ECE 720

Multivariable and Robust Control

Fall 2005

The CRN number required for registration for this course is: CRN 74550

You can download a .pdf version of the course syllabus.

Examples of course concepts

Objectives:

To provide students with the purposes, terminology, and fundamental mathematics of robust control theory.
To provide students with the terminology of multivariable control and to illustrate the differences between scalar systems and multivariable systems.
To enable students to intelligently evaluate various robust control techniques and to design controllers for scalar and multivariable systems that provide robust stability and performance.
To enable students to understand the literature and conduct research in the fields of multivariable control and robust control.

 

Topics Covered:

The control problem for scalar systems and for multivariable systems
The Smith-McMillan form and multivariable poles and zeros
Eigenstructure assignment for multivariable systems
Internal stability
Performance limitations in control systems
Modeling system uncertainty
Performance specifications and principal gains
Parametrization of all stabilizing controllers
Robust stability and robust performance
LQG problem, loop shaping, and loop transfer recovery
The H_infinity design methodology

 

Course Outline:

Chapters 1 and 2:  Introduction, definitions of multivariable and robust control, form of the standard control problem, performance characteristics and limitations -- 1.5 class periods.
Chapter 3:  Multivariable systems, the importance of eigenvectors, getting performance improvement through eigenstructure assignment, singular values, defining the poles and zeros of a multivariable system -- 1.5 class periods.
Chapter 4:  Controllability and observability, internal stability, parametrization of all stabilizing controllers, stability analysis, operator norms -- 2 class periods.
Chapter 5:  Performance limitations in SISO systems, constraints on the sensitivity and complementary sensitivity transfer functions, limitations on performance caused by right-half plane poles and zeros and time delays -- 2 class periods.
Chapter 6:  Performance limitations in MIMO systems, constraints on the sensitivity and complementary sensitivity transfer functions, limitations on performance caused by right-half plane poles and zeros and time delays -- 1 class period.
Chapter 7:  Models for system uncertainty, uncertainty in the frequency domain, stability robustness, performance robustness -- 2 class period.
Chapter 8:  Robust stability and performance for MIMO systems, robust stability with structured and unstructured uncertainty -- 1 class period.
Chapter 9:  The Linear Quadratic Gaussian (LQG) problem, robustness of the linear regulator and of the Kalman filter, loss of robustness with the LQG structure, maintaining robustness through loop transfer recovery (LTR), formulating the H_infinity problem, the model matching problem, and a numerical robust control design algorithm -- 4 class periods.

 

Course Requirements:

Project 1 -- Multivariable Control Design Project -- 30%
Project 2 -- Robust Control Design Project -- 40%
Project 3 -- Robust Control Paper Review -- 30%

 

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Latest revision was made on Monday, May 15, 2006 9:00 PM