Modern control systems

Design Examples and Design Problems (DP) CHAPTER Example Example Example COP I DPI.I DP1.2 DP1.3 DPI.4 DP 1.5 DP1.6 I Turntable Speed Control Insulin Delivery Control System Disk Drive Read System Traction Drive Motor Control Automobile Noise Control Automobile Cruise Control Dairy Farm Automation Welder Control Automobile Traction Control Huhble Telescope Vibration Reduction CHAPTER Example Example Example Example Example CDP2.1 DP2.1 DP2.2 DP2.3 DP2.4 Electric Traction Motor Control Mechanical Accelerometer Laboratory Robot Low-Pass Filter Disk Drive Read System Traction Drive Motor Control Selection of Transfer Functions Television Beam Circuit Transfer Function Determination Op Amp Diffcrentiating Circuit CHAPTER Example Example CDP3.1 DP3.1 DP3.2 Printer Belt Drive Disk Drive Read System Traction Drive Motor Control Shock Absorher for Motorcycle Diagonal Matrix Differential Equation Aircraft Arresting Gear Bungi Jumping System DP3.3 DP3.4 CHAPTER English Channel Boring Example Machines Mars Rover Vehicle Example Disk Drive Read System Example Traction Drive Motor Control CDP4.1 Speed Control System DP4.1 Airplane Roll Angle Control DP4.2 Velocity Control System DP4.3 Laser Eye Surgery DP4.4 Pulse Generating Op Amp DP4.5 Circuit PAGE 21 22 23 30 30 30 30 30 30 31 72 75 77 78 94 115 116 116 116 116 147 155 170 170 170 171 17l 191 194 202 218 218 218 218 219 220 CHAPTER Hubble Telescope Pointing Example Control Disk Drive Read System Example Traction Drive Motor Control CDP5.1 Jet Fighter Roll Angle Control DP5.1 Welding Arm Position Control DP5.2 Automobile Activc Suspension DP5.3 System Space Satellite Orientation DP5.4 Control Deburring Rohot for Machined DP5.5 Parts DC Motor Position Control DP5.6 CHAPTER Example Example CDP6.1 DP6.1 DP6.2 DP6.3 DP6.4 DP6.5 Dpo.6 Tracked Vehicle Turning Control Disk Drive Read System Traction Drive Motor Control Automohile Ignition Control Mars Guidcd Vehicle Control Parameter Selection Space Shuttle Rocket Tratlic Control System Robot Steered Motorcycle CHAPTER Laser Manipulator Control" Example System Rohot Control System Example Disk Drive Read System Example Traction Drive Motor Control CDP7.1 Pitch Rate Aircraft Control DP7.1 Two-Rotor Helicopter Velocity DP7.2 Control Mars Rover DP7.3 Remotely Controlled Welder DP7.4 High-Performance Jet Aircraft DP7.5 Automatic Control of Walking DP7.o Motion OP Amp Control System DP7.7 Robot Arm Elbow Joint Actuator DP7.8 Four- Wheel-Steered Automobile DP7.9 Pilot Crane Control DP7.1O Planetary RO\u Vehicle DP7.11 AutoIllobile Distance Control DP7.12 Roll Angle Aircraft Autopilot DP7.13 259 271 285 285 286 286 286 287 287 307 317 328 328 328 328 328 328 329 368 371 379 398 398 398 398 399 399 399 400 400 400 401 401 402 403 CHAPTER Example Engraving Machine Control System Example Disk Drive Read System CDP8.] Traction Drive Motor Control DP8.1 Automobile Steering System DP8.2 Autonomous Planetary ExplorerAmbler DPS.3 Vial Position Control Under a Dispenser DP8.4 Automatic Anesthesia Control System CHAPTER Example Remotely Controlled Reconnaissance Vehicle Example Disk Drive Read System CDP9.1 Traction Drive Motor Control DP9.1 Mobile Robot for Toxic Waste Cleanup DP9.2 Control of a Flexible Arm DP9.3 Automatic Blood Pressure Regulator DP9.4 Robot Tennis Player DP9.5 Electrohydraulic Actuator DP9.6 Steel Strip-Rolling Mill DP9.7 Lunar Vehicle Control DP9.8 High-Speed Steel-Rolling Mill DP9.9 Two- Tank Temperature Control DP9.10 Hot Ingot Robot Control CHAPTER Example Example