1  20
Next
 Nikiforov, Vladimir O., author.
 Cham, Switzerland : Springer, 2022.
 Description
 Book — 1 online resource (xvi, 358 pages) : illustrations (some color).
 Summary

 1. Problem Statement
 2. Internal Model Principle: Overview of Theoretical Approaches
 3. Basic Schemes of Adaptation Algorithms
 4. Parametric Models for Adaptive Control Design
 5. Adaptive Tracking Reference Signals
 6. Adaptive Rejecting External Disturbances
 7. Adaptive Tracking in Systems with Input Delay
 8. Adaptive Compensation in Systems with Input Delay
 9. Internal Model Principle: Overview of Practical Applications.
3. A guide to feedback theory [2021]
 Dawson, Joel L. (Joel Lawrence) author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021
 Description
 Book — 1 online resource
 Summary

 Preface
 1. Linear Systems: What You Missed the First Time
 2. The Basics of Feedback
 3. The Nyquist Stability Criterion
 4. Some Common Loose Ends
 5. Feedback in the Real World
 6. Conclusion and Further Reading
 Notes
 Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
4. Hybrid Feedback Control [2021]
 Sanfelice, Ricardo G.
 Princeton : Princeton University Press, [2021]
 Description
 Book — 1 online resource
 Summary

 Cover
 Title
 Copyright
 Dedicaiton
 Contents
 Preface
 List of Symbols
 1 Introduction
 1.1 Overview
 1.2 Why Hybrid Control?
 1.2.1 Hybrid Models Capture Rich Behavior
 1.2.2 ContinuousTime Systems not Stabilizable via Continuous StateFeedback Can Be Stabilized via Hybrid Control
 1.2.3 Almost Global Asymptotic Stability Turns Global
 1.2.4 Nonrobust Stability Becomes Robust
 1.2.5 Controlled Intersample Behavior and Aperiodic Sampling
 1.2.6 Hybrid Feedback Control Improves Performance
 1.3 Exercises
 1.4 Notes
 2 Modeling Framework
 2.1 Overview
 2.2 On Truly Hybrid Models
 2.3 Modeling
 2.3.1 From Plants and Controllers to ClosedLoop Systems
 2.3.2 Hybrid Basic Conditions
 2.3.3 Solution Concept
 2.3.4 Existence of Solutions to ClosedLoop Systems
 2.3.5 Hybrid System Models with Disturbances
 2.4 Numerical Simulation
 2.5 Exercises
 2.6 Notes
 3 Notions and Analysis Tools
 3.1 Overview
 3.2 Notions
 3.2.1 Asymptotic Stability
 3.2.2 Invariance
 3.2.3 Robustness to Disturbances
 3.3 Analysis Tools
 3.3.1 Hybrid Lyapunov Theorem
 3.3.2 Hybrid Invariance Principle
 3.3.3 Robustness from KL PreAsymptotic Stability
 3.4 Exercises
 3.5 Notes
 4 Uniting Control
 4.1 Overview
 4.2 Hybrid Controller
 4.3 ClosedLoop System
 4.4 Design
 4.5 Exercises
 4.6 Notes
 5 EventTriggered Control
 5.1 Overview
 5.2 Hybrid Controller
 5.3 ClosedLoop System
 5.4 Design
 5.4.1 Completeness of Maximal Solutions
 5.4.2 Minimum Time in Between Events
 5.4.3 PreAsymptotic Stability
 5.5 Exercises
 5.6 Notes
 6 ThrowCatch Control
 6.1 Overview
 6.2 Hybrid Controller
 6.3 ClosedLoop System
 6.4 Design
 6.4.1 Design of Local Stabilizer k0
 6.4.2 Design of Local Stabilizers ki, s and Sets Ai, s
 6.4.3 Design of OpenLoop Control Laws
 6.4.4 Design of Bootstrap Controller and Sets
 6.5 Exercises
 6.6 Notes
 7 Synergistic Control
 7.1 Overview
 7.2 Hybrid Controller
 7.3 ClosedLoop System
 7.4 Design
 7.4.1 The General Case
 7.4.2 The Control Affine Case
 7.5 Exercises
 7.6 Notes
 8 Supervisory Control
 8.1 Overview
 8.2 Hybrid Controller
 8.3 ClosedLoop System
 8.4 Design
 8.5 Exercises
 8.6 Notes
 9 PassivityBased Control
 9.1 Overview
 9.2 Passivity
 9.3 PreAsymptotic Stability from Passivity
 9.4 Design
 9.5 Exercises
 9.6 Notes
 10 Feedback Design via Control Lyapunov Functions
 10.1 Overview
 10.2 Control Lyapunov Functions
 10.3 Design
 10.3.1 Nominal Design
 10.3.2 Robust Design
 10.4 Exercises
 10.5 Notes
 11 Invariants and InvarianceBased Control
 11.1 Overview
 11.2 Nominal and Robust Forward Invariance
 11.2.1 Forward Invariance
 11.2.2 Weak Forward Invariance
 11.2.3 Robust Forward Invariance
 11.3 Design
 11.4 Exercises
 11.5 Notes
 12 Temporal Logic
 12.1 Overview
(source: Nielsen Book Data)
5. Feedback [2020]
 Moir, Tom.
 Cham, Switzerland : Springer, 2020.
 Description
 Book — 1 online resource (xvi, 471 pages)
 Summary

 Introduction to Feedback Control
 The Laplace Transform and Linear TimeInvariant Systems
 Transfer Function Approach
 Speed and PositionControl Systems
 Frequency Response Methods
 Stability and Design of ClosedLoop Systems
 Statespace control
 Digital sampled systems
 Implementation of digital controllers
 Discretetime statespace
 Systems with random noise
 Kalman filtering
 Implementing digital realtime servos
 Nonlinear systems
 Feedback in mathematical algorithms
 Introduction to optimal control.
(source: Nielsen Book Data)
6. Feedback control of dynamic systems [2019]
 Franklin, Gene F., author.
 Eighth edition.  Boston : Pearson, [2019]
 Description
 Book — 902 pages
 Online
Engineering Library (Terman)
Engineering Library (Terman)  Status 

