MOdern control systems 12th by dorf

Design Examples and Design Problems (DP) CHAPTER PAGE 22 Example Hybrid Fuel Vehicles 23 Example Wind Power 24 Example Embedded Computers 28 Example Smart Grid Control Systems 30 Example Rotating Disk Speed Control Example Insulin Delivery Control System 31 32 Example Disk Drive Read System 46 CDP1.1 Traction Drive Motor Control 46 Automobile Noise Control DP1.1 Automobile Cruise Control 46 DP1.2 46 DP1.3 Dairy Farm Automation 46 DPI Welder Control 46 DPI Automobile Traction Control 47 DP1.6 Hubble Telescope Vibration 47 DPI.7 Nanorobotics in Medicine 47 DP1.8 Human Transportation Vehicle CHAPTER Example Photovoltaic Generators Example Fluid Flow Modeling Example Electric Traction Motor Control Example Mechanical Accelerometer Example Laboratory Robot Example Low-Pass Filter Example Disk Drive Read System CDP2.1 Traction Drive Motor Control Selection of Transfer Functions DP2.1 DP2.2 Television Beam Circuit DP2.3 Transfer Function Determination DP2.4 Op Amp Differentiating Circuit Grandfather Clock Pendulum DP2.5 CHAPTER Example Modeling the Orientation of a Space Station Example Printer Belt Drive Example Disk Drive Read System CDP3.1 Traction Drive Motor Control Shock Absorber for Motorcycle DP3.1 Diagonal Matrix Differential DP3.2 Equation Aircraft Arresting Gear DP3.3 Bungi Jumping System DP3.4 State Variable Feedback DP3.5 CHAPTER Example English Channel Boring Machines Example Mars Rover Vehicle Example Blood Pressure Control Example Disk Drive Read System CDP4.1 Traction Drive Motor Control DP4.1 Speed Control System DP4.2 Airplane Roll Angle Control 91 94 104 106 109 111 128 155 155 155 155 155 156 193 200 209 230 230 230 230 230 231 254 257 259 273 296 296 297 DP43 DP4.4 DP4.5 DP4.6 DP4.7 DP4.8 Velocity Control System Laser Eye Surgery Pulse Generating Op Amp Hydrobot Unmanned Underwater Vehicles Mobile Remote-Controlled Video Camera CHAPTER Example Hubble Telescope Pointing Example Attitude Control of an Airplane Example Disk Drive Read System CDP5.1 Traction Drive Motor Control Jet Fighter Roll Angle Control DP5.1 DP5.2 Welding Arm Position Control DP5.3 Automobile Active Suspension DP5.4 Satellite Orientation Control Deburring Robot for Machined DP5.5 Parts DC Motor Position Control DP5.6 Three-Dimensional Cam DP5.7 DP5.8 Spray Paint Robot CHAPTER Example Tracked Vehicle Turning Example Robot-Controlled Motorcycle Example Disk Drive Read System CDP6.1 Traction Drive Motor Control Automobile Ignition Control DP6.1 DP6.2 Mars Guided Vehicle Control DP6.3 Parameter Selection Space Shuttle Rocket DP6.4 DP6.5 Traffic Control System DP6.6 State Variable Feedback Inner and Outer Loop Control DP6.7 DP6.8 PD Controller Design CHAPTER Example Wind Turbine Speed Control Example Laser Manipulator Control Example Robot Control System Example Automobile Velocity Control Example Disk Drive Read System CDP7.1 Traction Drive Motor Control Pitch Rate Aircraft Control DP7.1 Helicopter Velocity Control DP7.2 Mars Rover DP7.3 Remotely Controlled Welder DP7.4 High-Performance Jet Aircraft DP7.5 Control of Walking Motion DP7.6 Mobile Robot with Vision DP7.7 OP Amp Control System DP7.8 Robot Arm Elbow Joint DP7.9 Actuator 297 297 298 298 298 299 343 346 360 379 379 379 379 380 380 380 381 381 404 406 421 438 438 439 439 439 439 439 440 440 497 500 502 505 516 543 543 543 544 544 544 545 545 545 546 DP7.10 DP7.11 DP7.12 DP7.13 DP7.14 Four-Wheel-Steered Automobile Pilot Crane Control Planetary Rover Vehicle Roll Angle Aircraft Autopilot PD Control of a Marginally Stable Process CHAPTER Example Maximum Power Pointing Tracking Example Engraving Machine Control Example Control of a Six-Legged Robot Example Disk Drive Read System CDP8.1 Traction Drive Motor Control DP8.1 Automobile Steering System DP8.2 Autonomous Planetary Explorer-Ambler Vial Position Control Under a DP8.3 Dispenser DP8.4 Automatic Anesthesia Control Black Box Control DP8.5 DP8.6 State Variable System Design DP8.7 PID Controller Design CHAPTER Example PID Control of Wind Turbines Example Remotely Controlled Reconnaissance Vehicle Example Hot Ingot Robot Control 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 