ECE 449/549: Continuous System Modeling

Textbook: F.E. Cellier, Lecture notes

References:

• F.E. Cellier, Continuous System Modeling, Springer-Verlag, New York, 1991.

Course Coordinator: Dr. François E. Cellier, Professor of ECE.

Goals: The goal of this course is to provide students with an introduction to problems and techniques of describing the dynamics of systems that can be modeled through either differential equations (ordinary and partial) or difference equations. Application areas include: electrical circuits, mechanical systems, thermodynamics, chemical reaction networks, and population dynamics. After completing the course, the student will have a solid understanding of mechanisms and tools that allow him to derive sets of differential or difference equations for a large variety of physical and engineering systems. The class provides also an introduction to the interface between continuous system modeling and artificial intelligence.

Prerequisites by topic: description of signals and linear systems in the time and frequency domains, state-space description, transfer function, matrix algebra, programming experience in at least one of the following languages: Fortran, Pascal, C, or Ada

Topics:

1. Introduction, scope, definitions: What is a System? What is an Experiment? What is a Model? What is a Simulation? Why is Modeling Important? Why is Simulation Important? The Dangers of Simulation. Good Reasons to Use Simulation. The Types of Mathematical Models. Direct Versus Inverse Problems. (1 class)

2. Basic principles of continuous system modeling: Single-assignment languages and differential equation models, introduction to the modern continuous system modeling and simulation environment Modelica. (1 class)

3. Introduction to object-oriented continuous system modeling: Basic models and connection models, hierarchical data structures, information hiding. (2 classes)
4. Basic principles of electrical circuit modeling: RLC circuits, mesh equations, node equations, disadvantages of mesh and node equations, state-space models, algebraic loops, structural singularities, disadvantages of state-space models. (3 classes)

5. Differential-algebraic equation systems: Systems with algebraic loops and higher index systems (systems with structural singularities), index-reduction algorithms by Pantelides and Tarjan. (3 classes)

6. Basic principles of mechanical system modeling: Newton's law for translational motions, Newton's law for rotational motions, the d'Alembert principle, Euler and Lagrange equations, the Hamiltonian, modeling electro-mechanical systems. (3 classes)

7. Industrial systems modeling: Modeling transfer functions, modeling static characteristics, dynamic table load, large scale system modeling. (2 classes)

8. Advanced topics in electrical circuit modeling: Topological modeling, models of active devices in Pspice and Modelica, hierarchical modeling in Pspice and Modelica, transient analysis in PSpice and Modelica. (2 classes)

9. Graphical modeling: Block diagrams, signal flow graphs, power bonds, bond graphs for electrical systems, bond graphs for mechanical systems, energy transducers, electro-mechanical systems, bond graph modeling in Modelica. (3 classes)

10. Modeling non-equilibrium thermodynamics: Energy flow, the heat equation, the method-of-lines, thermal conduction, thermal convection, thermal radiation, thermodynamic bond graphs, irreversible thermodynamics and state-space models, thermobonds in Modelica. (3 classes)

11. Thermal modeling of buildings: Conduction, convection, and radiation in a building, the effects of humidity, condensation and evaporation, thermal modeling of Biosphere-II. (2 classes)

12. Modeling chemical reaction kinetics: Chemical reactions, chemical thermodynamics, the equation of state, chemical reaction bond graphs, energies of formation, continuous reactors, photochemistry, electrochemistry. (3 classes)

13. Modeling discontinuous systems: Electrical switches, impacts and clutches in mechanical system, models of mechanical friction. (2 classes)

14. Ecological systems modeling: Growth and decay, predator-prey models, competition and cooperation, chaos, evolution. (2 classes)

15. System dynamics: Basic principles of inductive modeling, levels and rates, sources and sinks, laundry lists, influence diagrams, structure diagrams, causality, STELLA. (2 classes)

16. Inductive reasoning: The base system, the data system, the behavior system, learning behavior, forecasting behavior, the structure system, causality, SAPS-II. (6 classes)

• Engineering Science: 1 credit, or 33%
  
• Engineering Design: 2 credits, or 67%

• homework: 20%
  
• midterms: 45% (15% each)
  
• final exam: 35%