Table of Contents

MATHEMATICAL MODELING
Introduction
Derivation of a Mathematical Model
Difference Equations
A First Look at Discrete-Time Systems
Case Study- Population Dynamics (Single Species)
CONTINUOUS-TIME SYSTEMS
Introduction
First-Order Systems
Second-Order Systems
Simulation Diagrams
Higher Order Systems
State Variables
Nonlinear Systems
Case Study- Submarine Depth Control System
ELEMENTARY NUMERICAL INTEGRATION
Introduction
Discrete-Time System Approximation of a Continuous-Time Integrator
Euler Integration
Trapezoidal Integration
Numerical Integration of First Order and Higher Continuous-Time Systems
Improvements to Euler Integration
Case Study- Vertical Ascent of a Diver
LINEAR SYSTEMS ANALYSIS
Introduction
The Laplace Transform
The Transfer Function
Stability of LTI Continuous-Time Systems
Frequency Response of LTI Continuous-Time Systems
The z-Transform
The z-Domain Transfer Function
Stability of LTI Discrete-Time Systems
Frequency Response of Discrete-Time Systems
The Control System Toolbox
Case Study- Longitudinal Control of an Aircraft
Case Study- Notch Filter for ECG Waveform
SIMULINK
Introduction
Building a Simulink Model
Simulation of Linear Systems
Algebraic Loops
More Simulink Blocks
Subsystems
Discrete-Time Systems
MATLAB/Simulink Interface
Hybrid Systems-Continuous-Time and Discrete-Time Components
Monte Carlo Simulation
Case Study- Pilot Ejection
INTERMEDIATE NUMERICAL INTEGRATION
Introduction
Runga-Kutta (One-Step Methods)
Adaptive Techniques
Multistep Methods
Stiff Systems
Lumped Parameter Approximation of Distributed Parameter Systems
Systems with Discontinuities
Case Study- Spread of an Epidemic
SIMULATION TOOLS
Introduction
Steady-State Solver
Optimization of Simulink Models
Linearization
ADVANCED NUMERICAL INTEGRATION
Introduction
Dynamic Errors (Characteristic Roots, Transfer Function)
Stability of Numerical Integrators
Multirate Integration
Real-Time Simulation
Additional Methods of Approximating Continuous-Time System Models
REFERENCES
INDEX