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 State Variable Feedback Control DP9.11 Nuclear Reactor Control CHAPTER 10 Example Rotor Winder Control System Example The X-Y Plotter Example Milling Machine Control System Example Disk Drive Read System CDP10.1 Traction Drive Motor Control DPI 0.1 Two Cooperating Robots DPI 0.2 Heading Control of a Bi-Wing Aircraft DPI 0.3 Mast Flight System DP 10.4 High-Speed Train Tilt Control DP10.5 Tape Transport Speed Control DPI 0.6 Automobile Engine Control 546 547 547 548 DPI 0.7 DP10.8 DP10.9 DP10.10 DP10.11 548 583 585 588 602 628 628 628 628 628 630 630 631 674 678 681 700 735 735 735 735 735 735 735 738 738 738 739 739 783 787 790 802 826 826 826 826 826 828 828 Aircraft Roll Angle Control Windmill Radiometer Control with Time Delay Loop Shaping Polymerase Chain Reaction Control CHAPTER 11 Example Automatic Test System Example Diesel Electric Locomotive Example Disk Drive Read System CDP11.1 Traction Drive Motor Control DP11.1 Levitation of a Steel Ball DPI 1.2 Automobile Carburetor DPI 1.3 State Variable Compensation DP11.4 Helicopter Control DP11.5 Manufacturing of Paper DP 11.6 Coupled-Drive Control DPI 1.7 Tracking a Reference Input CHAPTER 12 Example Aircraft Autopilot Example Space Telescope Control Example Robust Bobbin Drive Example Ultra-Precision Diamond Turning Machine Example Digital Audio Tape Controller Example Disk Drive Read System CDP12.1 Traction Drive Motor Control DP12.1 Turntable Position Control DP12.2 Robust Parameter Design DP12.3 Dexterous Hand Master DP12.4 Microscope Control DP12.5 Microscope Control DPI 2.6 Artificial Control of Leg Articulation DP12.7 Elevator Position Control DP12.8 Electric Ventricular Assist Device DP12.9 Space Robot Control DP12.10 Solar Panel Pointing Control DP12.11 Magnetically Levitated Train DP12.12 Mars Guided Vehicle Control DP 12.13 Benchmark Mass-Spring CHAPTER 13 Example Worktable Motion Control Example Fly-by-wire Aircraft Control Example Disk Drive Read System CDP13.1 Traction Drive Motor Control DP13.1 Temperature Control System DP13.2 Disk Drive Read-Write Head- DP13.3 DP13.4 DPI3.5 DPI 3.6 Positioning System Vehicle Traction Control Machine-Tool System Polymer Extruder Control Sampled-Data System 828 828 829 830 830 873 876 888 903 903 903 903 904 904 905 905 935 935 938 940 943 958 974 974 974 974 975 976 976 977 978 978 979 979 979 979 1009 1011 1023 1034 1034 1034 1034 1035 1035 1035 Modern Control Systems TWELFTH EDITION Richard C Dorf University of California, Davis Robert H Bishop Marquette University Prentice Hall Upper Saddle River Boston Columbus San Francisco New York Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town Vice President and Editorial Director, ECS: Marcia J Horton Senior Editor: Andrew Gilfillan Associate Editor: Alice Dworkin Editorial Assistant: William Opaluch Vice President, Production: Vince O'Brien Senior Managing Editor: Scott Disanno Production Liaison: Jane Bonnell Production Editor: Maheswari PonSaravanan,TexTech International Senior Operations Supervisor: Alan Fischer Operations Specialist: Lisa McDowell Executive Marketing Manager: Tim Galligan Marketing Assistant: Mack Patterson Senior Art Director and Cover Designer: Kenny Beck Cover Images: Front: Scarlet macaw flying/Frans Lanting/Corbis; Back: Courtesy of Dr William Kaiser and Dr Philip Rundel of UCLA, and National Instruments Art Editor: Greg Dulles Media Editor: Daniel Sandin Composition/Full-Service Project Management: TexTech International Lab VIEW is a trademark of National Instruments MATLAB is a registered trademark of The Math Works, Inc Company and product names mentioned herein are the trademarks or registered trademarks of their respective owners Copyright © 2011,2008,2005,2001 by Pearson Education, Inc., Upper Saddle River, New Jersey 07458 All rights reserved Manufactured in the United States of America This publication is protected by Copyright and permissions should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use materials from this work, please submit a written request to Pearson Higher Education, Permissions Department, Lake