BU-EE

 

EE 453

 

Title: LINEAR SYSTEM THEORY

 

Credits: 4

 

Catalog Description: Introduction to realization theory for single-input, single-output (SIAO) systems.  Solution of the state space equations.  Structural properties: controllability, observability, detectability, stabilizability.  State feedback design, observer design and design of observer-based compensators for SISO systems.

 

Prerequisites: EE 303, EE 352.

 

Coordinator: Kadri Özçaldıran, Professor of Electrical Engineering

 

Goals: This course aims to expose the senior year students to analysis and design of linear systems (time-invariant and single-input, single-output more often than time varying and multi-input, multi-output) in time domain.  Basic notions and tools of state-space analysis as well as basic design techniques for linear systems (e.g., state feedback, observers) are introduced.

 

Learning Objectives: At the end of this course, students will be able to:

  1. Find a realization of a given proper transfer function.
  2. Solve state-space equations for linear systems.
  3. Design a state feedback law to stbilize and/or pole assign a linear system.
  4. Design an observer.
  5. Combine state feedback design and observer design to build an observer-based dynamic compensator.

Textbook: T. Kailath, Linear Systems, Prentice-Hall, 2000.

 

Reference Texts: 

  1. W.L. Brogan, Modern Control Theory, 3rd. edition,  Prentice-Hall,1991,
  2. W.J. Rugh, Linear System Theory, 2nd. Edition, Prentice-Hall, 1996.
  3. P.J. Antsaklis and A.N. Michel, Linear Systems,  Mc Graw Hill, 1997.

Prerequisites by Topic:

  • Linear algebra
  • Classical control theory
  • Linear circuits
  • Laplace Transform
  • Ordinary differential equations

Topics:

  1. An overview of linear algebra (2-4 weeks)
  2. An introduction to realization theory. (2 weeks)
  3. Solving the state-space equations. (1 week)
  4. Controllability.  State feedback design.  Stabilizability. (3 weeks)
  5. Observability.  Observer design.  Detectability. (2 weeks)
  6. Design of observer based compensators. (1 week)
  7. (Time permitting) Introduction to optimal control and optimal estimation. (2 weeks)

Course Structure: The class meets for two lectures a week, each consisting of two 50-minute sessions. 3-4 sets of homework problems are assigned per semester but they are not collected.  There are two in-class mid-term exams and a final exam.

 

Computer Resources: Students are encouraged to use MATLAB to solve their homework problems.

 

Laboratory Resources: None.

 

Grading:

  1. Two mid-term exams (25% each).
  2. A final exam (50%).

Outcome Coverage:

  • Apply math, science and engineering knowledge.  This course is about first order vector valued ordinary differential equations and a number of control concepts developed for such models.  Different tools from mathematics (linear algebra, differential equations, complex variables) as well as from sciences (physics) and engineering (dynamics) are heavily drawn upon during lectures, homework sets and exams.

  • Design a system, component or process to meet desired needs. Designing a state feedback law to arbitrarily assign the closed-loop eigenvalues, designing an observer to estimate the state and designing an observer-based dynamic compensator account for more than half of the course time.

  • Use of modern engineering tools. Students use MATLAB and a number of MATLAB packages (like Control Toolbox, Simulink) for their homework assignments.

Prepared By: Kadri Özçaldıran

 

Last revised: May 1, 2003

 

 

 
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