ECE 67500 - Introduction to Analysis of Non-Linear Systems

Course Details

Credits: 3

Areas of Specialization:

  • Automatic Control

Counts as:

Normally Offered:

Spring - even years

Campus/Online:

On-campus and online

Requisites:

MA 51100 (required); ECE 60200 or equivalent (recommended).

Catalog Description:

An introduction to modeling of dynamic control systems. State plane and numerical methods for solving modeling equations. Linearization and describing function techniques. Stability concepts. Controller and state estimator design for nonlinear systems. Variable structure sliding mode control. Vector field techniques. Introduction to chaos.

Required Text(s):

None.

Recommended Text(s):

None.

Learning Outcomes

A student who successfully fulfills the course requirements will have demonstrated an ability to:

  • Define a dynamical system notion and determine if it is a linear or nonlinear system
  • Construct models of dynamical systems arising in various applications such as mechanical, electrical, economic, and biological systems and analyze their behavior
  • Apply different properties of dynamical systems, such as: stability, controllability, observability, stabilizability, detectability to system models
  • Design advanced controllers and observers for nonlinear systems, using modern control engineer tools, such as: linear matrix inequalities, vector field methods, sliding mode approach, and graph theory
  • Validate controller designs using simulation tools, such as MATLAB and Simulink

Lecture Outline:

Weeks Topic
1 Dynamic System Concept
2 Formulation of the control problem
3 Modeling
5 Numerical integration
4 State plane methods
6 Linearization
7 Describing function techniques
8 Stability concepts
9 Variable structure sliding control mode; Conditions for existence of a sliding mode; Switching surface design and construction of switched feedback gains
10 Vector field techniques
11 State estimation of nonlinear systems
12 Combined controller-estimator compensators
13 Neural network based controllers
14 Introduction to chaos

Assessment Method:

Quizzes, homework, exams.