Street, Upper Saddle River, NJ 07458 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 make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book The author and publisher shall not 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 Library of Congress Cataloging-in-Publication Data Dorf, Richard C Modern control systems / Richard C Dorf, Robert H Bishop — 12th ed p cm ISBN-13:978-0-13-602458-3 ISBN-10:0-13-602458-0 Feedback control systems I Bishop, Robert H II Title TJ216.D67 2010 629.83-dc22 2010015651 Prentice Hall is an imprint of 10 www.pearsonhighered.com ISBN-13:978-0-13-602458-3 ISBN-10: 0-13-602458-0 Of the greater teachers— when they are gone, their students will say: we did it ourselves Dedicated to Lynda Ferrera Bishop and Joy MacDonald Dorf In grateful appreciation Contents Preface xi About the Authors xxii 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 CHAPTER Mathematical Models of Systems 49 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 CHAPTER Introduction Brief History of Automatic Control Examples of Control Systems 10 Engineering Design 17 Control System Design 18 Mechatronic Systems 21 Green Engineering 25 The Future Evolution of Control Systems 27 Design Examples 28 Sequential Design Example: Disk Drive Read System 32 Summary 34 Skills Check 35 • Exercises 37 • Problems 39 • Advanced Problems 44 • Design Problems 46 • Terms and Concepts 48 Introduction 50 Differential Equations of Physical Systems 50 Linear Approximations of Physical Systems 55 The Laplace Transform 58 The Transfer Function of Linear Systems 65 Block Diagram Models 79 Signal-Flow Graph Models 84 Design Examples 90 The Simulation of Systems Using Control Design Software 113 Sequential Design Example: Disk Drive Read System 128 Summary 130 Skills Check 131 • Exercises 135 • Problems 141 • Advanced Problems 153 • Design Problems 155 • Computer Problems 157 • Terms and Concepts 159 State Variable Models 3.1 3.2 161 Introduction 162 The State Variables of a Dynamic System 162 VI Contents 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 CHAPTER Feedback Control System Characteristics 234 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 CHAPTER The State Differential Equation 166 Signal-Flow Graph and Block Diagram Models 171 Alternative Signal-Flow Graph and Block Diagram Models 182 The Transfer Function from the State Equation 187 The Time Response and the State Transition Matrix 189 Design Examples 193 Analysis of State Variable Models Using Control Design Software 206 Sequential Design Example: Disk Drive Read System 209 Summary 213 Skills Check 214 • Exercises 217 • Problems 220 • Advanced Problems 227 • Design Problems 230 • Computer Problems 231 • Terms and Concepts 232 Introduction 235 Error Signal Analysis 237 Sensitivity of Control Systems to Parameter Variations 239 Disturbance Signals in a Feedback Control System 242 Control of the Transient Response 247 Steady-State Error 250 The Cost of Feedback 253 Design Examples 254 Control System Characteristics Using Control Design Software 268 Sequential Design Example: Disk Drive Read System 273 Summary 277 Skills Check 279 • Exercises 283 • Problems 287 • Advanced Problems 293 • Design Problems 296 • Computer Problems 300 • Terms and Concepts 303 The Performance of Feedback Control Systems 304 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Introduction 305 Test Input Signals 305 Performance of Second-Order Systems 308 Effects of a Third Pole and a Zero on the Second-Order System Response 314 The 5-Plane Root Location and the Transient Response 320 The Steady-State Error of Feedback Control Systems 322 Performance Indices 330 The Simplification of Linear Systems 339 Design Examples 342 System Performance Using Control Design Software 356 Sequential Design Example: Disk Drive Read System 360 Index Absolute stability, A system description that reveals whether a system is stable or not stable without consideration of other system attributes such as degree of stability, 387,442 Acceleration error constant, Ka, The constant evaluated as lim[i G r (5')G(s)] The steadys—»0 state error for a parabolic