On reserve: Ask at Engineering circulation desk  
TJ216 .F723 2019  Unknown 1day loan 
TJ216 .F723 2019  Unknown 1day loan 
ENGR10501
 Course
 ENGR10501  Feedback Control Design
 Instructor(s)
 Michaelle Mayalu
 Bharadwaj, S. K.
 [S.l.] : NEW AGE INTERNATIONAL PUB, 2019.
 Description
 Book — 1 online resource
 Veloni, Anastasia, author.
 Boca Raton : CRC Press, [2018]
 Description
 Book — pages ; cm
 Summary

 CHAPTER 1: INTRODUCTION 1.1 INTRODUCTION 1.2 DESCRIPTION OF ANALOG AND DIGITAL CONTROL SYSTEMS 1.3 ADVANTAGES OF DIGITAL CONTROL SYSTEMS AND APPLICATIONS
 CHAPTER 2: Z  TRANSFORM 2.1 INTRODUCTION 2.2 FROM LAPLACE TRANSFORM TO Z  TRANSFORM 2.3 Z  TRANSFORM PROPERTIES 2.4 INVERSE Z  TRANSFORM 2.5 FORMULAS TABLE 2.6 SOLVED EXERCISES
 CHAPTER 3: TRANSFER FUNCTION 3.1 INTRODUCTION 3.2 OPEN LOOP SAMPLEDDATA CONTROL SYSTEM 3.3 CLOSED LOOP SAMPLEDDATA CONTROL SYSTEM 3.4 SIGNAL FLOW GRAPHS 3.5 MASON'S FORMULA 3.6 DIFFERENCE EQUATIONS 3.7 FORMULAS TABLE 3.8 SOLVED EXERCISES
 CHAPTER 4: TRANSFER FUNCTION DISCRETIZATION 4.1 INTRODUCTION 4.2 DISCRETIZATION METHODS 4.3 COMPARISON OF DISCRETIZATION METHODS 4.4 FORMULAS TABLE 4.5 SOLVED EXERCISES
 CHAPTER 5: STATESPACE REPRESENTATION 5.1 INTRODUCTION 5.2 DISCRETE TIME STATESPACE EQUATIONS 5.3 SOLUTION OF STATE EQUATIONS 5.4 STATE SPACE REPRESENTATION 5.5 CONTROLLABILITY AND OBSERVABILITY 5.6 STATESPACE DISCRETIZATION 5.7 FORMULAS TABLE 5.8 SOLVED EXERCISES
 CHAPTER 6: STABILITY OF DIGITAL CONTROL SYSTEMS 6.1 STABILITY 6.2 UNITCIRCLE CRITERION 6.3 ROUTH CRITERION USING THE BILINEAR MOBIUS TRANSFORMATION 6.4 JURY CRITERION 6.5 ROOT LOCUS METHOD 6.5.1 RULES FOR APPROXIMATE ESTABLISHMENT OF ROOT LOCUS 6.6 NYQUIST STABILITY CRITERION 6.7 BODE STABILITY CRITERION 6.8 FORMULAS TABLE 6.9 SOLVED EXERCISES ã
 CHAPTER 7: TIME AND HARMONIC RESPONSE ANALYSIS STEADYSTATE ERRORS 7.1 TIME RESPONSE 7.2 STEADYSTATE ERRORS 7.3 HARMONIC RESPONSE OF DISCRETE SYSTEMS 7.4 FORMULAS TABLE 7.5 SOLVED EXERCISES
 CHAPTER 8: COMPENSATION OF DIGITAL CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 INDIRECT DESIGN METHODS 8.3 DIRECT DESIGN METHODS 8.4 PID DIGITAL CONTROLLER 8.4.1 DIGITAL PID CONTROLLER TUNING 8.5 DEADBEAT DIGITAL CONTROLLER 8.6 PHASELEAD/LAG DIGITAL COMPENSATORS 8.7 FORMULAS TABLE 8.8 SOLVED EXERCISES
 CHAPTER 9: SIMULATION TOOLS MATLABSIMULINK  LABVIEW  COMPREHENSIVE CONTROL (CC) 9.1 INTRODUCTION 9.2 CONTROL SYSTEMS SIMULATION USING MATLAB 9.3 SIMULINK 9.4 Program CC BIBLIOGRAPHY.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Veloni, Anastasia, author.
 Boca Raton : CRC Press, [2018]
 Description
 Book — 1 online resource
 Summary

 chapter 1 Introduction
 chapter 2 zTransform
 chapter 3 Transfer Function
 chapter 4 Transfer Function Discretization
 chapter 5 StateSpace Representation
 chapter 6 Stability of Digital Control Systems
 chapter 7 Time and Harmonic Response Analysis SteadyState Errors
 chapter 8 Compensation of Digital Control Systems
 chapter 9 Simulation Tools: MATLAB, Simulink, LabVIEW, Comprehensive Control
 Chen, Mou, author.
 Hoboken, NJ : John Wiley & Sons, 2017.
 Description
 Book — 1 online resource.
 Summary