Example CDP10.1 DPIO.I DPIO.2 DPIO.3 DPIO.4 DPIO.5 DPIO.6 DPIO.7 DPIO.S DPIO.9 10 Rotor Winder Control System The X- Y Plotter Disk Drive Read System Traction Drive Motor Control Two Cooperating Robots Heading Control of a Bi- Wing Aircraft Mast Flight System Robot Control Using Vision High-Speed Train Tilt Control Large Antenna Control Tape Transport Speed Control Automobile Engine Control Aircraft Roll Angle Control CHAPTER II Example Automatic Test System Example Disk Drive Read System 435 444 484 464 CDPI1.l DPl1.l DPIl.2 DPI \.3 DPIl.4 DPIl.5 DPI1.6 Traction Drive Motor Control Levitation of a Steel Ball Automobile Carburetor Control Diesel-Electric Locomotive Helicopter Control Manufacturing of Paper Coupled-Drive Control CHAPTER Example Example Example Example 12 Aircraft Autopilot Space Telescope Control System Robust Bobbin Drive Ultra-Precision Diamond Turning Machine Disk Drive Read System Traction Drive Motor Control Turntable Position Control Control of a DAT Player Pointing Accuracy of the GRID Device Dexterous Hand Master Microscope Control Microscope Control Artificial Control of Leg Articulation Elevator Position Control Electric Ventricular Assist Device Space Robot Control Solar Panel Pointing Control Magnetically Levitated Train Control Mars Guided Vehicle Control with PID Benchmark Mass-Spring System 674 674 674 674 675 676 676 464 465 466 505 519 546 546 546 546 548 54S 548 549 549 549 550 592 595 605 624 624 624 625 625 626 627 627 627 627 655 666 Example CDPI2.1 DP12.1 DP12.2 DP12.3 DPI2.4 DP12.5 DP12.6 DP12.7 DP12.8 DP12.9 DP12.10 DP12.11 DP12.12 DP12.13 DP12.14 CHAPTER 13 Example Worktable Motion Control System Example Disk Drive Read System CDPl3.1 Traction Drive Motor Control DPI3.1 Temperature Control System DP13.2 Disk Drive Read-Write HeadPositioning System DP13.3 Vehicle Traction Control DPI3.4 Machine-Tool System DP13.5 Polymer Extruder Control 702 703 705 710 719 733 733 733 735 735 736 737 737 738 738 739 739 740 740 740 762 774 782 782 782 782 782 782 Modem Control Systems NINTH EDITION Richard C Dorf University of California, Davis ; Robert H Bishop _ The University of Texas at Austin Library of Congress Cataloging-in-Publication Data Dorf Richard C Modern control systems / Richard C Dorf and Robert H Bishop.-9th ed p.cm Includes bibliographical references and index ISBN 0-13-030660-6 Feedback comol systems Control theory L Bishop, Robert H., 1957-11.Title TJ21 D67 2000 629.8'3-dc21 00-039967 Vice-president and Editorial Director: Marcia Horton Acquisitions editor: Eric Frank Editorial assistant: Jennie Diblasi • Executive managing editor: Vince O'Brien Managing editor: David A George Vice-President of production and manufacturing: David l¥ Riccardi Editorial supervision: Scott Disanno Cover director: Carole Anson Cover: John Christiana Marketing manager: Danny Hoyt Manufacturing buyer: Pat Brown Peter Menzel Photography/Mark Tilden's Robots-Analog Nervous Net-"Unibug 1.0" Walking Past Desert Flowers at Great Sand Dunes National Monument in Colorado Image is from upcoming photography book "Robo sapiens," by Peter Menzel and Faith D' Aluisio Material World Books M.LT Press Fall, 2000 ©2001 by Prentice-Hall, Inc Upper Saddle River, New Jersey 07458 All rights reserved No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher The author and publisher of this book have used their best efforts in preparing this book These efforts include the development, research, and testing of the theories and programs to determine their effectiveness The author