input, r{t) = Ar/2, is equal to A/Ka, 325,384 Acceleration input, steady-state error, 324-325 Accelerometer, 71,91,106-109 Ackermann's formula, 834,845-846, 850,855-856,887-889,898 Across-variable, A variable determined by measuring the difference of the values at the two ends of an element, 51,53 Actuator, The device that causes the process to provide the output The device that provides the motive power to the process, 70,159 Additive perturbation, A system perturbation model expressed in the additive form G„(s) = G(s) + A(s), where C(s) is the nominal process function, A(s) is the perturbation that is bounded in magnitude, and Ga(s) is the family of perturbed process functions, 916,982 Agricultural systems, 15 Aircraft, and computer-aided design, 20 unmanned, 16 Aircraft attitude control, 346-356 Aircraft autopilot, 935 Airplane control, 292,532,539-540, 826-827 All-pass network, A nonminimum phase system that passes all frequencies with equal gain, 573-574,633 Alternative signal-flow graph, and block diagram models, 182-187 Ambler, 588 Amplidyne, 143 Amplifier, feedback, 241-242 Amplitude quantization error, The sampled signal available only with a limited precision The error between the actual signal and the sampled signal, 989-990,1037 Analogous variables, Variables associated with electrical, mechanical, thermal, and fluid systems possessing similar solutions providing the analyst with the ability to extend the solution of one system to all analogous systems with the same describing differential equations 55 Analog-to-digital converter, 985,989 Analysis of robustness, 916-918 Anesthesia, blood pressure control during, 259-267 Angle of departure The angle at which a locus leaves a complex pole in the j-plane, 458-459, 462,477-479,551 Angle of the asymptotes The angle that the asymptote makes with respect to the real axis, 4>A, 451.454.551 Antiskid braking systems, 973 Arc welding, 431 Armature-controlled motor, 72,73, 77,89.105,128,153,155 Array operations in MATLAB, 1045-1046 Artificial hand, 12,15.44 Assumptions, Statements that reflect situations and conditions that are taken for granted and without proof In control systems, assumptions are often employed to simplify the physical dynamical models of systems under consideration to make the control design problem more tractable, 50,94-95,159 Asymptote, The path the root locus follows as the parameter becomes very large and approaches infinity The number of asymptotes is equal to the number of poles minus the number of zeros, 451,551 of root locus, 451 Asymptote centroid, The center of the linear asymptotes crA, 452,551 Asymptotic approximation for a Bode diagram, 562 Automated guided vehicle (AGV), 820 Automatic control, history of, 5-9 Automatic fluid dispenser, 229 Automatic test system, 873-875 Automation, The control of a process by automatic means, 7,48 Automobile steering control system, 10 Automobile velocity control, 505-510 Automobiles, hybrid fuel vehicles, 22,48 Auxiliary polynomial The equation that immediately precedes the zero entry in the Routh array, 396,442 Avemar ferry hydrofoil, 815-816 Axis shift, 400 Backward difference rule, A computational method of approximating the time derivative of a function given by x{kT) « x{kT) - x{{k - \)T) T where t - kT, Tis the sample time, and A: = 1,2 , 1008,1037 Bandwidth The frequency at which the frequency response has declined dB from its lowfrequency value 580,633, 663.742 ' 1071 1072 Index Bellman, R., Biological control system, 15 Black, H.S., 6,9,146,912 Block diagram Unidirectional, operational blocks that represent the transfer functions of the elements of the system, 79,80,159 Block diagram models, 79-84, 120-127 alternative signal-flow graphs, 182-187 signal-flow graphs, 171-182 Block diagram transformations, 81-82 Blood pressure control and anesthesia, 259-267 Bobbin drive, 938-940 Bode.H.W., 560,912 Bode plot The logarithm of magnitude of the transfer function is plotted versus the logarithm of (o, the frequency The phase, 4>, of the transfer function is separately plotted versus the logarithm of the frequency, 560-561,603,633,634 asymptotic approximation, 