UCLA Extension

Robust Control: Toolbox, Theory, and Applications

Robust control theory and its aerospace applications have been around for more than 20 years. Robust Control Toolbox—released in 1989—has certainly made significant contributions to the control community. For over 20 years, it has proven that robust control theory and its related tools are the ultimate control analysis and synthesis methodology to capture the issues of system uncertainty, stability, performance, and the essential trade-offs between them.

Complete Details

The Robust Control Toolbox itself is a collection of functions and tools that help you to analyze and design MIMO control systems with uncertain elements. It allows you to build uncertain LTI system models containing uncertain parameters and uncertain dynamics, and obtain tools to analyze MIMO system stability margins and worst-case performance. The toolbox includes a selection of control synthesis tools that compute controllers which optimize worst-case performance and identify worst-case parameter values; simplifies and reduces the order of complex models with model reduction tools that minimize additive and multiplicative error bounds; provides tools for implementing advanced robust control methods, such as H-infinity, H2, Linear Matrix Inequalities (LMI), and μ-synthesis robust control; and shape MIMO system frequency responses and design uncertainty tolerant controllers, etc.

This course covers four major topic areas with hands-on experience: background and basics, robust control modeling, robust control analysis, and robust control synthesis. Although designed for practitioners, the fundamental theory behind the tools also is highlighted and derived. More importantly, numerous real-life aerospace design examples, such as spacecraft attitude control, supermaneuverable fighter flight control, large space structure vibration control, and disk drive suspension servo control, are illustrated in detail.

Using Robust Control Toolbox and design methodologies presented in this course, participants should be able to analyze robustness of their existing control systems and modeling system uncertainty, perform model reduction on their complicated large size plants, and eventually design a robust control system to perform within specifications in the presence of all of those anticipated uncertainties.

Course Materials

The text, Multivariable Feedback Control: Analysis and Design, Sigurd Skogestad and Ian Postlethwaite (John Wiley & Sons, 1996); lecture notes; MATLAB tools; and published papers are distributed on the first day of the course. The notes are for participants only and are not for sale.

Coordinator and Lecturer

Richard Y. Chiang, PhD, Boeing Technical Fellow, Spacecraft Attitude Control System Engineering Department, Boeing Satellite Development Center, El Segundo, California. Dr. Chiang is a nationally and internationally recognized expert in robust control system design and system identification. He is the leading author on the MATLAB software, Robust Control Toolbox, of which nearly 30,000 copies have been sold worldwide across industries and academia for the last 20 years. His control design methodology has become a universal standard in the field.

Dr. Chiang began his career 30 years ago as a control system analyst at Garrett AiResearch. During the 1990s, he also worked for Northrop Aircraft on F-18 supermaneuver flight control and at JPL on large space structure vibration control. Since joining Boeing in the late ’90s, he has designed attitude control systems for 15 satellites and analyzed system stability for 20 programs. He has taught senior control courses at USC and has given control seminars at DEC, Northrop, General Dynamics, and JPL in the 1990s and several at Boeing from 2002 to the present. He also has published 17 journal papers and 45 conference papers, and has five issued U.S. patents and five patent applications pending related to spacecraft control system design.

Daily Schedule

Day 1
Morning and Afternoon

Robust Control Basics

Big picture of robust control design

  • What is a “robust” control system?
  • Robust control design objectives (why are we doing this?)
  • Brief history of classical/modern/robust control theory

Robust control problems and their solution formations

  • Terminologies
  • Robust stability: robustness against uncertainty
  • Robust performance
  • Feedback fundamental limitations and trade-offs
  • Mixed sensitivity problem formulation

Canonical robust control problem

  • Loop-shaping: classical versus modern
  • Robust control design process

Math basics

  • Norm of signals, norm of systems, H2, Hinf
  • Singular values, structured singular values
  • Hankel norm
  • Coprime factorization
  • Lyapunov and Riccati equations
  • Generalized state-space representation: descriptor systems
  • Linear fraction transformation and state-space interconnections
  • Bilinear transform (regular, pole-shinfing) and sampled-data implications
  • Tools and examples

Exercises and references

Day 2

Robust Control Modeling

Modeling of robust systems

  • Uncertainty sources
  • Uncertainty modeling (additive, multiplicative, structured, unstructured)
  • Model reduction robustness for stability and performance
  • Classical model reduction methods
  • Modern model reduction techniques and their error bounds
  • Square-root balancing, Schur balancing, Hankel MDA
  • Stochastic balancing
  • Modal truncation
  • Tools, GUI, and examples

Exercises and references


Robust Control Analysis

Robustness analysis

  • SISO stability margins
  • Small Gain Theorem (necessary and sufficient)
  • Structured singular values (upper/lower bounds)
  • MIMO stability margins
  • Mu-plots and its upper bounds
  • Osborne method
  • Perron eigen structure
  • Optimization
  • Real-parameters
  • Slow time-varying parameters
  • Repeated parameters
  • LMI and IQC
  • Tools, GUI, and examples

Exercises and references

Day 3
Morning and Afternoon

Robust Control Synthesis

Synthesis methods

  • Classical loop shaping
  • Modern control (LQG/LTR)
  • H2/Hinf loop shaping and weighting strategy
  • Mu-synthesis (D-K iteration)
  • Km-synthesis without D-K iteration (multiplier approach)
  • Co-prime factorization synthesis
  • Tools, GUI and examples

Design case studies

  • ACC two-mass-spring benchmark problem
  • Feedforward loopshing and H-infinity filtering
  • Mixed-sensitivity loopshaping for ACOSSII spacecraft
  • Spacecraft attitude control against uncertain fuel slosh dynamics
  • Disk drive servo suspension control system
  • JPL large space structure vibration suppression control
  • F-18 HARV supermaneuverable fighter flight control
  • ISAT flexible satellite control

Exercises and references

Advanced Topics

  • Robust control design for system with friction
  • Robust control design and system identification

For more information contact the Short Course Program Office:
shortcourses@uclaextension.edu (310) 825-3344 | fax (310) 206-2815