Title: LINEAR SYSTEM THEORY
Catalog Description: EE 453 Linear System Theory (4+0+0) 4
Introduction to realization theory for single-input, single-output (SISO) 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 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.
At the end of this course, students will be able to:
CLO 1 - Find a realization of a given proper transfer function.
CLO 2 - Solve state-space equations for linear systems.
CLO 3 - Design a state feedback law to stabilize and/or pole assign a linear system.
CLO 4 - Design an observer.
Combine state feedback design and observer design to build an observer-based dynamic compensator.
Textbook: T. Kailath, Linear Systems, Prentice-Hall, 2000.
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.
4. C.-T. Chen, Linear System Theory and Design, Holt-Saunders, 1984.
Prerequisites by Topic:
1. Linear algebra
2. Classical control theory
3. Linear circuits
4. Laplace Transform
5. Ordinary differential equations
0. An overview of linear algebra (2-4 weeks)
1. An introduction to realization theory. (2 weeks)
2. Solving the state-space equations. (1 week)
3. Controllability. State feedback design. Stabilizability. (3 weeks)
4. Observability. Observer design. Detectability. (2 weeks)
5. (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.
Two mid-term exams (30% each).
A final exam (40%).
1. Outcome (a): 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.
2. Outcome (c): 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 almost half the course. However, it should be stressed that, the approach taken in EE 453 is more of a synthesis rather than design approach.
Relation Between CLOs and Outcomes:
CLOs 1&2 are clearly related to Outcome (a), whereas CLOs 3&4 are geared towards Outcome (c).
Relation Between CLOs and Program Objectives:
All four CLOs of this course serve the first two educational objectives of the program that state that graduates of the program will
(i) have a strong background in basic sciences, mathematics and engineering to be successful in their graduate studies;
(ii) have broad skills and solid technical background to be successful in their professional careers.
It should be clear to any engineer that a strong background in linear system theory means a strong background in mathematics, especially in linear ordinary differential equations. Of the four CLOs, CLO 1 and CLO 2 guarantee that program objective (i) is served adequately. Linear system theory is also one of the most heavily applied theories in engineering and constitutes a scientific pillar for a wide range of engineering applications. Thus, CLO 3 and CLO 4 serve program objective (ii).
Prepared By: Kadri Özçaldıran