562 Boring machine system, 254-257 Bounded response, 387 Branch, A unidirectional path segment in a signal-flow graph that relates the dependency of an input and an output variable, 84 Break frequency The frequency at which the asymptotic approximation of the frequency response for a pole (or zero) changes slope, 562,565,633 Breakaway point The point on the real axis where the locus departs from the real axis of the v-plane, 454-456,551 Bridge, Tacoma Narrows, 388-390 Camera control, 335-339,371 Canonical form, A fundamental or basic form of the state variable model representation, including phase variable canonical form, input feedforward canonical form, diagonal canonical form, and Jordan canonical form, 173,232 Capek,KareI, 12 Cascade compensation network, A compensator network placed in cascade or series with the system process, 745,747-751,833 Cauchy's theorem If a contour encircles Z zeros and P poles of F(s) traversing clockwise, the corresponding contour in the F(,v)-plane encircles the origin of the F(s)-plane N = Z - P times clockwise, 635,638-642,742 Characteristic equation The relation formed by equating to zero the denominator of a transfer function, 60,159,418 Circles, constant, 663 Closed-loop feedback control system, A system that uses a measurement of the output and compares it with the desired output to control the process, 3,48 Closed-loop feedback sampled-data system 995-999 Closed-loop frequency response, The frequency response of the closedloop transfer function T(jto), 661,742 Closed-loop system, A system with a measurement of the output signal and a comparison with the desired output to generate an error signal that is applied to the actuator, 236.303 Closed-loop transfer function, A ratio of the output signal to the input signal for an interconnection of systems when all the feedback or feedforward loops have been closed or otherwise accounted for Generally obtained by block diagram or signal-flow graph reduction, 82,93,159.417-418 Command following An important aspect of control system design wherein a nonzero reference input is tracked, 857,908 Compensation, Tlie alteration or adjustment of a control system in order to provide a suitable performance, 744,833 of controls systems 796 using a phase-lag network on the Bode diagram, 767 using a phase-lag network on the •v-plane, 768 using a phase-lead network on the Bode diagram 751 using a phase-lead network on the 5-plane, 757 using analytical methods, 776 using integration networks, 764 using state-variable feedback, 834 Compensator, An additional component or circuit that is inserted into the system to compensate for a performance deficiency, 535,744,833,835 Compensator design, full-state feedback and observer, 851 Complementary sensitivity function, The function Gc(s)G(s) r W - i • CMOM '•*• satisfies the relationship S(s) + T{s) = 1, where S(s) is the sensitivity function The function T(s) is the closed-loop transfer function, 238,916,982 Complexity A measure of the structure, intricateness, or behavior of a system that characterizes the relationships and interactions between various components, 17,303 in cost of feedback, 253-254 Complexity of design The intricate pattern of interwoven parts and knowledge required, 17,48 Components, The parts, subsystems, or subassemblies that comprise a total system, 303 in cost of feedback, 253 Computer control systems, 984,985 for electric power plant, 14 Computer-aided design, 20 Computer-aided engineering (CAE), 22 Conditionally stable system, 534 Conformal mapping, A contour mapping that retains the angles on the v-plane on the F(s)-plane, 637,742 Congress, 16 Constant M circles, 664 Constant N circles, 664 Continuous design problem (CDP), 46,155,230,296.379,438,543, 628,735.826,903,974,1034 Contour map, A contour or trajectory in one plane is mapped into another plane by a relation F(s), 636,742 Contours in the v-plane, 636-642 Control engineering, 2.7-8.10 1073 Index Control system An interconnection of components forming a system configuration that will provide a desired response, 2,48,235 characteristics using m-files, 269 design, 18-21 modern examples 10-17 Controllability, 835-841 Controllability matrix, A linear system is (completely) controllable if and only if the controllability matrix P r = [B AB A B A ' - ' B ] has full rank, where A is an n x n matrix For single-input, singleoutput linear systems, the system is controllable if and only if the determinant of the n x n controllability matrix P c is nonzero, 836,908 ControDable system, A system is controllable on the interval [?