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Simulation of Dynamic Systems with MATLAB® and Simulink®, 3rd Edition

Name: Simulation of Dynamic Systems with MATLAB® and Simulink®, 3rd Edition
ISBN: 9781498787802

by Harold Klee, Randal Allen

February 2018

Intermediate to advanced

852 pages

24h 42m

English

CRC Press

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Cover Page
Half Title page
Title Page
Copyright Page
Dedication
Contents
Foreword
Preface
About the Authors
Chapter 1 Mathematical Modeling
1.1 Introduction1.1.1 Importance of Models1.2 Derivation of A Mathematical Model1.3 Difference Equations1.4 First Look at Discrete-Time Systems1.4.1 Inherently Discrete-Time Systems1.5 Case Study: Population Dynamics (Single Species)

Chapter 2 Continuous-Time Systems
2.1 Introduction2.2 First-Order Systems2.2.1 Step Response of First-Order Systems2.3 Second-Order Systems2.3.1 Conversion of Two First-Order Equations to a Second-Order Model2.4 Simulation Diagrams2.4.1 Systems of Equations2.5 Higher-Order Systems2.6 State Variables2.6.1 Conversion from Linear State Variable Form to Single Input–Single Output Form2.6.2 General Solution of the State Equations2.7 Nonlinear Systems2.7.1 Friction2.7.2 Dead Zone and Saturation2.7.3 Backlash2.7.4 Hysteresis2.7.5 Quantization2.7.6 Sustained Oscillations and Limit Cycles2.8 Case Study: Submarine Depth Control System
Chapter 3 Elementary Numerical Integration
3.1 Introduction3.2 Discrete-Time System Approximation of a Continuous First-Order System3.3 Euler Integration3.3.1 Explicit Euler Integration3.3.2 Implicit Euler Integration3.4 Trapezoidal Integration3.5 Discrete Approximation of Nonlinear First-Order Systems3.6 Discrete State Equations3.7 Improvements to Euler Integration3.7.1 Improved Euler Integration3.7.2 Modified Euler Integration3.7.3 Discrete-Time System Matrices3.8 Case Study: Vertical Ascent of a Diver
Chapter 4 Linear Systems Analysis
4.1 Introduction4.2 Laplace Transform4.2.1 Properties of the Laplace Transform4.2.2 Inverse Laplace Transform4.2.3 Laplace Transform of the System Response4.2.4 Partial Fraction Expansion4.3 Transfer Function4.3.1 Impulse Function4.3.2 Relationship between Unit Step Function and Unit Impulse Function4.3.3 Impulse Response4.3.4 Relationship between Impulse Response and Transfer Function4.3.5 Systems with Multiple Inputs and Outputs4.3.6 Transformation from State Variable Model to Transfer Function4.4 Stability of Linear Time Invariant Continuous-Time Systems4.4.1 Characteristic Polynomial4.4.2 Feedback Control System4.5 Frequency Response of LTI Continuous-Time Systems4.5.1 Stability of Linear Feedback Control Systems Based on Frequency Response4.6 z-Transform4.6.1 Discrete-Time Impulse Function4.6.2 Inverse z-Transform4.6.3 Partial Fraction Expansion4.7 z-Domain Transfer Function4.7.1 Nonzero Initial Conditions4.7.2 Approximating Continuous-Time System Transfer Functions4.7.3 Simulation Diagrams and State Variables4.7.4 Solution of Linear Discrete-Time State Equations4.7.5 Weighting Sequence (Impulse Response Function)4.8 Stability of LTI Discrete-Time Systems4.8.1 Complex Poles of H(z)4.9 Frequency Response of Discrete-Time Systems4.9.1 Steady-State Sinusoidal Response4.9.2 Properties of the Discrete-Time Frequency Response Function4.9.3 Sampling Theorem4.9.4 Digital Filters4.10 Control System Toolbox4.10.1 Transfer Function Models4.10.2 State-Space Models4.10.3 State-Space/Transfer Function Conversion4.10.4 System Interconnections4.10.5 System Response4.10.6 Continuous-/Discrete-Time System Conversion4.10.7 Frequency Response4.10.8 Root Locus4.11 Case Study: Longitudinal Control of an Aircraft4.11.1 Digital Simulation of Aircraft Longitudinal Dynamics4.11.2 Simulation of State Variable Model4.12 Case Study: Notch Filter for Electrocardiograph Waveform4.12.1 Multinotch Filters
Chapter 5 Simulink®
5.1 Introduction5.2 Building a Simulink Model5.2.1 The Simulink Library5.2.2 Running a Simulink Model5.3 Simulation of Linear Systems5.3.1 Transfer Fcn Block5.3.2 State-Space Block5.4 Algebraic Loops5.4.1 Eliminating Algebraic Loops5.4.2 Algebraic Equations5.5 More Simulink Blocks5.5.1 Discontinuities5.5.2 Friction5.5.3 Dead Zone and Saturation5.5.4 Backlash5.5.5 Hysteresis5.5.6 Quantization5.6 Subsystems5.6.1 PHYSBE5.6.2 Car-Following Subsystem5.6.3 Subsystem Using Fcn Blocks5.7 Discrete-Time Systems5.7.1 Simulation of an Inherently Discrete-Time System5.7.2 Discrete-Time Integrator5.7.3 Centralized Integration5.7.4 Digital Filters5.7.5 Discrete-Time Transfer Function5.8 MATLAB and Simulink Interface5.9 Hybrid Systems: Continuous- and Discrete-Time Components5.10 Monte Carlo Simulation5.10.1 Monte Carlo Simulation Requiring Solution of a Mathematical Model5.11 Case Study: Pilot Ejection5.12 Case Study: Kalman Filtering5.12.1 Continuous-Time Kalman Filter5.12.2 Steady-State Kalman Filter5.12.3 Discrete-Time Kalman Filter5.12.4 Simulink Simulations5.12.5 Summary5.13 Case Study: Cascaded Tanks with Flow Logic Control
