Continuous-System Modeling
Required for CE and EE
Catalog Data: 

3 units.  Techniques for modeling systems described by differential equations and difference equations. Physical modeling, mass and energy balance equations, bond graphs, system dynamics, qualitative modeling, inductive reasoning, neural networks
Grading: Regular grades for this course: A B C D E.
Identical to:  C SC 449.
May be convened with:  ECE 449.
Usually offered:  Fall.


Brown, F., 2007, Engineering System Dynamics, A Unified Graph-Centered Approach. CRC Press, Taylor & Francis Group

Course Learning Outcomes: 

By the end of this course, the student will be able to:

  1. Understand energy and power conjugate variables and the relationships between them.
  2. Model continuous systems that cross boundaries of multiple engineering disciplines through bond graph modeling.
  3. Understand the difference between, and implications of, differential and integral causality.
  4. Use similarity transformations to move between bond-graph state variables and common, domain specific, state variables.
  5. Map a bond graph to a block diagram.
  6. Create system differential equations by inspection of a bond graph.
  7. Obtain differential equations in the presence of algebraic loops and structural singularities.
  8. Understand the Tarjan for equation sorting.
  9. Understand the Pantelides algorithms relaxing structural singularities.
  10. Utilize switching in bond graph models.
  11. Understand bi-causal elements where necessary.
  12. Understand the mapping between Lagrange equations and the Hamiltonian formulation.
  13. Understand the Lagrangian bond graph.
  14. Understand Thermodynamic conjugate relationships and the Legendre transformation.
  15. Create difference equations from differential equations.
  16. Understand potential problems created by numerical integration techniques.
  17. Determine the domain of numerical stability for a given integration scheme.
Course Topics: 
  • Introduction
  • Source-Load Synthesis
  • Simple Dynamic Models
  • Analysis of Linear Models
  • Basic Modeling
  • Mathematical Formulation from Bond Graphs
Class/Laboratory Schedule: 

Two 90-minute lectures per week

Relationship to Student Outcomes: 

a)  an ability to apply knowledge of mathematics, science, and engineering (High)
c)  an ability to design a system, component, or process to meet desired needs
     within realistic constraints such as economic, environmental, social, political,
     ethical, health and safety, manufacturability, and sustainability (Medium)
e)  an ability to identify, formulate, and solve engineering problems (High)
k)  an ability to use the techniques, skills, and modern engineering tools necessary for
     engineering practice.  (High)

Prepared by: 
Dr. Hal Tharp
Prepared Date: 

University of Arizona College of Engineering