Physiological Control Systems: Analysis, Simulation, and Estimation (IEEE Press Series on Biomedical Engineering)

331 Pages·1999·8.03 MB·English

by  Michael C. K. Khoo

PHYSIOLOGICAL
CONTROL SYSTEMS
IEEE PRESS SERIES IN BIOMEDICAL ENGINEERING
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PHYSIOLOGICAL
CONTROL SYSTEMS
Analysis, Simulation, and Estimation
Michael C. K. Khoo
BiomedicalEngineering Department
University ofSouthern California
IEEE Engineering inMedicine andBiology Society, Sponsor
IEEE Press Series onBiomedical Engineering
Metin Akay, Series Editor
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TheInstituteofElectricalandElectronics Engineers,Inc.,NewYork
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Library of Congress Cataloging-in-Publication Data
Khoo,MichaelC. K.
Physiological controlsystems:analysis, simulation, and
estimation / Michael C. K.Khoo
p. em.- (IEEEPressseriesonbiomedical engineering)
Includesbibliographical references andindex.
ISBN0-7803-3408-6
I. Physiology-Mathematical models. 2. Biological control
systems-Mathematical models, I. Title. II.Series.
QP33.6.M36K48 1999 99-27107
571.7'OI5118--<lc 21 CIP
Contents
PREFACE xiii
ACKNOWLEDGMENTS xvii
CHAPTER 1 Introduction 1
1.1 Preliminary Considerations
1.2 Historical Background 2
1.3 Systems Analysis: Fundamental Concepts 3
1.4 Physiological Control Systems Analysis: A Simple
Example 5
1.5 Differences between Engineering and Physiological
Control Systems 7
1.6 The Science (and Art) ofModeling 9
Bibliography 11
Problems 11
CHAPTER 2 Mathematical Modeling 13
2.1 Generalized System Properties 13
2.2 Models with Combinations ofSystem Elements 16
2.3 Linear Models ofPhysiological Systems: Two
Examples 19
2.4 Distributed-Parameter versus Lumped-Parameter
Models 21
2.5 Linear Systems and the Superposition Principle 23
2.6 Laplace Transforms and Transfer Functions 24
2.7 The Impulse Response and Linear Convolution 26
vii
viii Contents
2.8 State-Space Analysis 28
2.9 Computer Analysis and Simulation-MATLAB and
SIMULINK 30
Bibliography 35
Problems 35
CHAPTER 3 Static Analysis of Physiological Systems 39
3.1 Introduction 39
3.2 Open-Loop versus Closed-Loop Systems 40
3.3 Determination ofthe Steady-State Operating Point 42
3.4 Steady-State Analysis Using SIMULINK 45
3.5 Regulation ofCardiac Output 48
3.5.1 TheCardiacOutputCurve 49
3.5.2 TheVenous ReturnCurve 51
3.5.3 Closed-Loop Analysis: HeartandSystemicCirculation
Combined 54
3.6 Regulation ofGlucose 55
3.7 Chemical Regulation ofVentilation 59
3.7.1 TheGasExchanger 59
3.7.2 TheRespiratory Controller 61
3.7.3 Closed-Loop Analysis: LungsandControllerCombined 62
Bibliography 65
Problems 66
CHAPTER 4 Time-DomainAnalysis ofLinearControlSystems 69
4.1 Linearized Respiratory Mechanics: Open-Loop versus
Closed-Loop 69
4.2 Open-Loop and Closed-Loop Transient Responses:
First-Order Model 71
4.2.1 ImpulseResponse 71
4.2.2 StepResponse 73
4.3 Open-Loop versus Closed-Loop Transient Responses:
Second-Order Model 73
4.3.1 ImpulseResponses 73
4.3.2 StepResponses 78
4.4 Descriptors ofImpulse and Step Responses 81
4.4.1 Generalized Second-Order Dynamics 81
4.4.2 TransientResponseDescriptors 84
4.5 Open-Loop versus Closed-Loop Dynamics: Other
Considerations 86
4.5.1 Reduction oftheEffectsofExternalDisturbances 86
4.5.2 Reduction oftheEffectsofParameterVariations 87
4.5.3 Integral Control 88
4.5.4 Derivative Feedback 90
4.6 Transient Response Analysis Using MATLAB 91
Contents ix
4.7 SIMULINK Application: Dynamics ofNeuromuscular
Reflex Motion 91
4.7.1 AModel ofNeuromuscularReflex Motion 92
4.7.2 SIMULINK Implementation 94
Bibliography 96
Problems 97
CHAPTER 5 Frequency-Domain Analysisof Linear Control Systems 101
5.1 Steady-State Responses toSinusoidal Inputs 101
5.1.1 Open-Loop Frequency Response 101
5.1.2Closed-Loop Frequency Response 105
5.1.3Relationship between Transient andFrequency Responses 105
5.2 GraphicalRepresentationsofFrequencyResponse 108
5.2.1 BodePlotRepresentation 108
5.2.2Nichols Charts III
5.2.3 Nyquist Plots 113
5.3 Frequency-Domain Analysis UsingMATLAB and
SIMULINK 114
5.3.1 UsingMATLAB 114
5.3.2 Using SIMULINK 116
5.4 Frequency Response ofaModelofCirculatory
Control 119
5.4.1 TheModel 119
5.4.2 Simulations withtheModel 121
5.4.3 Frequency Response oftheModel 121
5.5 Frequency Response ofGlucose-Insulin Regulation 124
5.5.1 TheModel 124
5.5.2 Simulations withtheModel 125
5.5.3Frequency Responses oftheModel 125
Bibliography 128
Problems 129
CHAPTER 6 Stability Analysis: Linear Approaches 131
6.1 Stability andTransient Response 131
6.2 RootLocusPlots 134
6.3 Routh-Hurwitz Stability Criterion 137
6.4 NyquistCriterion forStability 139
6.5 Relative Stability 143
6.6 Stability Analysis ofthePupillary LightReflex 146
6.6.1 Routh-Hurwitz Analysis 147
6.6.2 Nyquist Analysis 149
6.7 ModelofCheyne-Stokes Breathing 151
6.7.1 CO Exchange intheLungs 151
2
6.7.2 Transport Delays 153