 Preface xi
 Series Preface xv
 Symbols and Acronyms xvii
 1 Introduction 1
 2 Fractional Calculus and FractionalOrder Systems 9
 2.1 Fractional Calculus 9
 2.1.1 Several Important Functions of Fractional Calculus 9
 2.1.2 Fractional Integral and Derivatives 11
 2.1.3 Some Important Lemmas 12
 2.2 Some Typical FractionalOrder Systems 16
 2.2.1 FractionalOrder Lorenz System 16
 2.2.2 FractionalOrder Van Der Pol Oscillator 18
 2.2.3 FractionalOrder GenesioTesi System 18
 2.2.4 FractionalOrder Arneodo System 20
 2.2.5 FractionalOrder LotkaVolterra System 21
 2.2.6 FractionalOrder Financial System 23
 2.2.7 FractionalOrder NewtonLeipnik System 25
 2.2.8 FractionalOrder Duffing System 27
 2.2.9 FractionalOrder Lu System 29
 2.2.10 FractionalOrder ThreeDimensional System 33
 2.2.11 FractionalOrder Hyperchaotic Oscillator 35
 2.2.12 FractionalOrder FourDimensional Hyperchaotic System 37
 2.2.13 FractionalOrder Hyperchaotic Cellular Neural Network 39
 2.3 Conclusion 41
 3 FractionalOrder PID Controller and FractionalOrder Disturbance Observer 43
 3.1 Problem Statement 43
 3.2 FractionalOrder PID Controller 44
 3.2.1 IntegerOrder PID Controller 44
 3.2.2 FractionalOrder PI?D? Controller 44
 3.2.3 Control Based on FractionalOrder PI?D? Controller 45
 3.3 FrequencyDomain FractionalOrder Disturbance Observer 48
 3.3.1 Classical IntegerOrder Disturbance Observer 48
 3.3.2 FractionalOrder Disturbance Observer 49
 3.3.3 Estimation Performance of FractionalOrder Disturbance Observer 51
 3.3.4 Control Based on FractionalOrder Disturbance Observer 52
 3.4 Conclusion 53
 4 Design of FractionalOrder Controllers for Nonlinear Chaotic Systems and Some Applications 55
 4.1 FractionalOrder Control for a Novel Chaotic SystemWithout Equilibrium 55
 4.1.1 Problem Statement 55
 4.1.2 Design of Chaotic System and Circuit Implementation 56
 4.1.2.1 A Novel Chaotic System 56
 4.1.2.2 Circuit Implementation 58
 4.1.3 Design of FractionalOrder Controller and Stability Analysis 59
 4.1.4 Numerical Simulation 62
 4.1.4.1 Novel Chaotic System 62
 4.1.4.2 Chaotic Systems with Equilibrium 63
 4.2 Application of Chaotic System without Equilibrium in Image Encryption 68
 4.2.1 Image Encryption Scheme 69
 4.2.2 Histogram Analysis 69
 4.2.3 Correlation of Two Adjacent Pixels 71
 4.2.4 AntiAttack Ability of Image Encryption Scheme 71
 4.2.5 Sensitivity Analysis of Key 71
 4.3 Synchronization Control for FractionalOrder Nonlinear Chaotic Systems 73
 4.3.1 Problem Description 73
 4.3.2 Design of Synchronization Controller 73
 4.3.3 Simulation Examples 75
 4.3.3.1 FractionalOrder Chen System 76
 4.3.3.2 FractionalOrder Lorenz System 79
 4.3.4 Application of Synchronization Control Scheme in Secure Communication 82
 4.4 Conclusion 83
 5 SlidingMode Control for FractionalOrder Nonlinear Systems Based on Disturbance Observer 85
 5.1 Problem Statement 85
 5.2 Adaptive Control Design Based on FractionalOrder SlidingMode Disturbance Observer 86
 5.2.1 Design of FractionalOrder SlidingMode Disturbance Observer 86
 5.2.2 Controller Design and Stability Analysis 87
 5.3 Simulation Examples 89
 5.3.1 Example 1 89
 5.3.2 Example 2 91
 5.4 Conclusion 94
 6 DisturbanceObserverBased Neural Control for Uncertain FractionalOrder Rotational Mechanical System 95
 6.1 Problem Statement 95
 6.2 Adaptive Neural Control Design 96
 6.2.1 Design of FractionalOrder Disturbance Observer 96
 6.2.2 Controller Design and Stability Analysis 97
 6.3 Simulation Example 101
 6.4 Conclusion 105
 7 Adaptive Neural Tracking Control for Uncertain FractionalOrder Chaotic Systems Subject to Input Saturation and Disturbance 107
 7.1 Problem Statement 107
 7.2 Adaptive Neural Control Design Based on FractionalOrder Disturbance Observer 108
 7.3 Simulation Examples 115
 7.3.1 FractionalOrder Chaotic Electronic Oscillator 116
 7.3.2 FractionalOrderModified Jerk System 118
 7.4 Conclusion 121
 8 Stabilization Control of ContinuousTime Fractional Positive Systems Based on Disturbance Observer 123
 8.1 Problem Statement 123
 8.1.1 Notation and Definitions 123
 8.1.2 Preliminaries 123
 8.2 Main Results 126
 8.2.1 Fractional Disturbance Observer 126
 8.2.2 Stabilization Control of Fractional Positive System 128
 8.2.3 Simulation of Fractional Positive System 130
 8.2.4 Stabilization Control of Fractional Bounded Positive System 131
 8.2.5 Simulation of Fractional Bounded Positive System 133
 8.3 Conclusion 137
 9 SlidingMode Synchronization Control for FractionalOrder Chaotic Systems with Disturbance 139
 9.1 Problem Statement 139
 9.2 Design of FractionalOrder Disturbance Observer 139
 9.3 DisturbanceObserverBased Synchronization Control of FractionalOrder Chaotic Systems 141
 9.4 Simulation Examples 144
 9.4.1 Synchronization Control of Modified FractionalOrder Jerk System 144
 9.4.2 Synchronization Control of FractionalOrder Liu System 148
 9.5 Conclusion 152
 10 AntiSynchronization Control for FractionalOrder Nonlinear Systems Using Disturbance Observer and Neural Networks 153
 10.1 Problem Statement 153
 10.2 Design of Disturbance Observer 153
 10.3 AntiSynchronization Control of FractionalOrder Nonlinear Systems 155
 10.4 Simulation Examples 158
 10.4.1 AntiSynchronization Control of FractionalOrder Lorenz System 159
 10.4.2 AntiSynchronization Control of FractionalOrder Lu System 161
 10.5 Conclusion 167
 11 Synchronization Control for FractionalOrder Systems Subjected to Input Saturation 169
 11.1 Problem Statement 169
 11.2 Synchronization Control Design of FractionalOrder Systems with Input Saturation 170
 11.3 Simulation Examples 172
 11.3.1 FractionalOrderModified Chua's Circuit with Sine Function 172
 11.3.2 FractionalOrder FourDimensional Modified Chua's Circuit 174
 11.4 Conclusion 179
 12 Synchronization Control for FractionalOrder Chaotic Systems with Input Saturation and Disturbance 181
 12.1 Problem Statement 181
 12.2 Design of FractionalOrder Disturbance Observer 181
 12.3 Design of Synchronization Control 183
 12.4 Simulation Examples 185
 12.4.1 FractionalOrder Chua's Circuit 185
 12.4.2 FractionalOrder Hyperchaos Chua's Circuit 189
 12.5 Conclusion 197
 Appendix A Fractional Derivatives of Some Functions 199
 A.1 Fractional Derivative of Constant 199
 A.2 Fractional Derivative of the Power Function 199
 A.3 Fractional Derivative of the Exponential Function 200
 A.4 Fractional Derivatives of Sine and Cosine Functions 201
 Appendix B Table of Caputo Derivatives 203
 Appendix C Laplace Transforms Involving Fractional Operations 205
 C.1 Laplace Transforms 205
 C.2 Special Functions for Laplace Transforms 205
 C.3 Laplace Transform Tables 205
 References 211
 Index 227.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Huang, AnChyau.
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2015.
 Description
 Book — 1 online resource (x, 218 p.) : ill. (some col.).
 Summary

