Introduction to modeling and system analysis (SC2010ET)

Summary:
This course deals with modeling and analysis of continuous-time and discrete-time dynamical systems. Abstract systematic modeling of physical processes with the help of mathematical equations is discussed. Analogies among the electrical, mechanical, hydraulic and thermodynamic domains are stressed. Starting points for modeling are the conservation laws and constitutive relations among the individual components. On an abstract level systems can be described by input-output relations like differential and difference equations, and also by state-space equations. These system descriptions can be used to determine the systems properties (linearity, time-invariance, stability). The analysis part of the course focuses on linear time-invariant systems; for these systems the time response and frequency response will be determined. Other topics that will be discussed are: the relations between the different system descriptions, system transfer operator, block diagrams, linearization, poles and zeros, controllability and observability.

Teaching team:
Dr. ir. V. Verdult, OCP building, room 8C-2-23, phone: 85768, email: v.verdult@dcsc.tudelft.nl
Dr. ir. J. M. A. Scherpen , OCP building, room 8C-3-20, phone: 86152, email: j.m.a.scherpen@dcsc.tudelft.nl

Study load:
3 ECTS / 84 hours

More information:

• Prerequisites
• Objectives
• Contents
• Course Notes
• Schedule
• Examination

Downloadables (slides, etc.)

Assignments (exercises + solutions)

Prerequisites

• Propedeuse
• Signaaltransformaties (ET2 028)
• Lineaire Algebra II (WI2 137ET)
• Differentiaalvergelijkingen (WI2 138ET)

Objectives

• to model dynamical systems based on first principle physical modeling.
• to represent continuous-time and discrete-time systems using different types of system descriptions.
• to analyze the dynamic behavior of both continuous-time and discrete-time linear time-invariant systems.

More detailed objectives can be found in the course notes.

Contents

1. System Descriptions
   • Dynamical Systems
   • State-Space System Descriptions
2. Basics of Bond Graphs
   • Physical Domains
   • Power Conjugate Variables
   • The Physical Model Structure and Bond Graphs
   • Energy Storage and Physical States
   • Free Energy Dissipation
   • Ideal Transformations and Gyrations
   • Ideal Sources
   • Kirchhoff's Laws, Junctions and the Network Structure
   • Bond Graph Modeling of Electrical Networks
   • Bond Graph Modeling of Mechanical Systems
3. Motion Equations and Models of Electromechanical Systems
   • Hamilton's Principle
   • The Euler-Lagrange Equation
   • Hamiltonian Systems
4. Linear Time-Invariant Systems
   • Linearization
   • System Transfer Operator
   • Block Diagrams
   • Input-Output Descriptions
5. Continuous-Time LTI System Response
   • Solution to the State Equation
   • System Transfer Function
   • Solution to the Differential Equation
   • Generalized Signals
   • Convolution
   • Frequency response
   • First and Second-Order Systems
6. Discrete-Time LTI System Response
   • Solution to the State Equation
   • System Transfer Function
   • Solution to the Difference Equation
   • Convolution
   • Frequency response
7. Stability of LTI Systems
   • Internal Stability
   • Lyapunov Stability Criteria
   • Input-Output Stability
8. LTI State-Space Realizations
   • Controllability and Observability
   • Minimal State-Space Realization
   • Canonical Forms
   • Realization by Sums or Products of Systems

Course notes

• Lecture notes for the course SC2010ET Introduction to Modeling and System Analysis, by Vincent Verdult, Jacquelien Scherpen, and Ton van den Boom, Delft, January, 2004 (sold by "diktatenverkoop").

Schedule

In 2003-2004 this course will be organized in the third and fourth quarter (January-June).

• Lecture 1: Monday 21-02-2005, 8.45-10.30
  Introduction: Chapter 1 of the course notes.
• Lecture 2: Monday 07-03-2005, 8.45-10.30
  Bond Graphs: Chapter 2.
• Lecture 3: Monday 14-03-2005, 8.45-10.30
  Bond Graphs and classical mechanical methods: Chapter 2 and 3.
• Lecture 4: Monday 21-03-2005, 8.45-10.30
  Bond Graphs and classical mechanical methods: Chapter 2 and 3.
• Lecture 5: Thursday 14-04-2005, 8.45-10.30
  LTI systems: Chapter 4.
• Lecture 6: Thursday 21-04-2005, 8.45-10.30
  State-space system response: Sections 5.1, 5.2, 6.1, and 6.2.
• Lecture 7: Thursday 28-04-2005, 8.45-10.30
  Input-output system response: Sections 5.3, 5.4, 5.5, 6.3 and 6.4.
• Lecture 8: Thursday 12-05-2005, 8.45-10.30
  Frequency response: Sections 5.6, 5.7 and 6.5.
• Lecture 9: Thursday 19-05-2005, 8.45-10.30
  Stability: Chapter 7.
• Lecture 10: Thursday 26-05-2005, 8.45-10.30
  State-space realization: Chapter 8.

The lectures will be held in room C of the ITS/EWI building.

Contrary to what is listed in some other sources, there are no lectures on the Mondays 07-02-2005, 14-02-2004, 28-02-2004 and on Thursday 02-06-2005.

Examination

The next examination ("closed-book"!) will take place on Tuesday, June 14, 2005, 14.00-17.00 h. A selected list of formulas will be provided during the exam. They can be downloaded from the blackboard site. The examination will concern the lecture notes and slides. Note that this material cannot be used during the examination; it is a "closed-book" examination. It is also not allowed to use a calculator during the exam.

It is no longer possible to take a separate exam for the old courses ET2038 and ET2039. If you have not completed both ET2038 and ET2039 you should take the exam for SC2010ET.

• Exam Introduction to modeling and system analysis SC2010ET: Tuesday June 14, 2005.
  Chapters 1-8 of the course notes.
• Exam Introduction to modeling and system analysis SC2010ET: Tuesday August 30, 2005.
  Chapters 1-8 of the course notes.