Process Dynamics

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.