(>,*/] if there exists a continuous input u{t) such that any initial state x(/ ) can be driven to any arbitrary trial state x(zy), in a finite time interval tf-tQ>0, 836,908 conv function, 116,1053 Convolution signal 307 Corner frequency See Break frequency Cost of feedback, 253-254 Coulomb damper, A type of mechanical damper where the model of the friction force is a nonlinear function of the mass velocity and possesses a discontinuity around zero velocity Also known as dry friction, 53 Critical damping, The case where damping is on the boundary between underdamped and overdamped, 62,114,159 Critically damped system, 114 Damped oscillation An oscillation in which the amplitude decreases with time, 64,159 Dampers, 53 Damping ratio, A measure of damping A dimensionless number for the second-order characteristic equation, 62,159,308,310, 312-313 estimation of, 312 DC amplifier, 78 DC motor An electric actuator that uses an input voltage as a control variable, 70 armature controlled 72,89,159 field controlled, 71 Deadbeat response, A system with a rapid response, minimal overshoot and zero steady-state error for a step input, 781,833 Decade, A factor of 10 in frequency (e.g., the range of frequencies from rad/s to 10 rad/s is one decade), 562,633 of frequencies, 562 Decibel (dB), The units of the logarithmic gain 561,633 Decoupled state variable model, 183 Design, The process of conceiving or inventing the forms, parts, and details of a system to achieve a reasoned purpose, 17-18,48 Design gap, A gap between the complex physical system and the design model intrinsic to the progression from the initial concept to the final product, 17,48 Design of a control system, The arrangement or the plan of the system structure and the selection of suitable components and parameters, 744,833 robot control, 431 in time domain, 835 using a phase-lag network on the Bode diagram, 772 using a phase-lag network on the s-plane, 767,768 using a phase-lead network on the Bode diagram, 751 using a phase-lead network on the v-plane, 757 using integration networks, 764 using state-feedback, 834 Design specifications, A set of prescribed performance criteria, 305,384 Detectable, A system in which the states that are unobservable are naturally stable 839,908 Dexterous Hand Master (DHM), 974 Diagonal canonical form A decoupled canonical form displaying the n distinct system poles on the diagonal of the state variable representation A matrix 183,232 Diesel electric locomotive control, 876-882 Differential equations An equation including differentials of a function, 50,67,159 Differential operator, 60 Differentiating circuit, 76 Digital audio tape controller, 943-952 Digital computer compensator, A system that uses a digital computer as the compensator element, 1001-1004,1037 Digital control system, A control system using digital signals and a digital computer to control a process, 984-1037 Digital control systems using control design software, 1018-1023 Digital controllers, implementation of, 1008-1009 Digital-to-analog converter, 988 Direct-drive arm, 721 Discrete-time approximation, 217 Disk drive read system See Sequential design example Disturbance, An unwanted input signal that affects the output signal, 3,48 Disturbance rejection property, 243-246 Disturbance signal An unwanted input signal that affects the system's output signal 242-247.303 Dominant rools The roots of the characteristic equation that represent or dominate the closed-loop transient response, 315,384,463,551,581,633 Drebbel, Cornells, Dynamics of physical systems, 49 Electric power industry, 13,14 Electric traction motor, 91,104-106, 114,126 Electric ventricular assist device (EVAD) 734-735 Electrohydraulic