## Table of Contents

**I. PROCESS MODELING.**

**1. Introduction.**

Motivation. Models. Systems. Background of the Reader. How To Use This Textbook. Courses Where This Textbook Can Be Used.

**2. Process Modeling.**

Background. Balance Equations. Material Balances. Constitutive Relationships. Material and Energy Balances. Distributes Parameter Systems. Dimensionless Models. Explicit Solutions to Dynamic Models. General Form of Dynamic Models.

**II. NUMERICAL TECHNIQUES.**

**3. Algebraic Equations.**

Notations. General Form for a Linear System of Equations. Nonlinear Functions of a Single Variable. MATLAB Routines for Solving Functions of a Single Variable. Multivariable Systems. MATLAB Routines for Systems of Nonlinear Algebraic Equations.

**4. Numerical Integration.**

Background. Euler Integration. Runge-Kutta Integration. MATLAB Integration Routines.

**III. LINEAR SYSTEMS ANALYSIS.**

**5. Linearization of Nonlinear Models: The State-Space Formulation.**

State Space Models. Linearization of Nonlinear Models. Interpretation of Linearization. Solution of the Zero-Input Form. Solution of the General State-Space Form. MATLAB Routines step and initial.

**6. Solving Linear nth Order ODE Models.**

Background. Solving Homogeneous, Linear ODEs with Constant Coefficients. Solving Nonhomogeneous, Linear ODEs with Constant Coefficients. Equations with Time-Varying Parameters. Routh Stability Criterion—Determining Stability Without Calculating Eigenvalues.

**7. An Introduction to Laplace Transforms.**

Motivation. Definition of the Laplace Transform. Examples of Laplace Transforms. Final and Initial Value Theorems. Application Examples.

**Table of Laplace Transforms.**

**8. Transfer Function Analysis of First-Order Systems.**

Perspective. Responses of First-Order Systems. Examples of Self-Regulating Processes. Integrating Processes. Lead-Lag Models.

**9. Transfer Function Analysis of Higher-Order Systems.**

Responses of Second-Order Systems. Second-Order Systems with Numerator Dynamics. The Effect of Pole-Zero Locations on System Step Responses. Pad Approximation for Deadtime. Converting the Transfer Function Model to State-Space Form. MATLAB Routines for Step and Impulse Response.

**10. Matrix Transfer Functions.**

A Second-Order Example. The General Method. MATLAB Routine ss2tf.

**11. Block Diagrams.**

Introduction to Block Diagrams. Block Diagrams of Systems in Series. Pole-Zero Cancellation. Systems in Series. Blocks in Parallel. Feedback and Recycle Systems. Routh Stability Criterion Applied to Transfer Functions. SIMULINK.

**12. Linear Systems Summary.**

Background. Linear Boundary Value Problems. Review of Methods for Linear Initial Value Problems. Introduction to Discrete-Time Models. Parameter Estimation of Discrete Linear Systems.

**IV. NONLINEAR SYSTEMS ANALYSIS.**

**13. Phase-Plane Analysis.**

Background. Linear System Examples. Generalization of Phase-Plane Behavior. Nonlinear Systems.

**14. Introduction Nonlinear Dynamics: A Case Study of the Quadratic Map.**

Background. A Simple Population Growth Model. A More Realistic Population Model. Cobweb Diagrams. Bifurcation and Orbit Diagrams. Stability of Fixed-Point Solutions. Cascade of Period-Doublings. Further Comments on Chaotic Behavior.

**15. Bifurcation Behavior of Single ODE Systems.**

Motivation. Illustration of Bifurcation Behavior. Types of Bifurcations.

**16. Bifurcation Behavior of Two-State Systems.**

Background. Single-Dimensional Bifurcations in the Phase-Plane. Limit Cycle Behavior. The Hopf Bifurcation.

**17. Introduction to Chaos: The Lorenz Equations.**

Introduction. Background. The Lorenz Equations. Stability Analysis of the Lorenz Equations. Numerical Study of the Lorenz Equations. Chaos in Chemical Systems. Other Issues in Chaos.

**IV. REVIEW AND LEARNING MODULES.**

Module 1 Introduction to MATLAB. Module 2 Review of Matrix Algebra. Module 3 Linear Regression. Module 4 Introduction to SIMULINK. Module 5 Stirred Tank Heaters. Module 6 Absorption. Module 7 Isothermal Continuous Stirred Tank Chemical Reactors. Module 8 Biochemical Reactors. Module 9 Diabatic Continuous Stirred Tank Reactors. Module 10 Ideal Binary Distillation.

**Index.**

Process Dynamics: Modeling, Analysis and Simulation

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