CENG 382 Analysis of Dynamic Systems with Feedback
Spring 06

Instructor:
Dr. Sibel Tari/Office: A403

Textbook
1. Introduction to Dynamic Systems: Theory, Models, and Applications, D.Luenberger, John Wiley, 1979 (Chapters 1-8)


Catalogue description:
Mathematical Modelling of Systems. Difference and Differential Equations. State-Space Representation. Solutions of State Equations. Linear-Time-Invariant Systems and Impulse Response (Discrete and Continuous Time). Stability. Routh-Hurwitz Method. Feedback. Controllability. Observability. An introduction to Nonlinear Systems.
Prerequisites: MATH 253 Differential Equations, MATH 260 Linear Algebra.


Grading system
2 Midterm Exams 40%
Final Exam 35%
4 Matlab Homeworks 25%

Course objectives/goals
i. To teach the fundamental concepts of dynamical systems with an emphasis on discrete time/continuous state systems . In particular, to teach

1. mathematical modeling with the help of classical examples;
2. analytical solutions of difference equations;
3. state space concept;
4. stability;
5. feedback.

ii. To perform analysis particularly within the framework of dynamical systems (program educational objectives 2 and 4).
iii. To explore the mathematical representation of dynamical systems (program educational objectives 4 and 5).


OUTLINE

  1. (4 hrs) Basic Concepts of Systems: Mathematical Modeling, Unifying Concepts (Input, output, transform); Classification( i.e. linear/nonlinear, forced/unforced, time varying/time Invariant, static/dynamic); Dynamic Phenomena; Stages of Dynamical System Analysis; [Chapter 1]
  2. (6 hrs) Discrete and Continuous Time Linear Dynamical Systems: Difference Equations, Unit Advance/Delay Operator, Differential Equations, Homogenous and Particular Solutions (Emphasis is on Discrete Time Systems) [Chapter 2]
  3. (8 hrs) Linear State Equations: Systems of First Order Equations, State Vector, State Space; Conversion to State Form; Dynamic Diagrams; Discrete Time Systems, Fundamental Set of Solutions, State Transition Matrix, General Solution, Time Invariant Case and the Impulse Response; Continuous Time Systems; [Chapter 4, skip 4.8]
  4. (5 hrs) Linear Time-Invariant Systems: Geometric Sequences, Exponentials; System Eigenvectors; Diagonalization, Diagram Interpretation of Diagonalization; Multiple Eigenvalues; [Chapter 5.1,2,3,6]
  5. (3 hrs) Equilibrium Points; Stability; Oscillations; Dominant Modes; [Chapter 5.7-5.11]
  6. (8 hrs) Concepts of Control: Output Feedback, State Feedback, State Feedback Matrix, Eigenvalue Placement and Controllability, Controllable Canonic Form, Observer Design, Observability, Observerable Canonic Form [Chapter 8.6-8.10]
  7. (3 hrs) Introduction to Nonlinear Systems