 Introduction
 Preliminaries
 Underactuated System Dynamics and Coordinate Transformation
 Controller Design
 Cart Pole System
 Overhead Cranes
 TORA System
 Rotary Inverted Pendulum
 Vibration Absorber
 Pendubot
 Bibliography
 Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
12. Feedback control of dynamic systems [2015]
 Franklin, Gene F., author.
 Seventh edition.  Boston : Pearson, [2015]
 Description
 Book — xx, 860 pages : illustrations ; 24 cm
 Summary

Feedback Control of Dynamic Systems covers the material that every engineer, and most scientists and prospective managers, needs to know about feedback controlincluding concepts like stability, tracking, and robustness. Each chapter presents the fundamentals along with comprehensive, workedout examples, all within a realworld context and with historical background information. The authors also provide case studies with close integration of MATLAB throughout. ' Teaching and Learning Experience This program will provide a better teaching and learning experiencefor you and your students. It will provide: ' *An Understandable Introduction to Digital Control: This text is devoted to supporting students equally in their need to grasp both traditional and more modern topics of digital control. *Realworld Perspective: Comprehensive Case Studies and extensive integrated MATLAB/SIMULINK examples illustrate realworld problems and applications.*Focus on Design: The authors focus on design as a theme early on and throughout the entire book, rather than focusing on analysis first and design much later.
(source: Nielsen Book Data)
 Online
Engineering Library (Terman)
Engineering Library (Terman)  Status 

Permanent reserve: Ask at circulation desk  
TJ216 .F723 2015  Unknown 
13. Digital Control Engineering [2014]
 Gopal, M., author.
 Second edition.  New Delhi : New Age International Limited Publishers, [2014]
 Description
 Book — 1 online resource (xiii, 510 pages)
 Boca Raton : Taylor & Francis, 2013.
 Description
 Book — xiii, 278 p. : ill.
 Summary

 Introduction Preliminaries Delta Operator Definition H Performance Index Operations on Systems Some Other Definitions and Lemmas NonFragile State Feedback Control with NormBounded Gain Uncertainty Introduction Problem Statement NonFragile Guaranteed Cost Controller Design Example Conclusion NonFragile Dynamic Output Feedback Control with NormBounded Gain Uncertainty Introduction Problem Statement NonFragile H Dynamic Output Feedback Controller Design Example Conclusion Robust NonFragile Kalman Filtering with NormBounded Gain Uncertainty Introduction Problem Statement Robust NonFragile Filter Design Example Conclusion NonFragile Output Feedback Control with IntervalBounded Coefficient Variations Introduction NonFragile H Controller Design for DiscreteTime Systems NonFragile H Controller Design for ContinuousTime Systems NonFragile H Controllers Design with Sparse Structures Conclusion NonFragile H Filtering with IntervalBounded Coefficient Variations Introduction NonFragile H Filtering for DiscreteTime Systems NonFragile H Filter Design for Linear ContinuousTime Systems Sparse Structured H Filter Design Conclusion Insensitive H Filtering of ContinuousTime Systems Introduction Problem Statement Insensitive H Filter Design Computation of Robust H Performance Index Comparison with the Existing Design Method Example Conclusion Insensitive H Filtering of Delta Operator Systems Introduction Problem Statement Insensitive H Filter Design Example Conclusion Insensitive H Output Tracking Control Introduction Problem Statement Insensitive H Tracking Control Design Example Conclusion Insensitive H Dynamic Output Feedback Control Introduction Problem Statement Insensitive H Controller Design Example Conclusion Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Boca Raton : Taylor & Francis, 2013
 Description
 Book — 1 online resource (xiii, 278 pages)
 Summary

 1. Introduction
 2. Preliminaries
 3. Nonfragile state feedback control with normbounded gain uncertainty
 4. Nonfragile dynamic output feedback control with normbounded gain uncertainty
 5. Robust nonfragile kalman filtering with normbounded gain uncertainty
 6. Nonfragile output feedback control with intervalbounded coefficient variations
 7. Nonfragile H8 filtering with intervalbounded coefficient variations
 8. Insensitive H8 filtering of continuoustime systems
 9. Insensitive H8 filtering of delta operator systems
 10. Insensitive H8 output tracking control
 11. Insensitive H8 dynamic output feedback control
16. Feedback control systems [2011]
 Phillips, Charles L.
 5th ed.  Boston : Prentice Hall, c2011.
 Description
 Book — x, 774 p. : ill. ; 24 cm.
 Summary

