a. System forExample 9.7;b. system withrate feedbackcompensation;c. equivalentcompensatedsystem;d. equivalentcompensatedsystem, showingunity feedback

©2000, John Wiley & Sons, Inc.

Nise/Control Systems Engineering, 3/e

Chapter 13: Digital Control Systems29

Figure 13.25a. Digital controlsystem showingthe digital computerperformingcompensation;b. continuous systemused for design;c. transformed digitalsystem

©2000, John Wiley & Sons, Inc.

Nise/Control Systems Engineering, 3/e

Chapter 13: Digital Control Systems30

Figure 13.26Closed-loop responsefor the compensatedsystem of Example13.12 showing effectof three differentsampling frequencies

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Figure 9 - DINUSdinus.ac.id/repository/docs/ajar/kd-slide-10_file_2013-03-20... · 33 Chapter 9: Design via Root Locus Figure 9.27 s-plane picture used to calculate the location of