and publisher shall nqt be liable in any event for incidental or consequential damages in connection with, or arising out of the furnishing, performance, or use of these programs MATLAB is a registered trademark of The MathWorks, Inc 24 Prime Park Way, Natick, MA 01760-1520 Phone: (508) 653-1415, Fax: (508) 653-2997 Email: info@mathworks.com Printed in the United States of America 10 ISBN 0-13-030660-6 Pearson Pearson Prentice Pearson Pearson Pearson Pearson Prentice Education Limited (UK) Education Australia Pty Ltd Hall Canada Ltd Educaci6n de Mexico, S.A de C.V Education Japan KK Education China Ltd Education Asia Pte Ltd Hall, Upper Saddle River, New Jersey Of the greater teacherswhen they are gone, their students will say: we did it ourselves Dedicated to: Lynda Ferrera Bishop and Joy MacDonald Darf In grateful appreciation Contents CHAPTER Introduction to Control Systems 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 CHAPTER Introduction History of Automatic Control Two Examples of the Use of Feedback Control Engineering Practice Examples of Modern Control Systems Automatic Assembly and Robots 16 The Future Evolution of Control Systems 16 Engineering Design 18 Control System Design 19 Design Example: Turntable Speed Control 21 Design Example: Insulin Delivery Control System 22 Sequential Design Example: Disk Drive Read System 23 Exercises 24 Problems 25 Design Problems 30 Terms and Concepts 31 Mathematical Models of Systems 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 32 Introduction 33 Differential Equations of Physical Systems 33 Linear Approximations of Physical Systems 38 The Laplace Transform 41 The Transfer Function of Linear Systems 47 Block Diagram Models 62 Signal-Flow Graph Models 66 Computer Analysis of Control Systems 71 Design Examples 72 The Simulation of Systems Using MATLAB 80 Sequential Design Example: Disk Drive Read System Summary 97 Exercises 98 Problems 104 Advanced Problems 115 Design Problems 115 MATLABProblems 116 Terms and Concepts 118 94 v vi CHAPTER Contents State Variable Models 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 CHAPTER 119 Introduction 120 The State Variables of a Dynamic System 121 The State Differential Equation 123 Signal-Flow Graph State Models 126 Alternative Signal-Flow Graph State Models 132 The Transfer Function from the State Equation 136 The Time Response and the State Transition Matrix 138 A Discrete-Time Evaluation of the Time Response 142 Design Example: Printer Belt Drive 147 Analysis of State Variable Models Using MATLAB 152 Sequential Design Example: Disk Drive Read System 155 Summary 159 Exercises 159 Problems 161 Advanced Problems 168 Design Problems 170 MATLABProblems 171 Terms and Concepts 172 Feedback Control System Characteristics 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 173 Open- and Closed-Loop Control Systems 174 Sensitivity of Control Systems to Parameter Variations 176 Control of the Transient Response of Control Systems 179 Disturbance Signals in a Feedback Control System 183 Steady-State Error 187 The Cost of Feedback 190 Design Example: English Channel Boring Machines 191 Design Example: Mars Rover Vehicle 194 Control System Characteristics Using MATLAB 196 Sequential Design Example: Disk Drive Read System 202 Summary 205 Exercises 207 Problems 209 Advanced Problems 215 Design Problems 218 MATLABProblems 220 Terms and Concepts 222 vii ix Contents :5 - The Performance of Feedback Control Systems 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.U 5.13 • 5.14 The