 1 INTRODUCTION 1.1 The Control Problem 1.2 Examples of Control Systems 1.3 Short History of Control References
 2 MODELS OF PHYSICAL SYSTEMS 2.1 System Modeling 2.2 Electrical Circuits 2.3 Block Diagrams and Signal Flow Graphs 2.4 Masonis Gain Formula 2.5 Mechanical Translational Systems 2.6 Mechanical Rotational Systems 2.7 Electromechanical Systems 2.8 Sensors 2.9 Temperaturecontrol System 2.10 Analogous Systems 2.11 Transformers and Gears 2.12 Robotic Control System 2.13 System Identification 2.14 Linearization 2.15 Summary References Problems
 3 STATEVARIABLE MODELS 3.1 StateVariable Modeling 3.2 Simulation Diagrams 3.3 Solution of State Equations 3.4 Transfer Functions 3.5 Similarity Transformations 3.6 Digital Simulation 3.7 Controls Software 3.8 Analog Simulation 3.9 Summary References Problems
 4 SYSTEM RESPONSES 4.1 Time Response of FirstOrder Systems 4.2 Time Response of Secondorder Systems 4.3 Time Response Specifications in Design 4.4 Frequency Response of Systems 4.5 Time and Frequency Scaling 4.6 Response of Higherorder Systems 4.7 Reducedorder Models 4.8 Summary References Problems
 5 CONTROL SYSTEM CHARACTERISTICS 5.1 Closedloop Control System 5.2 Stability 5.3 Sensitivity 5.4 Disturbance Rejection 5.5 Steadystate Accuracy 5.6 Transient Response 5.7 Closedloop Frequency Response 5.8 Summary References Problems
 6 STABILITY ANALYSIS 6.1 RouthHurwitz Stability Criterion 6.2 Roots of the Characteristic Equation 6.3 Stability by Simulation 6.4 Summary Problems
 7 ROOTLOCUS ANALYSIS AND DESIGN 7.1 RootLocus Principles 7.2 Some RootLocus Techniques 7.3 Additional RootLocus Techniques 7.4 Additional Properties of the Root Locus 7.5 Other Configurations 7.6 RootLocus Design 7.7 Phaselead Design 7.8 Analytical PhaseLead Design 7.9 PhaseLag Design 7.10 PID Design 7.11 Analytical PID Design 7.12 Complementary Root Locus 7.13 Compensator Realization 7.14 Summary References Problems
 8 FREQUENCYRESPONSE ANALYSIS 8.1 Frequency Responses 8.2 Bode Diagrams 8.3 Additional Terms 8.4 Nyquist Criterion 8.5 Application of the Nyquist Criterion 8.6 Relative Stability and the Bode Diagram 8.7 ClosedLoop Frequency Response 8.8 Summary References Problems
 9 FREQUENCYRESPONSE DESIGN 9.1 Control System Specifications 9.2 Compensation 9.3 Gain Compensation 9.4 PhaseLag Compensation 9.5 PhaseLead Compensation 9.6 Analytical Design 9.7 LagLead Compensation 9.8 PID Controller Design 9.9 Analytical PID Controller Design 9.10 PID Controller Implementation 9.11 FrequencyResponse Software 9.12 Summary References Problems
 10 MODERN CONTROL DESIGN 10.1 PolePlacement Design 10.2 Ackermannis Formula 10.3 State Estimation 10.4 ClosedLoop System Characteristics 10.5 ReducedOrder Estimators 10.6 Controllability and Observability 10.7 Systems with Inputs 10.8 Summary References Problems
 11 DISCRETETIME SYSTEMS 11.1 DiscreteTime System 11.2 Transform Methods 11.3 Theorems of the zTransform 11.4 Solution of Difference Equations 11.5 Inverse zTransform 11.6 Simulation Diagrams and Flow Graphs 11.7 State Variables 11.8 Solution of State Equations 11.9 Summary References Problems
 12 SAMPLEDDATA SYSTEMS 12.1 Sampled Data 12.2 Ideal Sampler 12.3 Properties of the Starred Transform 12.4 Data Reconstruction 12.5 Pulse Transfer Function 12.6 OpenLoop Systems Containing Digital Filters 12.7 ClosedLoop DiscreteTime Systems 12.8 Transfer Functions for ClosedLoop Systems 12.9 State Variables for SampledData Systems 12.10 Summary References Problems
 13 ANALYSIS AND DESIGN OF DIGITAL CONTROL SYSTEMS 13.1 Two Examples 13.2 Discrete System Stability 13.3 Juryis Test 13.4 Mapping the sPlane into the zPlane 13.5 Root Locus 13.6 Nyquist Criterion 13.7 Bilinear Transformation 13.8 RouthnHurwitz Criterion 13.9 Bode Diagram 13.10 SteadyState Accuracy 13.11 Design of Digital Control Systems 13.12 PhaseLag Design 13.13 PhaseLead Design 13.14 Digital PID Controllers 13.15 RootLocus Design 13.16 Summary References Problems
 14 DISCRETETIME POLEASSIGNMENT AND STATE ESTIMATION 14.1 Introduction 14.2 Pole Assignment 14.3 State Estimtion 14.4 ReducedOrder Observers 14.5 Current Observers 14.6 Controllability and Observability 14.7 Systems and Inputs 14.8 Summary References Problems
 15 NONLINEAR SYSTEM ANALYSIS 15.1 Nonlinear System Definitions and Properties 15.2 Review of the Nyquist Criterion 15.3 Describing Function 15.4 Derivations of Describing Functions 15.5 Use of the Describing Function 15.6 Stability of Limit Cycles 15.7 Design 15.8 Application to Other Systems 15.9 Linearization 15.10 Equilibrium States and Lyapunov Stability 15.11 State Plane Analysis 15.12 LinearSystem Response 15.13 Summary References Problems APPENDICES A Matrices B Laplace Transform C Laplace Transform and zTransform Tables D MATLAB Commands Used in This Text E Answers to Selected Problems INDEX.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
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17. Feedback control of dynamic systems [2010]
 Franklin, Gene F.
 6th ed.  Upper Saddle River [N.J.] : Pearson, c2010.
 Description
 Book — xviii, 819 p. : ill. (some col.) ; 24 cm.
 Summary

