Systems Modeling and Simulation
Introducing students to basic methods and techniques of dynamic systems modeling and simulation. Qualifying the students for dynamic system simulation using block oriented languages.
- list methods of mathematical and graphical description of dynamic systems
- explain the dynamic changes in the system based on mathematical models
- apply physical laws for description of the system by differential equations, difference equations, transfer functions and state space equations
- use a mathematical description of the system for design of block diagrams, signal flow graphs and bond graphs
- analyze the behavior of the system in steady state and during transient responses
- identify system parameters based on dinamic system measurements
- assemble different type of models in a single model
- assess the credibility of models based on steady state estimates and comparisons with real system responses
Forms of Teaching
Two hours lecture per weekExams
Homeworks Mid term exame Final exam in written form Oral final examConsultations
After each lectureOther
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Homeworks||50 %||20 %||0 %||10 %|
|Mid Term Exam: Written||50 %||30 %||0 %|
|Final Exam: Written||50 %||30 %|
|Final Exam: Oral||20 %|
|Exam: Written||50 %||40 %|
|Exam: Oral||50 %|
It is necessary to complete all homeworks for taking the final exam.
Week by Week Schedule
- Topics overview, literature, organization of teaching and exams. Significance of the modeling. The process and model classification. Model equivalence. Forms of the mathematical representation of dynamic systems. Standard structures of the model representation. Transformations between standard structures. (Differential equation, transfer function, state space representation, differences equation, transfer function and state space of the discrete system, recursive equation).
- Graphical representation of the dynamic system. (Block scheme, bond graph). Examples. Transformation of the graphics system representation into the mathematical representation of the system and vise versa. Examples of the direct methods for determining the state space representation of the system from the block scheme and bond graph representation.
- Mathematical model determination based on the physical laws, using phenomenological and dynamic equilibrium equations.
- Mathematical modeling of processes in the class of linear and rotary motion.
- Mathematica modeling of the processes based on the heat and fluid dinamics.
- Mathematical modeling of the electrical systems. Modeling of the signals defined by analytical functions.
- Modeling the system with distributed parameters. System description by partial differential equations. Examples.
- Midterm exam.
- Application of the finite element method for representation of the dynamic system with distributed parameters. Examples.
- Simulation of the dynamic system by block oriented language. Numerical integration methods.
- Determining the dynamic system model parameters. Survey parameter identification methods, determining the model parameters by optimization process.
- Numerical optimization methods without constrains. Bisection optimization method, golden section optimization, simplex optimization method.
- Gradient method of optimization. Optimization with constraints. Using penalty function.
- Discrete event system representation.
- Final exam.