Stability of Linear Feedback Systems ~6 l 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 # - l 224 Introduction Test Input Signals 225 Performance of a Second-Order System 227 Effects of a Third Pole and a Zero on the Second-Order Response 233 Estimation of the Damping Ratio 238 The s-Plane Root Location and the Transient Response The Steady-State Error of Feedback Control Systems The Steady-State Error of Nonunity Feedback Systems Performance Indices 247 The Simplification of Linear Systems 256 Design Example: Hubble Telescope Pointing Control System Performance Using MATLAB 262 Sequential Design Example: Disk Drive Read System Summary 277 Exen;~=,es 275 Problems 279 Advanced Problems 284 Design Problems 285 287 MATLAB Problems Terms and Concepts 289 223 System 239 240 245 259 271 - 290 The Concept of Stability 291 The Routh-Hurwitz Stability Criterion 295 The Relative Stability of Feedback Control Systems 303 The Stability of State Variable Systems 304 Design Example: Tracked Vehicle Turning Control 307 System Stability Using MATLAB 309 317 Sequential Design Example: Disk Drive Read System Summary 320 Exercises 321 Problems 322 Advanced Problems 326 Design Problems 328 329 MATLAB Problems Terms and Concepts 330 viii Contents CHAPTER The Root Locus Method 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 331 Introduction 332 The Root Locus Concept 332 The Root Locus Procedure 339 An Example of a Control System Analysis and Design Utilizing the Root Locus Method 351 Parameter Design by the Root Locus Method 354 Sensitivity and the Root Locus 359 Three-Term (PID) Controllers 366 Design Example: Laser Manipulator Control System 368 The Design of a Robot Control System 371 The Root Locus Using MATLAB 373 Sequential Design Example: Disk Drive Read System 379 Summary 380 Exercises 384 Problems 386 -Advanced Problems 396 Design Problems 398 MATLABProblems 404 Terms and Concepts 405 / CHAPTER Frequency Response Methods 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 CHAPTER 406 Introduction 407 Frequency Response Plots 409 An Example of Drawing the Bode Diagram 426 Frequency Response Measurements 430 Performance Specifications in the Frequency Domain Log Magnitude and Phase Diagrams 435 Design Example: Engraving Machine Control System Frequency Response Methods Using MATLAB 439 Sequential Design Example: Disk Drive Read System Summary 446 Exercises 451 Problems 454 Advanced Problems 462 Design Problems 464 MATLABProblems 466 Terms and Concepts 468 Stability in the Frequency Domain 9.1 9.2 Introduction 470 Mapping Contours in the s-Plane 471 469 432 435 444 ix Contents 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 aMPTER The Nyquist Criterion 476 Relative Stability and the Nyquist Criterion 487 Time-Domain Performance Criteria Specified in the Frequency Domain 493 System Bandwidth 500 The Stability of Control Systems with Time Delays 501 Design Example: Remotely Controlled Reconnaissance Vehicle 505 PID Controllers in the Frequency Domain 508 Stability in the Frequency Domain Using MATLAB 509 Sequential Design Example: Disk Drive Read System 519 Summary 521 Exercises 528 Problems 534 Advanced Problems 544 Design Problems 546 MATLABProblems 551 Terms and Concepts 552 10 The Design of Feedback Control Systems 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 10.14 10.15 10.16 553 554 Introduction Approaches to System Design 555 Cascade Compensation Networks 557 Phase-Lead Design Using the Bode Diagram 561 Phase-Lead Design Using the Root Locus 567 System Design