 1 An Overview and Brief History of Feedback Control 1 A Perspective on Feedback Control 1 Chapter Overview 2 1.1 A Simple Feedback System 3 1.2 A First Analysis of Feedback 6 1.3 A Brief History 9 1.4 An Overview of the Book 14 Summary 16 Review Questions 16 Problems 17
 2 Dynamic Models 20 A Perspective on Dynamic Models 20 Chapter Overview 21 2.1 Dynamics of Mechanical Systems 21 2.1.1 Translational Motion 21 2.1.2 Rotational Motion 27 2.1.3 Combined Rotation and Translation 36 2.1.4 Distributed Parameter Systems 38 2.1.5 Summary: Developing Equations of Motion for Rigid Bodies 40 2.2 Models of Electric Circuits 41 2.3 Models of Electromechanical Systems 45 2.4 Heat and FluidFlow Models 50 2.4.1 Heat Flow 50 2.4.2 Incompressible Fluid Flow 54 2.5 Historical Perspective 60 Summary 62 Review Questions 63 Problems 64
 3 Dynamic Response 74 A Perspective on System Response 74 Chapter Overview 75 3.1 Review of Laplace Transforms 75 3.1.1 Response by Convolution 75 3.1.2 Transfer Functions and Frequency Response 80 3.1.3 The L Laplace Transform 87 3.1.4 Properties of Laplace Transforms 89 3.1.5 Inverse Laplace Transform by PartialFraction Expansion 91 3.1.6 The Final Value Theorem 93 3.1.7 Using Laplace Transforms to Solve Problems 94 3.1.8 Poles and Zeros 96 3.1.9 Linear System Analysis Using MATLAB 97 3.2 System Modeling Diagrams 102 3.2.1 The Block Diagram 102 3.2.2 Block Diagram Reduction Using MATLAB 107 3.3 Effect of Pole Locations 108 3.4 TimeDomain Specifications 116 3.4.1 Rise Time 116 3.4.2 Overshoot and Peak Time 117 3.4.3 Settling Time 118 3.5 Effects of Zeros and Additional Poles 120 3.6 Stability 130 3.6.1 Bounded InputBounded Output Stability 130 3.6.2 Stability of LTI Systems 131 3.6.3 Routh's Stability Criterion 132 3.7 Obtaining Models from Experimental Data 140 3.7.1 Models from TransientResponse Data 142 3.7.2 Models from Other Data 146 3.8 Amplitude and Time Scaling 147 3.8.1 Amplitude Scaling 147 3.8.2 Time Scaling 148 3.9 Historical Perspective 149 Summary 150 Review Questions 151 Problems 152
 4 A First Analysis of Feedback 170 A Perspective on the Analysis of Feedback 170 Chapter Overview 171 4.1 The Basic Equations of Control 171 4.1.1 Stability 173 4.1.2 Tracking 174 4.1.3 Regulation 174 4.1.4 Sensitivity 175 4.2 Control of SteadyState Error to Polynomial Inputs: SystemType 178 4.2.1 System Type for Tracking 179 4.2.2 System Type for Regulation and Disturbance Rejection 183 4.3 The ThreeTerm Controller: PID Control 186 4.3.1 Proportional Control (P) 187 4.3.2 Proportional Plus Integral Control (PI) 187 4.3.3 PID Control 188 4.3.4 ZieglerNichols Tuning of the PID Controller 192 4.4 Introduction to Digital Control 198 4.5 History of Control Theory and Practice 203 Summary 205 Review Questions 206 Problems 207
 5 The RootLocus Design Method 220 A Perspective on the RootLocus Design Method 220 Chapter Overview 221 5.1 Root Locus of a Basic Feedback System 221 5.2 Guidelines for Determining a Root Locus 226 5.2.1 Rules for Plotting a Positive (180a) Root Locus 228 5.2.2 Summary of the Rules for Determining a Root Locus 233 5.2.3 Selecting the Parameter Value 234 5.3 Selected Illustrative Root Loci 236 5.4 Design Using Dynamic Compensation 248 5.4.1 Design Using Lead Compensation 249 5.4.2 Design Using Lag Compensation 254 5.4.3 Design Using Notch Compensation 255 5.4.4 Analog and Digital Implementations 257 5.5 A Design Example Using the Root Locus 260 5.6 Extensions of the RootLocus Method 266 5.6.1 Rules for Plotting a Negative (0a) Root Locus 266 5.6.2 Consideration of Two Parameters 270 5.6.3 Time Delay 272 5.7 Historical Perspective 274 Summary 276 Review Questions 278 Problems 278
 6 The FrequencyResponse Design Method 296 A Perspective on the FrequencyResponse 296 Design Method 296 Chapter Overview 297 6.1 Frequency Response 297 6.1.1 Bode Plot Techniques 304 6.1.2 SteadyState Errors 315 6.2 Neutral Stability 317 6.3 The Nyquist Stability Criterion 319 6.3.1 The Argument Principle 320 6.3.2 Application to Control Design 321 6.4 Stability Margins 334 6.5 Bode's GainPhase Relationship 341 6.6 ClosedLoop Frequency Response 346 6.7 Compensation 347 6.7.1 PD Compensation 348 6.7.2 Lead Compensation 348 6.7.3 PI Compensation 360 6.7.4 Lag Compensation 360 6.7.5 PID Compensation 365 6.7.6 Design Considerations 371 6.7.7 Specifications in Terms of the Sensitivity Function 373 6.7.8 Limitations on Design in Terms of the Sensitivity Function 377 6.8 Time Delay 381 6.9 Alternative Presentation of Data 382 6.9.1 Nichols Chart 382 6.10 Historical Perspective 386 Summary 386 Review Questions 388 Problems 389
 7 StateSpace Design 413 A Perspective on StateSpace Design 413 Chapter Overview 413 7.1 Advantages of StateSpace 414 7.2 System Description in StateSpace 416 7.3 Block Diagrams and StateSpace 421 7.3.1 Time and Amplitude Scaling in StateSpace 424 7.4 Analysis of the State Equations 425 7.4.1 Block Diagrams and Canonical Forms 425 7.4.2 Dynamic Response from the State Equations 436 7.5 ControlLaw Design for FullState Feedback 442 7.5.1 Finding the Control Law 443 7.5.2 Introducing the Reference Input with FullState Feedback 451 7.6 Selection of Pole Locations for Good Design 455 7.6.1 Dominant SecondOrder Poles 456 7.6.2 Symmetric Root Locus (SRL) 457 7.6.3 Comments on the Methods 466 7.7 Estimator Design 466 7.7.1 FullOrder Estimators 466 7.7.2 ReducedOrder Estimators 472 7.7.3 Estimator Pole Selection 476 7.8 Compensator Design: Combined Control Law and Estimator 478 7.9 Introduction of the Reference Input with the Estimator 491 7.9.1 A General Structure for the Reference Input 492 7.9.2 Selecting the Gain 501 7.10 Integral Control and Robust Tracking 502 7.10.1 Integral Control 503 7.10.2 Robust Tracking Control: The ErrorSpace Approach 505 7.10.3 The Extended Estimator 516 7.11 Loop Transfer Recovery (LTR) 519 7.12 Direct Design with Rational Transfer Functions 524 7.13 Design for Systems with Pure Time Delay 527 7.14 Historical Perspective 530 Summary 533 Review Questions 534 Problems 536
 8 Digital Control 558 A Perspective on Digital Control 558 Chapter Overview 559 8.1 Digitization 559 8.2 Dynamic Analysis of Discrete Systems 561 8.2.1 zTransform 561 8.2.2 zTransform Inversion 562 8.2.3 Relationship between s and z 565 8.2.4 Final Value Theorem 566 8.3 Design Using Discrete Equivalents 568 8.3.1 Matched PoleZero (MPZ) Method 571 8.3.2 Modified Matched PoleZero (MMPZ) Method 575 8.3.3 Comparison of Digital Approximation Methods 575 8.3.4 Applicability Limits of the Discrete Equivalent Design Method 576 8.4 Hardware Characteristics 577 8.4.1 AnalogtoDigital (A/D) Converters 577 8.4.2 DigitaltoAnalog (D/A) Converters 578 8.4.3 AntiAlias Prefilters 578 8.4.4 The Computer 579 8.5 SampleRate Selection 580 8.5.1 Tracking Effectiveness 581 8.5.2 Disturbance Rejection 581 8.5.3 Effect of AntiAlias Prefilter 582 8.5.4 Asynchronous Sampling 583 8.6 Discrete Design 583 8.6.1 Analysis Tools 583 8.6.2 Feedback Properties 585 8.6.3 Discrete Design Example 586 8.6.4 Discrete Analysis of Designs 588 8.7 Historical Perspective 590 Summary 591 Review Questions 592 Problems 593
 9 Nonlinear Systems 599 Perspective on Nonlinear Systems 599 Chapter Overview 600 9.1 Introduction and Motivation: Why Study Nonlinear Systems? 600 9.2 Analysis by Linearization 602 9.2.1 Linearization by SmallSignal Analysis 603 9.2.2 Linearization by Nonlinear Feedback 608 9.2.3 Linearization by Inverse Nonlinearity 608 9.3 Equivalent Gain Analysis Using the Root Locus 609 9.3.1 Integrator Antiwindup 615 9.4 Equivalent Gain Analysis Using Frequency Response: Describing Functions 619 9.4.1 Stability Analysis Using Describing Functions 625 9.5 Analysis and Design Based on Stability 629 9.5.1 The Phase Plane 630 9.5.2 Lyapunov Stability Analysis 636 9.5.3 The Circle Criterion 642 Summary 649 Review Questions 650 Problems 650
 10 Control System Design: Principles and Case Studies 660 A Perspective on Design Principles 660 Chapter Overview 661 10.1 An Outline of Control Systems Design 662 10.2 Design of a Satellite's Attitude Control 667 10.3 Lateral and Longitudinal Control of a Boeing 747 684 10.3.1 Yaw Damper 689 10.3.2 AltitudeHold Autopilot 696 10.4 Control of the FuelAir Ratio in an Automotive Engine 702 10.5 Control of the Read/Write Head Assembly of a Hard Disk 709 10.6 Control ofRTP Systems in SemiconductorWafer Manufacturing 717 10.7 Chemotaxis or How E. Coli Swims Away from Trouble 731 10.8 Historical Perspective 739 Summary 741 Review Questions 742 Problems 743 Appendix A LaplaceTransforms 757 A.1 The L Laplace Transform 757 A.1.1 Properties of Laplace Transforms 757 A.1.2 Inverse LaplaceTransform by PartialFraction Expansion 766 A.1.3 The Initial Value Theorem 769 A.1.4 Final Value Theorem 770 Appendix B Solutions to the EndofChapter Questions 772 Appendix C MATLAB(R) Commands 788 Bibliography 793 Index 803.
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TJ216 .F723 2010  Unknown 
TJ216 .F723 2010  Unknown 
 Åström, Karl J. (Karl Johan), 1934
 Princeton, N.J. : Princeton University Press, c2008.
 Description
 Book — xii, 396 p. : ill., map ; 27 cm.
 Summary

