Course Syllabus
ECE 682 – State Variable in Automatic Control
Department:
Course Number:
Course Title:
Credit Units:
Electrical & Computer Engineering
ECE 682
State Variable in Automatic Control
3
Course Description
Definition and modeling of system using state variables. Application of state-space method to
the analysis and synthesis of feedback control systems; matrices, vectors and vector spaces,
coordinate transformations, solution of vector matrix differential equation, stability,
controllability and observability, optimal control system.
Prerequisite by Topic
Students taking this course should have complete familiarity with the topics of control systems
(ECE 480) course. Specifically students should be familiar with evaluation of system response,
Mason’s Gain Formula, stability discussion using Routh-Hurwitz criterion, Root-Locus, Nyquist
criterion. Students should be familiar with frequency response of system, and understand the idea
of Phase and Gain Margin. Understanding time domain (continuous and discrete), S-domian, Zdomain, and frequency domain (continuous and discrete) in modeling, analyzing and solving
linear digital systems is also the main prerequisite for taking this course.
Text, References & Software
Recommended Text:
Modern Control Engineering, Katsuhiko Ogata, 3rd Ed., Prentice Hall 1995,
ISBN 0-13-227307-1.
Additional References:
Automatic Control System, Kuo, 7th. Ed. Prentice Hall 1995, Discrete Time Control Systems,
2nd Ed. Prentice Hall 1995.
Software:
MATLAB: Control and Simulink Tool Boxes, Math Works Inc.
Internet Resources:
http//hpme12.me.edu/matlab/html/
Course Objectives – After completing this course the students should be able to:
1. Have complete familiarity with Linear Algebra.
1. Use simulation to model systems in continuous and discrete state variable forms.
2. Model systems in variety of forms such as First and Second Canonical Forms, Diagonal
Form and Cascade Form.
3. Solve continuous state variable equations using discrete t-domain, and S-domain.
4. Solve discrete state variable equations using discrete k-domain, and Z-domain.
5. Understand and discuss Controllability and Observability.
6.
7.
8.
9.
Design system using pole-placement method.
Discuss system stability using Liapunov stability criteria.
Solve Quadratic Optimal Control problem.
Be able to use Digital Controller to design systems and evaluate system response.
Topics Covered/Course Outline
1. Concept of State and State Variables.
2. Modeling of Systems Using State Variables.
3. Matrices and Vectors. Matrix Operations. Vectors and Vector Spaces. Eigenvalues and
Eigenvectors. Function of a Matrix.
4. Canonical Forms.
5. System Transformation.
6. Solution of State Variables.
7. Controllability and Observability.
8. Design of Control Systems Using Pole Placement Method.
9. Stability Analysis and Different Types of Stability.
10. Liapunov Stability Analysis.
11. Quadratic Optimal Control.
Relationship to Program Outcomes
This supports the achievement of the following outcomes:
a) Ability to apply knowledge of advanced principles to the analysis of electrical and
computer engineering problems.
b) Ability to apply knowledge of advanced techniques to the design of electrical and
computer engineering systems.
c) Ability to apply the appropriate industry practices, emerging technologies, state-ofthe-art design techniques, software tools, and research methods of solving electrical
and computer engineering problems.
d) Ability to use the appropriate state-of-the-art engineering references and resources,
including IEEE research journals and industry publications, needed to find the best
solutions to electrical and computer engineering problems.
e) Ability to communicate clearly and use the appropriate medium, including written,
oral, and electronic communication methods.
f) Ability to maintain life-long learning and continue to be motivated to learn new
subject.
g) Ability to learn new subjects that are required to solve problems in industry without
being dependent on a classroom environment.
h) Ability to be competitive in the engineering job market or be admitted to an
excellent Ph. D. program.
Prepared by:
Ali Amini
January 16, 2003