Using Integration Networks 573 Phase-Lag Design Using the Root Locus 576 Phase-Lag Design Using the Bode Diagram 580 System Design on the Bode Diagram Using Analytical and Computer Methods 585 Systems with a Prefilter 586 Design for Deadbeat Response 589 Design Example: Rotor Winder Control System 592 Design Example: The X- Y Plotter 595 System Design Using MATLAB 598 Sequential Design Example: Disk Drive Read System 605 Summary 606 Exercises 608 Problems 610 Advanced Problems 621 Design Problems 624 MATLABProblems 628 Terms and Concepts 630 816 References 18 B C Crandall, Nanotechnology, MIT Press, Cambridge, Mass., 1996 19 E Colle, "Localization of an Autonomou& Vehicle with Beacons," International Journal of Robotics and Automation 8, no 1, 1993, pp 30-38 20 W Leventon, "Mountain Bike Suspension Allows Easy Adjustment," Design News, July 19, 1993, pp 75-77 21 A Cavallo et aI., Using MATLAB,'SIMULINK, and Control System Toolbox, Prentice Hall, Englewood Cliffs, N.J., 1996 , 22 M JiJ,J11shidi, Computer Aided Analysis and Design of Linear Comrol Systems, Prentice Hall, Englewood Cliffs, N.J., 1992 "'_.23 G E Carlson, Signal and Linear System AnaJysis, John Wiley & Sons, NY, 1998 24 M Fujita, "Synthesis of an ElectromagneticSuspension Syst~fn," Proceedings of the Conference on Decision and Control, IEEE Press)~ew York, 1992 25 D Cho, "Magnetic Levitation Systems," IEEE Control S~ems, February 1993, pp 42-::48 26 W J Palm, Modeling, Analysis, Control of Dynamic Systems, 2nd ed., John Wiley & Sons, NY, 2000: 27 H Kazerooni, "Human Extenders," Journal of Bynamic Systems, ASME, June 1993, pp 281-290 28 C N Dorny, Understanding Dynamic Systems, Prentice Hall, EJ.1glewoodCliffs, N.J., 1993 29 Chen, Chi-Tsing, Linear System Theory and Design, Oxford Univ Press, NY, 3rd Ed., 1998 , 30 G E Forsythe, M A Malcolm: and C B.Moler, Com- puter Methods for Mathematical Computations, Prentice Hall, Englewoo~.cliffs, N.J., 1977 Chapter "'1 R C Dorf, Electrical Engineering Handbook, 2nd ed., CRC Press, Boca Raton;"Fla., 1998 R C Dorf, Electric Circuits, 3rd ed., John Wiley & Sons, New York, 1996 C E Rohrs, J L Melsa, and D Schultz, Linear Control Systems, McGraw-Hill, New York, 1993 , P E Sarachik, Principles of Linear Systems,:Cambridge Univ Press, New York, 1997 B K Bose, Power Electronics and Variable Frequency Drives, IEEE Press, Piscataway, NJ.,,1997 J C Nelson, Operational Amplifier Circuits, Butterworth, New York, 1995 Motomatic Speed Control, Electro-Craft Corp., Hopkins, Minn., 1999 M W Spong et aI., Robot Control Dynamics, Motion Planning and Analysis, IEEE Press, New York, 1993 R C Dorf, Encyclopedia of Robotics, John Wiley & Sons, New York, 1988 10 D J Bak, "Dancer Arm Feedback Regulates Tension Control," Design News, April 6, 1987, pp 132-133 11 "The Smart Projector Demystified," Science Digest, May 1985, p 76 12 R Meier, "Control of Blood Pressure During Anesthesia," IEEE Control Systems, December 1992, pp 12-16 13 L Fortuna and G Muscato, "A Roll Stabilization Systern for a Monohull Ship," IEEE Transactions on Control Systems Technology, January 1996,pp 18-28 14 C N Dorny, Understanding Dynamic Systems, Prentice Hall, Englewood Cliffs, N.J., 1993 15 D W Clarke, "Sensor, Actuator, and Loop Validation," IEEE Control Systems, August 1995,pp 39 45 16 S P Parker, Encyclopedia of Engineering, 2nd ed., McGraw-Hill, New York, 1993 17 ¥ S.Markow, "An Automated Laser System for Eye Surgery," IEEE Engineering in Medicine and Biology, December 1989, pp 24-29 18 M Eslami, Theory of Sensitivity in