 Preface ix
 Chapter 1. Introduction 1 1.1 What Is Feedback? 1 1.2 What Is Control? 3 1.3 Feedback Examples 5 1.4 Feedback Properties 17 1.5 Simple Forms of Feedback 23 1.6 Further Reading 25 Exercises 25
 Chapter 2. System Modeling 27 2.1 Modeling Concepts 27 2.2 State Space Models 34 2.3 Modeling Methodology 44 2.4 Modeling Examples 51 2.5 Further Reading 61 Exercises 61
 Chapter 3. Examples 65 3.1 Cruise Control 65 3.2 Bicycle Dynamics 69 3.3 Operational Amplifier Circuits 71 3.4 Computing Systems and Networks 75 3.5 Atomic Force Microscopy 81 3.6 Drug Administration 84 3.7 Population Dynamics 89 Exercises 91
 Chapter 4. Dynamic Behavior 95 4.1 Solving Differential Equations 95 4.2 Qualitative Analysis 98 4.3 Stability 102 4.4 Lyapunov Stability Analysis 110 4.5 Parametric and Nonlocal Behavior 120 4.6 Further Reading 126 Exercises 126
 Chapter 5. Linear Systems 131 5.1 Basic Definitions 131 5.2 The Matrix Exponential 136 5.3 Input/Output Response 145 5.4 Linearization 158 5.5 Further Reading 163 Exercises 164
 Chapter 6. State Feedback 167 6.1 Reachability 167 6.2 Stabilization by State Feedback 175 6.3 State Feedback Design 183 6.4 Integral Action 195 6.5 Further Reading 197 Exercises 197
 Chapter 7. Output Feedback 201 7.1 Observability 201 7.2 State Estimation 206 7.3 Control Using Estimated State 211 7.4 Kalman Filtering 215 7.5 A General Controller Structure 219 7.6 Further Reading 226 Exercises 226
 Chapter 8. Transfer Functions 229 8.1 Frequency Domain Modeling 229 8.2 Derivation of the Transfer Function 231 8.3 Block Diagrams and Transfer Functions 242 8.4 The Bode Plot 250 8.5 Laplace Transforms 259 8.6 Further Reading 262 Exercises 262
 Chapter 9. Frequency Domain Analysis 267 9.1 The Loop Transfer Function 267 9.2 The Nyquist Criterion 270 9.3 Stability Margins 278 9.4 Bode's Relations and Minimum Phase Systems 283 9.5 Generalized Notions of Gain and Phase 285 9.6 Further Reading 290 Exercises 290
 Chapter 10. PID Control 293 10.1 Basic Control Functions 293 10.2 Simple Controllers for Complex Systems 298 10.3 PID Tuning 302 10.4 Integrator Windup 306 10.5 Implementation 308 10.6 Further Reading 312 Exercises 313
 Chapter 11. Frequency Domain Design 315 11.1 Sensitivity Functions 315 11.2 Feedforward Design 319 11.3 Performance Specifications 322 11.4 Feedback Design via Loop Shaping 326 11.5 Fundamental Limitations 331 11.6 Design Example 340 11.7 Further Reading 343 Exercises 344
 Chapter 12. Robust Performance 347 12.1 Modeling Uncertainty 347 12.2 Stability in the Presence of Uncertainty 352 12.3 Performance in the Presence of Uncertainty 358 12.4 Robust Pole Placement 361 12.5 Design for Robust Performance 369 12.6 Further Reading 374 Exercises 374
 Bibliography 377 Index 387.
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Engineering Library (Terman)
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Stacks  
TJ216 .A78 2008  Unknown 
19. Modern control systems [2008]
 Dorf, Richard C.
 11th ed.  Upper Saddle River, NJ : Pearson/Prentice Hall, c2008.
 Description
 Book — xxv, 1018 p. : col. ill. ; 25 cm.
 Summary

