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| Process Modeling | |
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| Introduction | |
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| Motivation | |
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| Models | |
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| Systems | |
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| Background of the Reader | |
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| How To Use This Textbook | |
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| Courses Where This Textbook Can Be Used | |
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| Process Modeling | |
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| Background | |
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| Balance Equations | |
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| Material Balances | |
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| Constitutive Relationships | |
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| Material and Energy Balances | |
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| Distributes Parameter Systems | |
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| Dimensionless Models | |
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| Explicit Solutions to Dynamic Models | |
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| General Form of Dynamic Models | |
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| Numerical Techniques | |
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| Algebraic Equations | |
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| Notations | |
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| General Form for a Linear System of Equations | |
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| Nonlinear Functions of a Single Variable | |
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| MATLAB Routines for Solving Functions of a Single Variable | |
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| Multivariable Systems | |
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| MATLAB Routines for Systems of Nonlinear Algebraic Equations | |
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| Numerical Integration | |
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| Background | |
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| Euler Integration | |
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| Runge-Kutta Integration | |
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| MATLAB Integration Routines | |
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| Linear Systems Analysis | |
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| Linearization of Nonlinear Models: The State-Space Formulation | |
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| State Space Models | |
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| Linearization of Nonlinear Models | |
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| Interpretation of Linearization | |
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| Solution of the Zero-Input Form | |
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| Solution of the General State-Space Form | |
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| MATLAB Routines step and initial | |
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| Solving Linear nth Order ODE Models | |
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| Background | |
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| Solving Homogeneous, Linear ODEs with Constant Coefficients | |
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| Solving Nonhomogeneous, Linear ODEs with Constant Coefficients | |
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| Equations with Time-Varying Parameters | |
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| Routh Stability Criterion-Determining Stability Without Calculating Eigenvalues | |
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| An Introduction to Laplace Transforms | |
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| Motivation | |
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| Definition of the Laplace Transform | |
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| Examples of Laplace Transforms | |
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| Final and Initial Value Theorems | |
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| Application Examples | |
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| Table of Laplace Transforms | |
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| Transfer Function Analysis of First-Order Systems | |
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| Perspective | |
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| Responses of First-Order Systems | |
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| Examples of Self-Regulating Processes | |
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| Integrating Processes | |
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| Lead-Lag Models | |
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| Transfer Function Analysis of Higher-Order Systems | |
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| Responses of Second-Order Systems | |
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| Second-Order Systems with Numerator Dynamics | |
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| The Effect of Pole-Zero Locations on System Step Responses | |
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| Pad Approximation for Deadtime | |
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| Converting the Transfer Function Model to State-Space Form | |
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| MATLAB Routines for Step and Impulse Response | |
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| Matrix Transfer Functions | |
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| A Second-Order Example | |
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| The General Method | |
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| MATLAB Routine ss2tf | |
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| Block Diagrams | |
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| Introduction to Block Diagrams | |
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| Block Diagrams of Systems in Series | |
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| Pole-Zero Cancellation | |
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| Systems in Series | |
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| Blocks in Parallel | |
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| Feedback and Recycle Systems | |
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| Routh Stability Criterion Applied to Transfer Functions | |
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| Simulink | |
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| Linear Systems Summary | |
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| Background | |
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| Linear Boundary Value Problems | |
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| Review of Methods for Linear Initial Value Problems | |
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| Introduction to Discrete-Time Models | |
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| Parameter Estimation of Discrete Linear Systems | |
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| Nonlinear Systems Analysis | |
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| Phase-Plane Analysis | |
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| Background | |
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| Linear System Examples | |
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| Generalization of Phase-Plane Behavior | |
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| Nonlinear Systems | |
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| Introduction Nonlinear Dynamics: A Case Study of the Quadratic Map | |
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| Background | |
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| A Simple Population Growth Model | |
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| A More Realistic Population Model | |
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| Cobweb Diagrams | |
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| Bifurcation and Orbit Diagrams | |
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| Stability of Fixed-Point Solutions | |
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| Cascade of Period-Doublings | |
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| Further Comments on Chaotic Behavior | |
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| Bifurcation Behavior of Single ODE Systems | |
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| Motivation | |
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| Illustration of Bifurcation Behavior | |
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| Types of Bifurcations | |
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| Bifurcation Behavior of Two-State Systems | |
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| Background | |
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| Single-Dimensional Bifurcations in the Phase-Plane | |
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| Limit Cycle Behavior | |
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| The Hopf Bifurcation | |
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| Introduction to Chaos: The Lorenz Equations | |
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| Introduction | |
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| Background | |
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| The Lorenz Equations | |
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| Stability Analysis of the Lorenz Equations | |
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| Numerical Study of the Lorenz Equations | |
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| Chaos in Chemical Systems | |
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| Other Issues in Chaos | |
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| Review And Learning Modules | |
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| Module 1 Introduction to MATLAB | |
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| Module 2 Review of Matrix Algebra | |
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| Module 3 Linear Regression | |
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| Module 4 Introduction to SIMULINK | |
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| Module 5 Stirred Tank Heaters | |
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| Module 6 Absorption | |
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| Module 7 Isothermal Continuous Stirred Tank Chemical Reactors | |
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| Module 8 Biochemical Reactors | |
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| Module 9 Diabatic Continuous Stirred Tank Reactors | |
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| Module 10 Ideal Binary Distillation | |
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| Index | |