Dynamic Systems, Springer-Verlag, New York, 1994 19 Y M Pulyer, Electromagnetic Devices for Motion Control, Springer-Verlag, New York, 1992 20 J R Layne, "Control for Cargo Ship Steering," IEEE Control Systems, December 1993, pp 23-33 21 S Begley, "Greetings From Mars," Newsweek, July 14, 1997,pp.23-29 22 M Carroll, "Assault on the Red Planet," Popular Science, January 1997, pp 44 49 23 C: S Powell, "Lilliput in Space," Discover, March 1999, p 38 Chapter I C M Close and D K Frederick, Modeling and Analysis of Dynamic Systems, 2nd ed., Houghton Mifflin, Boston, 1993 R C Dorf, Electric Circuits, 3rd ed., John Wiley & Sons, New York, 1996 B K Bose, Power Electronics aYl;dVariable Frequency Drives, IEEE Press, Pis~ataway, N.J., 1997 P R Clement, "A Note on Third-Order Linear Systerns," IRE Transactions on Automatic Control, June 1960, p 15l R N Clark, Introduction to Automatic Control Systems, John Wiley & Sons, New York, 1962, pp 115-124 D Graham and R C Lathrop, "The Synthesis of Optimum Response: Criteria and Standard Forms, Part 2," Trans of the AlEE 72, November 1953, pp 273-288 T L Floyd and D Buchla, Basic Operational Amplifiers, Prentice Hall, Upper Saddle River, 1999 817 References nd W Palm, Modeling, Analysis and Control, ed., John Wiley & Sons, NY, 2000 W Rugh, Linear System Theory, 2nd ed., Prentice Hall, Englewood Cliffs, N.1.,1997 F B Farquharson, "Aerodynamic Stability of Suspension Bridges, with Special Reference to the Tacoma Narrows Bridge," Bulletin 116, Part I, The Engineering Experiment Station, University of Washington, 1950 A Hurwitz, "On the Conditions Under Which an Equation Has Only Roots with Negative Real Parts," Mathematische Annalen 46, 1895, pp 273-284 Also in Selected Papers on Mathematical Trends in Control Theory, Dover, New York, 1964, pp 70-82 E.1 Routh, Dynamics of a System of Rigid Bodies, Macmillan, New York, 1892 G G.Wang, "Design of Turning Control for a Tracked • Vehicle," IEEE Control Systems, April 1990, pp 122-125 N Mohan, Power Electronics, John Wiley & Sons, New York, 1995 10 R C Dorf, Encyclopedia of Robotics, John Wiley & Sons, New York, 1988 11 R C Dorf and A Kusiak, Handbook of Manufacturing and Automation, John Wiley & Sons, New York,1994 12 A N Michel, "Stability: The Common Thread in the Evolution of Control," IEEE Control Systems, June 1996, pp 50-60 13 S P Parker, Encyclopedia of Engineering, 2nd ed., McGraw-Hill, New York, 1933 14 Levine et aI., "Control of Magnetic Bearings," IEEE Transactions on Control Systems Technology, September 1996, pp 524-544 15 F S.Ho, "Traffic Flow Modeling and Control," IEEE Control Systems, October 1996, pp.16-24 16 G E Young and K N Reid, "Control of Moving Webs," Journal of Dynamics, ASME, June 1993, pp 309-316 17 D W Freeman, "Jump-Jet Airliner," Popular Mechanics, June 1993, pp 38-40 18 B Sweetman, "Venture Star-21st-Century Space Shuttle," Popular Science, October 1996, pp 43-47 19 S Lee, "Intelligent Sensing and Control for Advanced Teleoperation," IEEE Control Systems, June 1993, pp 19-28 20 "Uplifting," The Economist, July 10,1993, p 79 21 R N Clark, "The Routh-Hurwitz Stability Criterion, Chapter Revisited," IEEE Control Systems, June 1992, pp R C Dorf, Electrical Engineering Handbook, 2nd 119-120 ed., CRC Press, Boca Raton, Fla., 1998 R C Dorf, Electric Circuits, 3rd ed., John Wiley & 22 S.G.Tzafestas, Applied Control, Marcel Dekker, New York, 1993, pp 274-276 Sons, New York, 1996 R C Dorf, Encyclopedia of Robotics, John Wiley & Sons, New York, 1988 L E Ryan, "Control of an Impact Printt