 1. Introduction to Control Systems. 2. Mathematical Models of Systems. 3. State Variable Models. 4. Feedback Control System Characteristics. 5. The Performance of Feedback Control Systems. 6. The Stability of Linear Feedback Systems. 7. The Root Locus Method. 8. Frequency Response Methods. 9. Stability in the Frequency Domain. 10. The Design of Feedback Control Systems. 11. The Design of State Variable Feedback Systems. 12. Robust Control Systems. 13. Digital Control Systems. Appendix A: MATLAB(R) Basics. Appendix B: LabVIEW MathScript Basics. WEB RESOURCES Appendix C: Symbols, Units, and Conversion Factors. Appendix D: Laplace Transform Pairs Appendix E: An Introduction to Matrix Algebra Appendix F: Decibel Conversion Appendix G: Complex Numbers Appendix H: zTransfer Pairs Preface
 Appendix I: DiscreteTime Evaluation of the Time Response References. Index.
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TJ216 .D67 2008  Unknown 
 Southampton, U.K. ; Boston : WIT Press, c2007.
 Description
 Book — xxvi, 465 p. : ill. ; 25 cm.
 Summary

 Chapter 1: Introduction: Part I  Design and information in biological systems Design, function and elegance
 Evolution and design
 Evolution and information
 Using the information
 Information and the origin of life
 Wider aspects of information transfer Chapter 2: Introduction: Part II  Genomes, genes and proteins Introduction
 Genome evolution
 Organisation of DNA for replication
 More on gene structure and function
 Gene sequence and cellular function
 How many genes are needed?
 Variations on a theme
 Concluding remarks Chapter 3: Green grass, red blood, blueprint: reflections on life, selfreplication, and evolution Of crystals and colloids
 Queen Christina's challenge
 Different views of life
 The beginnings of life on Earth
 Models of biogenesis: glimpses of the truth or justso stories?
 Information aspects of life, selfreplication and evolution
 Virtual worlds
 Von Neumann's selfreplicating automata
 In von Neumann's tracks artificial life
 Realworld selfreplication
 Selfreplicating probes for space exploration
 Selfreplication and nanotechnology
 A comparison of natural and artificial selfreplication
 Trivial vs. nontrivial selfreplication
 Epistemic cut and semantic closure
 Epilogue Chapter 4: The Human Genome Project Introduction
 The Human Genome Project
 The human genome sequence draft
 Functional genomics: assigning function to the genome
 Applications of the human genome sequence in medical sciences
 Concluding remarks Chapter 5: The laws of thermodynamics: entropy, free energy, information and complexity Introduction
 Application of classical thermodynamics to physics
 Application of laws of thermodynamics in engineering
 Application of thermodynamics to biology  glycolysis and the tricarboxylic acid (Krebs) cycle
 Equivalence of thermal and statistical entropy
 Role of entropy in contemporary studies
 Pros and cons of Shannon entropy
 Information and complexity
 Evolution  a universal paradigm
 Evolution of the biosphere
 Thermodynamics, life's emergence and Darwinian evolution
 Conclusion Chapter 6: The laws of thermodynamics and Homo sapiens the engineer Introduction
 Biology and thermodynamics: a bad start to the relationship
 The heat engine and the work engine
 The survival engine: e.g. the lizard
 Work engines and the dome of the Florence Cathedral
 Brunelleschi, the complexity engine
 Some consequences for Homo sapiens
 Is there a fourth law of thermodynamics?
 How mathematical is biology? How chaotic is evolution?
 Conclusion Chapter 7: Information theory and sensory perception Introduction
 Theories of perception
 Information and redundancy
 Information and noise in continuous signals
 Discussion
 Conclusion Chapter 8: Flight Introduction
 The origins of flight
 Flight roles and techniques
 Designs for flight The energetics of flight: power, speed, size and behavioural ecology
 Conclusions Chapter 9: Insect observations and hexapod design Introduction
 Justification for biologically inspired engineering
 Anatomy and leg structure of insects
 Insect behaviours
 Insect walking
 The swing/stance phases
 Rough terrain strategies
 Compliance
 Dynamic considerations
 Biological principles for hexapod design Chapter 10: The palm  a model for success? Introduction
 Evolutionary theory and complexity
 Botanical aspects of palms
 Engineering aspects of palms
 Conclusions
 Glossary Chapter 11: The human world seen as living systems Introduction
 The RSA
 The living systems approach
 Companies
 Changing society in the modern world
 The human factor
 Democracy and justice
 Globalisation
 Local communities
 Conclusion Chapter 12: Searching for improvement Introduction
 Fitness landscapes and interactions
 Some methods for design improvement
 Summary Chapter 13: Living systems, 'total design' and the evolution of the automobile: the significance and application of holistic design methods in automotive design, manufacture and operation Introduction
 Living systems, biomimesis and the 'closed loop' economy
 Total design, process and methods
 Sustainability and Life Cycle Assessment
 Three product case histories
 The need for change in automotive design, manufacture and operation
 Current trends in automotive design and manufacture
 Potential changes in the automotive industry
 LCA and automotive manufacture
 Conclusion Chapter 14: Emergent behaviours in autonomous robots Introduction
 Complexity from simplicity  emergent behaviour from simple rules
 Modern reactive robots
 More complex behaviours
 Hardware implementation
 Emergent behaviour through evolution
 Conclusion.
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QH508 .D47 2007  Available 
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