actuator, 73,74, 144-145 Electrohydraulic servomechanisms, 722 1074 Index Embedded control Feedback control system that employs on-board special-purpose digital computers as integral components of the feedback loop, 24 Energy storage systems (green engineering), 26 Engineering design The process of designing a technical system, 17-18,48 English channel tunnel boring system, 254-257,270-273 Engraving machine, 583,585-588 599-601 Environmental monitoring (green engineering), 26 Epidemic disease, model of, 184-185, 403-404 Equilibrium state, 185 Error, steady-state, 250-253 Error constants acceleration input, 324 position, 323 ramp, 324 velocity, 324 Error signal The difference between the desired output R(s) and the actual output V(5) Therefore, E(s) = R{s) - Y{s), 121,159,215,237,303 analysis, 237-238 Error-squared performance indices, 860 Estimation error, The difference between the actual state and the estimated stale e ( = x(/) - x(t), 847,908 Evans, R., 444 Examples of control systems, 10-17 Exponential matrix function, 167 Extender, 150-151,226,821-822 Federal Reserve Board, 15 Feedback, amplifier, 241-242 control system, 3,10-12, 796-802 cost of, 253-254 full-state control design, 841 negative, 3,6 positive, 39 of state variables, 860,862,909 Feedback control system, and disturbance signals, 242-247 feedback function, 122,123-124, 1053 Feedback signal, A measure of the output of the system used for feedback to control the system 3,48,121 Feedback systems, history of, Field current controlled motor, 71 Final value, The value that the output achieves after all the transient constituents of the response have faded Also referred to as the steady-state value 62,159 of response of y{t), 62 Final value theorem, The theorem that states that lira y(t) = I—>oo lim vF(s), where Y(s) is the Laplace transform of y(t), 62,159 Flow graph See Signal-flow graph Fluid flow modeling, 94-104 Flyball governor, A mechanical device for controlling the speed of a steam engine, 5-6,48 Fly-by-wire aircraft control surface, 1011-1017 Forward rectangular integration, A computational method of approximating the integration of a function given by x(kT) « x((k-l)T)+Tx((k-l)n where r = kT, T is the sample time,and A: = 1,2, , 1008, 1037 Fourier transform, The transformation of a function of time f(t) into the frequency domain, 556, 633 Fourier transform pair, A pair of functions, one in the time domain, denoted by f(t), and the other in the frequency domain, denoted by F(a>), related by the Fourier transform as F(a>) =9 {/()\ phase shift is -180°, 655,742 Logarithmic magnitude, The logarithm of the magnitude of the transfer function, usually expressed in units of 20 dB, thus 201ogio|G|, 563-566,582, 617-618,633 Logarithmic plot See Bode plot Logarithmic sensitivity, A measure of the sensitivity of the system performance to specific parameter changes, given by T S {S)= dT(s)/T{s) « clK/K 'Wher£ T(s) is the system transfer function and K is the parameter of interest, 473,551 Log-magnitude-phase diagram, 656 Loop, A closed path that originates and terminates on the same node of a signal-flow with no node being met twice along the path, 85 Loop gain, The ratio of the feedback signal to the controller actuating signal For a unity feedback system we have L(s) = Gc(s)G(s), 237 Loop on signal-flow graph, 77 Loss of gain, A reduction in the amplitude of the ratio of the output signal to the input signal through a system, usually measured in decibels, 253,303 in cost of feedback, 253 1076 Index Low-fidelity simulations, 101 Low-pass filter, 91,111-113 Isim function 209,210,329-331,332, 359,907.1019,1053 Lunar excursion module (LEM), 814 M circles, 664 Magnetic levitation, 146,822,979 Magnetic tape transport, 532 Manual control system, 10 Manual PID tuning The process of determining the PID controllergains by trial-and-error with minimal analytic analysis, 483,551 Mapping of contours in the 4-plane, 636 Margin, gain, 655,693-694, 703,742 phase, 656,660,693-694,703,742, 1003-1004 margin function, 692,832,1053 Marginally stable, A system is marginally stable if and only if the zero input response remains bounded as t —•