Chapter 6 Intermediate Numerical Integration
6.1 Introduction6.2 Runge–Kutta (RK) (One-Step Methods)6.2.1 Taylor Series Method6.2.2 Second-Order Runge–Kutta Method6.2.3 Truncation Errors6.2.4 High-Order Runge–Kutta Methods6.2.5 Linear Systems: Approximate Solutions Using RK Integration6.2.6 Continuous-Time Models with Polynomial Solutions6.2.7 Higher-Order Systems6.3 Adaptive Techniques6.3.1 Repeated RK with Interval Halving6.3.2 Constant Step Size (T = 1 min)6.3.3 Adaptive Step Size (Initial T = 1 min)6.3.4 RK–Fehlberg6.4 Multistep Methods6.4.1 Explicit Methods6.4.2 Implicit Methods6.4.3 Predictor–Corrector Methods6.5 Stiff Systems6.5.1 Stiffness Property in First-Order System6.5.2 Stiff Second-Order System6.5.3 Approximating Stiff Systems with Lower-Order Nonstiff System Models6.6 Lumped Parameter Approximation of Distributed Parameter Systems6.6.1 Nonlinear Distributed Parameter System6.7 Systems with Discontinuities6.7.1 Physical Properties and Constant Forces Acting on the Pendulum Bob6.8 Case Study: Spread of an Epidemic
Chapter 7 Simulation Tools
7.1 Introduction7.2 Steady-State Solver7.2.1 Trim Function7.2.2 Equilibrium Point for a Nonautonomous System7.3 Optimization of Simulink Models7.3.1 Gradient Vector7.3.2 Optimizing Multiparameter Objective Functions Requiring Simulink Models7.3.3 Parameter Identification7.3.4 Example of a Simple Gradient Search7.3.5 Optimization of Simulink Discrete-Time System Models7.4 Linearization7.4.1 Deviation Variables7.4.2 Linearization of Nonlinear Systems in State Variable Form7.4.3 Linmod Function7.4.4 Multiple Linearized Models for a Single System7.5 Adding Blocks to The Simulink Library Browser7.5.1 Introduction7.5.2 Summary7.6 Simulation Acceleration7.6.1 Introduction7.6.2 Profiler7.6.3 Summary7.7 Black Swans7.7.1 Introduction7.7.2 Modeling Rare Events7.7.3 Measurement of Portfolio Risk7.7.4 Exposing Black Swans7.7.5 Summary7.7.6 Acknowledgements7.7.7 References7.7.8 Appendix—Mathematical Properties of the Log-Stable Distribution7.8 The SIPmath Standard7.8.1 Introduction7.8.2 Standard Specification7.8.3 SIP Details7.8.4 SLURP Details7.8.5 SIPs/SLURPs and MATLAB7.8.6 Summary7.8.7 Appendix7.8.8 References
Chapter 8 Advanced Numerical Integration
8.1 Introduction8.2 Dynamic Errors (Characteristic Roots, Transfer Function)8.2.1 Discrete-Time Systems and the Equivalent Continuous-Time Systems8.2.2 Characteristic Root Errors8.2.3 Transfer Function Errors8.2.4 Asymptotic Formulas for Multistep Integration Methods8.2.5 Simulation of Linear System with Transfer Function H(s)8.3 Stability of Numerical Integrators8.3.1 Adams–Bashforth Numerical Integrators8.3.2 Implicit Integrators8.3.3 Runga–Kutta (RK) Integration8.4 Multirate Integration8.4.1 Procedure for Updating Slow and Fast States: Master/Slave = RK-4/RK-48.4.2 Selection of Step Size Based on Stability8.4.3 Selection of Step Size Based on Dynamic Accuracy8.4.4 Analytical Solution for State Variables8.4.5 Multirate Integration of Aircraft Pitch Control System8.4.6 Nonlinear Dual Speed Second-Order System8.4.7 Multirate Simulation of Two-Tank System8.4.8 Simulation Trade-Offs with Multirate Integration8.5 Real-Time Simulation8.5.1 Numerical Integration Methods Compatible with Real-Time Operation8.5.2 RK-1 (Explicit Euler)8.5.3 RK-2 (Improved Euler)8.5.4 RK-2 (Modified Euler)8.5.5 RK-3 (Real-Time Incompatible)8.5.6 RK-3 (Real-Time Compatible)8.5.7 RK-4 (Real-Time Incompatible)8.5.8 Multistep Integration Methods8.5.9 Stability of Real-Time Predictor–Corrector Method8.5.10 Extrapolation of Real-Time Inputs8.5.11 Alternate Approach to Real-Time Compatibility: Input Delay8.6 Additional Methods of Approximating Continuous-Time System Models8.6.1 Sampling and Signal Reconstruction8.6.2 First-Order Hold Signal Reconstruction8.6.3 Matched Pole-Zero Method8.6.4 Bilinear Transform with Prewarping8.7 Case Study: Lego MindstormsTM NXT8.7.1 Introduction8.7.2 Requirements and Installation8.7.3 Noisy Model8.7.4 Filtered Model8.7.5 Summary
References
Index

Content preview from Simulation of Dynamic Systems with MATLAB® and Simulink®, 3rd Edition

Simulation of Dynamic Systems with MATLAB® and Simulink®

Third Edition

Harold Klee and Randal Allen

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Simulation of Dynamic Systems with MATLAB® and Simulink®, 3rd Edition

by Harold Klee, Randal Allen

Simulation of Dynamic Systems with MATLAB® and Simulink®

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.